diff --git a/literature/figs/demo_10_deviations.json b/literature/figs/demo_10_deviations.json
index 2ef38b8..7742afd 100644
--- a/literature/figs/demo_10_deviations.json
+++ b/literature/figs/demo_10_deviations.json
@@ -2,40 +2,55 @@
  "figure": "demo_10_deviations",
  "generator": "codameter.deviations.oat_effects + fig_deviation_ranking",
  "codameter_version": "0.4.0",
- "git_commit": "d3a5c18b08d95872cfa54fa796f080daec94d20a",
- "generated_utc": "2026-09-13T13:48:43+00:00",
+ "git_commit": "c0f91f1f5d72ab3d7b4ed4be9294e7b023a372aa",
+ "generated_utc": "2026-09-13T17:03:25+00:00",
  "python": "3.12.13",
  "numpy": "2.4.3",
  "matplotlib": "3.10.9",
  "axes": [
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    "axes": "ax0",
-   "title": "(a) RMS error of each deviation",
+   "title": "(a) RMS error, common support",
    "xlabel": "RMS error vs truth (dv/v, %, log)",
    "ylabel": "",
    "lines": [
-    "best practice (0.032%)"
+    "_nolegend_",
+    "_nolegend_",
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-   "collections": [],
+   "collections": [
+    "_nolegend_"
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   },
   {
    "axes": "ax1",
-   "title": "(b) Distortion of the drop",
-   "xlabel": "drop error (%, symlog)",
+   "title": "(b) Error of the drop",
+   "xlabel": "step error (%, symlog)",
    "ylabel": "",
    "lines": [
-    "_child12"
+    "_nolegend_",
+    "_nolegend_",
+    "_child15"
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@@ -48,8 +63,15 @@
   "ax0/patch7/xywh",
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 }
diff --git a/literature/figs/demo_10_deviations.npz b/literature/figs/demo_10_deviations.npz
index e99bfd8..67f3fff 100644
Binary files a/literature/figs/demo_10_deviations.npz and b/literature/figs/demo_10_deviations.npz differ
diff --git a/literature/figs/demo_10_deviations.png b/literature/figs/demo_10_deviations.png
index 412ab35..7c89f1c 100644
Binary files a/literature/figs/demo_10_deviations.png and b/literature/figs/demo_10_deviations.png differ
diff --git a/literature/figs/demo_11_multiverse.json b/literature/figs/demo_11_multiverse.json
index 9d11cba..eccc276 100644
--- a/literature/figs/demo_11_multiverse.json
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@@ -2,8 +2,8 @@
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- "generated_utc": "2026-09-13T13:47:02+00:00",
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+     "reference": "fixed"
+    },
+    "reason": "MWCS needs at least three sub-windows for the delay-versus-lapse fit; the 4-14 s window holds 2 at 6 s length and 3 s step"
+   },
+   {
+    "config": {
+     "estimator": "MWCS",
+     "band": "0.4\u20131",
+     "window": "4\u201314",
+     "stack": "45",
+     "reference": "moving"
+    },
+    "reason": "MWCS needs at least three sub-windows for the delay-versus-lapse fit; the 4-14 s window holds 2 at 6 s length and 3 s step"
+   },
+   {
+    "config": {
+     "estimator": "MWCS",
+     "band": "0.8\u20132",
+     "window": "4\u201314",
+     "stack": "1",
+     "reference": "fixed"
+    },
+    "reason": "MWCS needs at least three sub-windows for the delay-versus-lapse fit; the 4-14 s window holds 2 at 6 s length and 3 s step"
+   },
+   {
+    "config": {
+     "estimator": "MWCS",
+     "band": "0.8\u20132",
+     "window": "4\u201314",
+     "stack": "1",
+     "reference": "moving"
+    },
+    "reason": "MWCS needs at least three sub-windows for the delay-versus-lapse fit; the 4-14 s window holds 2 at 6 s length and 3 s step"
+   },
+   {
+    "config": {
+     "estimator": "MWCS",
+     "band": "0.8\u20132",
+     "window": "4\u201314",
+     "stack": "10",
+     "reference": "fixed"
+    },
+    "reason": "MWCS needs at least three sub-windows for the delay-versus-lapse fit; the 4-14 s window holds 2 at 6 s length and 3 s step"
+   },
+   {
+    "config": {
+     "estimator": "MWCS",
+     "band": "0.8\u20132",
+     "window": "4\u201314",
+     "stack": "10",
+     "reference": "moving"
+    },
+    "reason": "MWCS needs at least three sub-windows for the delay-versus-lapse fit; the 4-14 s window holds 2 at 6 s length and 3 s step"
+   },
+   {
+    "config": {
+     "estimator": "MWCS",
+     "band": "0.8\u20132",
+     "window": "4\u201314",
+     "stack": "45",
+     "reference": "fixed"
+    },
+    "reason": "MWCS needs at least three sub-windows for the delay-versus-lapse fit; the 4-14 s window holds 2 at 6 s length and 3 s step"
+   },
+   {
+    "config": {
+     "estimator": "MWCS",
+     "band": "0.8\u20132",
+     "window": "4\u201314",
+     "stack": "45",
+     "reference": "moving"
+    },
+    "reason": "MWCS needs at least three sub-windows for the delay-versus-lapse fit; the 4-14 s window holds 2 at 6 s length and 3 s step"
+   }
+  ],
+  "cadence": 3,
   "axes": [
    "estimator",
    "band",
diff --git a/literature/figs/demo_11_multiverse.npz b/literature/figs/demo_11_multiverse.npz
index 50d6560..2ca1912 100644
Binary files a/literature/figs/demo_11_multiverse.npz and b/literature/figs/demo_11_multiverse.npz differ
diff --git a/literature/figs/demo_11_multiverse.png b/literature/figs/demo_11_multiverse.png
index 5402de0..33b00b6 100644
Binary files a/literature/figs/demo_11_multiverse.png and b/literature/figs/demo_11_multiverse.png differ
diff --git a/literature/figs/demo_12_bayes.json b/literature/figs/demo_12_bayes.json
index d83bf64..ad152d1 100644
--- a/literature/figs/demo_12_bayes.json
+++ b/literature/figs/demo_12_bayes.json
@@ -2,8 +2,8 @@
  "figure": "demo_12_bayes",
  "generator": "codameter.uq_bayes._build_bayes + _fig_bayes",
  "codameter_version": "0.4.0",
- "git_commit": "d3a5c18b08d95872cfa54fa796f080daec94d20a",
- "generated_utc": "2026-09-13T13:41:32+00:00",
+ "git_commit": "c0f91f1f5d72ab3d7b4ed4be9294e7b023a372aa",
+ "generated_utc": "2026-09-13T17:05:28+00:00",
  "python": "3.12.13",
  "numpy": "2.4.3",
  "matplotlib": "3.10.9",
@@ -61,7 +61,7 @@
   },
   {
    "axes": "ax3",
-   "title": "(c) time-dependent error;  $N_{eff}$=23/229",
+   "title": "(c) time-dependent error;  $N_{eff}$=29/229",
    "xlabel": "time (years)",
    "ylabel": "$\\sigma$ (dv/v, %)",
    "lines": [
@@ -143,8 +143,8 @@
  "bayes": {
   "tau": 0.0003612992348785833,
   "s": 12.098861625892763,
-  "corr_length_days": 39.20671143105746,
-  "n_eff": 22.760567115510465,
+  "corr_length_days": 5.702100823925634,
+  "n_eff": 28.950925940431706,
   "n_epochs": 229,
   "labels": [
    "stretching (TS) 0.4-1Hz 8-28s stack10d fixed",
diff --git a/literature/figs/demo_12_bayes.npz b/literature/figs/demo_12_bayes.npz
index 044eb39..2a6057b 100644
Binary files a/literature/figs/demo_12_bayes.npz and b/literature/figs/demo_12_bayes.npz differ
diff --git a/literature/figs/demo_12_bayes.png b/literature/figs/demo_12_bayes.png
index 1b4754f..79b83c3 100644
Binary files a/literature/figs/demo_12_bayes.png and b/literature/figs/demo_12_bayes.png differ
diff --git a/literature/figs/demo_18_stack_coherence.json b/literature/figs/demo_18_stack_coherence.json
index 507ec4a..b18189e 100644
--- a/literature/figs/demo_18_stack_coherence.json
+++ b/literature/figs/demo_18_stack_coherence.json
@@ -2,8 +2,8 @@
  "figure": "demo_18_stack_coherence",
  "generator": "codameter.synthetic_demo.fig_stack_coherence",
  "codameter_version": "0.4.0",
- "git_commit": "141e7bc25bb439420c5ee73223bf78eb4ca7a839",
- "generated_utc": "2026-09-10T18:41:24+00:00",
+ "git_commit": "c0f91f1f5d72ab3d7b4ed4be9294e7b023a372aa",
+ "generated_utc": "2026-09-13T16:54:15+00:00",
  "python": "3.12.13",
  "numpy": "2.4.3",
  "matplotlib": "3.10.9",
@@ -52,6 +52,14 @@
   "ax1/line2/x",
   "ax1/line2/y",
   "ax1/line3/x",
-  "ax1/line3/y"
- ]
+  "ax1/line3/y",
+  "data/snr0.5/median_cc",
+  "data/snr0.5/rms_pct",
+  "data/snr0.5/signed_step_error_pct",
+  "data/snr4/median_cc",
+  "data/snr4/rms_pct",
+  "data/snr4/signed_step_error_pct",
+  "data/stack_days"
+ ],
+ "step_error": "recovered minus true step amplitude, each the median of the 120 days after the event minus the median of the 120 days before (synthetic_demo.step_amplitude); negative = recovered drop deeper than the truth"
 }
diff --git a/literature/figs/demo_18_stack_coherence.npz b/literature/figs/demo_18_stack_coherence.npz
index 18de5dd..0464158 100644
Binary files a/literature/figs/demo_18_stack_coherence.npz and b/literature/figs/demo_18_stack_coherence.npz differ
diff --git a/literature/figs/demo_18_stack_coherence.png b/literature/figs/demo_18_stack_coherence.png
index 8c22864..447a655 100644
Binary files a/literature/figs/demo_18_stack_coherence.png and b/literature/figs/demo_18_stack_coherence.png differ
diff --git a/paper/build_calibration_table.py b/paper/build_calibration_table.py
index 5f9c153..eacdaed 100644
--- a/paper/build_calibration_table.py
+++ b/paper/build_calibration_table.py
@@ -20,6 +20,17 @@
 OUT = HERE / "calibration_table.tex"
 
 
+def _mean_se(values: list[float]) -> dict:
+    n = len(values)
+    mean = sum(values) / n
+    se = (
+        (sum((v - mean) ** 2 for v in values) / (n - 1)) ** 0.5 / n**0.5
+        if n > 1
+        else None
+    )
+    return {"mean": mean, "se": se, "n": n}
+
+
 def _pm(m: dict, scale: float = 1.0, digits: int = 3) -> str:
     if m is None or m.get("mean") is None:
         return "--"
@@ -46,19 +57,35 @@ def main() -> int:
         + f" ($n={r['summary']['n_realizations']}$)"
         for r in runs
     ]
+    for r in runs:  # per-realisation max of the finite split R-hats, then mean, se
+        vals = []
+        for x in r["results"]:
+            if not x.get("ok"):
+                continue
+            finite = [
+                float(x[k])
+                for k in ("rhat_tau2", "rhat_s2", "rhat_lambda")
+                if isinstance(x.get(k), int | float) and x[k] == x[k]
+            ]
+            if finite:
+                vals.append(max(finite))
+        r["summary"]["rhat_max_realisation"] = _mean_se(vals) if vals else None
     metrics = [
         ("Member 68\\%", "member_coverage68", 1, 3),
         ("Member 95\\%", "member_coverage95", 1, 3),
+        ("Member 95\\%, held-out half", "heldout_member_coverage95", 1, 3),
         ("Posterior 95\\%", "coverage95_posterior", 1, 3),
         (r"Median $\sigma_{C_d}$ (\%)", "median_sd", 100, 3),
         ("Bias (\\%)", "shared_bias", 100, 3),
         (r"RMSE($\mu$) (\%)", "rmse", 100, 3),
         (r"Rescale $s$", "s", 1, 2),
+        (r"Correlation length $L$ (d)", "corr_length_days", 1, 1),
+        (r"Split $\hat R$, largest of three", "rhat_max_realisation", 1, 3),
         (r"Prior scale share $\tau^2$", "prior_weight_tau2", 1, 2),
     ]
     rows = []
     for label, key, scale, digits in metrics:
-        cells = [_pm(r["summary"][key], scale, digits) for r in runs]
+        cells = [_pm(r["summary"].get(key), scale, digits) for r in runs]
         rows.append(label + " & " + " & ".join(cells) + r" \\")
     body = "\n".join(rows)
     header = "Quantity & " + " & ".join(headings) + r" \\"
@@ -71,8 +98,14 @@ def main() -> int:
         "target of the proposed single-member error scale; $z=1$ for the 68\\% "
         "level and $z=1.96$ for the 95\\% level. "
         "Posterior: fraction of epochs whose 95\\% credible band on $\\mu$ contains "
-        "the truth. Rescale $s$: the fitted factor on the within-method floor of "
-        "eq.~\\ref{eq:weaver}. "
+        "the truth. Held-out half: $C_d$ fitted on a random six of the twelve "
+        "members and scored on the other six. Rescale $s$: the fitted factor on the "
+        "within-method floor of eq.~\\ref{eq:weaver}. $L$: fitted temporal "
+        "correlation length of the residuals. Split $\\hat R$: two Gibbs chains "
+        "from different seeds, each split in halves, largest of the three scale "
+        "hyper-parameters per realisation. A realisation redraws the additive "
+        "noise on one fixed generating coda; the truth and the twelve "
+        "configurations are the same in every realisation. "
         "Means with standard errors across realisations; no realisation failed; "
         "$\\sigma_{C_d}$, bias and RMSE in percent; prior $\\tau^2$ is the fraction of "
         "conditional posterior rate supplied by the prior scale term (the $\\lambda$ ratio is "
@@ -80,8 +113,8 @@ def main() -> int:
         "Clock drift: $4\\times10^{-5}$\\,s/day from 40\\% of the record. "
         "Shared source: a seasonal source "
         "effect warping the coda beyond 6\\,s lapse with a spurious 0.2\\% "
-        "seasonal \\dvv, seen by every configuration. Generated from "
-        "\\texttt{paper/data/calibration/} by \\texttt{paper/build\\_calibration\\_table.py}.}\n"
+        "seasonal \\dvv, seen by every configuration. Generated from the archived "
+        "runs distributed with the paper.}\n"
         "\\label{tab:calibration}\n"
         "\\begin{tabularx}{\\textwidth}{@{}L"
         + "r" * len(runs)
diff --git a/paper/calibration_table.tex b/paper/calibration_table.tex
index b4c769d..8561577 100644
--- a/paper/calibration_table.tex
+++ b/paper/calibration_table.tex
@@ -1,6 +1,6 @@
 \begin{table}
 \footnotesize
-\caption{Coverage calibration of the Bayesian measurement model over independent synthetic realisations of the volcano scenario (2.5 years, SNR 7, 4-day cadence, 12-member ensemble). Member coverage: fraction of member epochs with $|m_k(t)-\mathrm{truth}(t)|\le z\,\sigma_{C_d}(t)$, the target of the proposed single-member error scale; $z=1$ for the 68\% level and $z=1.96$ for the 95\% level. Posterior: fraction of epochs whose 95\% credible band on $\mu$ contains the truth. Rescale $s$: the fitted factor on the within-method floor of eq.~\ref{eq:weaver}. Means with standard errors across realisations; no realisation failed; $\sigma_{C_d}$, bias and RMSE in percent; prior $\tau^2$ is the fraction of conditional posterior rate supplied by the prior scale term (the $\lambda$ ratio is below 0.01 throughout). Clock drift: $4\times10^{-5}$\,s/day from 40\% of the record. Shared source: a seasonal source effect warping the coda beyond 6\,s lapse with a spurious 0.2\% seasonal \dvv, seen by every configuration. Generated from \texttt{paper/data/calibration/} by \texttt{paper/build\_calibration\_table.py}.}
+\caption{Coverage calibration of the Bayesian measurement model over independent synthetic realisations of the volcano scenario (2.5 years, SNR 7, 4-day cadence, 12-member ensemble). Member coverage: fraction of member epochs with $|m_k(t)-\mathrm{truth}(t)|\le z\,\sigma_{C_d}(t)$, the target of the proposed single-member error scale; $z=1$ for the 68\% level and $z=1.96$ for the 95\% level. Posterior: fraction of epochs whose 95\% credible band on $\mu$ contains the truth. Held-out half: $C_d$ fitted on a random six of the twelve members and scored on the other six. Rescale $s$: the fitted factor on the within-method floor of eq.~\ref{eq:weaver}. $L$: fitted temporal correlation length of the residuals. Split $\hat R$: two Gibbs chains from different seeds, each split in halves, largest of the three scale hyper-parameters per realisation. A realisation redraws the additive noise on one fixed generating coda; the truth and the twelve configurations are the same in every realisation. Means with standard errors across realisations; no realisation failed; $\sigma_{C_d}$, bias and RMSE in percent; prior $\tau^2$ is the fraction of conditional posterior rate supplied by the prior scale term (the $\lambda$ ratio is below 0.01 throughout). Clock drift: $4\times10^{-5}$\,s/day from 40\% of the record. Shared source: a seasonal source effect warping the coda beyond 6\,s lapse with a spurious 0.2\% seasonal \dvv, seen by every configuration. Generated from the archived runs distributed with the paper.}
 \label{tab:calibration}
 \begin{tabularx}{\textwidth}{@{}Lrrr@{}}
 \toprule
@@ -8,11 +8,14 @@
 \midrule
 Member 68\% & 0.808 $\pm$ 0.001 & 0.795 $\pm$ 0.001 & 0.804 $\pm$ 0.001 \\
 Member 95\% & 0.9561 $\pm$ 0.0003 & 0.9496 $\pm$ 0.0004 & 0.9543 $\pm$ 0.0003 \\
+Member 95\%, held-out half & 0.937 $\pm$ 0.004 & 0.930 $\pm$ 0.004 & 0.936 $\pm$ 0.004 \\
 Posterior 95\% & 0.590 $\pm$ 0.004 & 0.340 $\pm$ 0.004 & 0.604 $\pm$ 0.004 \\
 Median $\sigma_{C_d}$ (\%) & 0.225 $\pm$ 0.001 & 0.330 $\pm$ 0.001 & 0.222 $\pm$ 0.001 \\
 Bias (\%) & -0.017 $\pm$ 0.001 & -0.045 $\pm$ 0.001 & -0.019 $\pm$ 0.001 \\
 RMSE($\mu$) (\%) & 0.0669 $\pm$ 0.0005 & 0.161 $\pm$ 0.001 & 0.0656 $\pm$ 0.0005 \\
 Rescale $s$ & 11.67 $\pm$ 0.03 & 12.70 $\pm$ 0.04 & 10.88 $\pm$ 0.03 \\
+Correlation length $L$ (d) & 6.11 $\pm$ 0.03 & 6.18 $\pm$ 0.04 & 6.16 $\pm$ 0.03 \\
+Split $\hat R$, largest of three & 1.024 $\pm$ 0.002 & 1.036 $\pm$ 0.005 & 1.030 $\pm$ 0.004 \\
 Prior scale share $\tau^2$ & 0.09 $\pm$ 0.01 & 0.025 $\pm$ 0.005 & 0.08 $\pm$ 0.01 \\
 \bottomrule
 \end{tabularx}
diff --git a/paper/data/bayes/README.md b/paper/data/bayes/README.md
new file mode 100644
index 0000000..0b215be
--- /dev/null
+++ b/paper/data/bayes/README.md
@@ -0,0 +1,15 @@
+# Checks of the Bayesian measurement model (audits UQ-03 and UQ-04)
+
+Both files are produced from the manuscript's Fig. 14 realisation
+(`codameter.uq_bayes._build_bayes`: seed 55, 2.5 years, SNR 7, 4-day cadence,
+12-member ensemble).
+
+- `duplication_check.json`, from `scripts/check_ensemble_duplication.py`: the
+  credible band on mu, the C_d scale, s, tau and the share of the precision of
+  mu supplied by the smoothness prior, for the ensemble as measured and with
+  every member duplicated and quadrupled.
+- `cd_whitening.json`, from `scripts/check_cd_whitening.py`: raw and whitened
+  lag autocorrelations of the member residuals about mu, the whitened variance
+  under the full C_d and under its diagonal alone.
+
+Rerun the two scripts to regenerate; each takes a few minutes.
diff --git a/paper/data/bayes/cd_whitening.json b/paper/data/bayes/cd_whitening.json
new file mode 100644
index 0000000..9ce4798
--- /dev/null
+++ b/paper/data/bayes/cd_whitening.json
@@ -0,0 +1,249 @@
+{
+ "script": "scripts/check_cd_whitening.py",
+ "generator": "codameter.uq_bayes._build_bayes (seed 55, cadence 4)",
+ "codameter_version": "0.4.0",
+ "git_commit": "c0f91f1f5d72ab3d7b4ed4be9294e7b023a372aa",
+ "generated_utc": "2026-09-13T18:55:56+00:00",
+ "lags_epochs": [
+  1,
+  2,
+  3,
+  5,
+  10
+ ],
+ "cadence_days": 4.0,
+ "n_members": 12,
+ "n_epochs_per_member": [
+  229,
+  229,
+  229,
+  229,
+  229,
+  229,
+  229,
+  229,
+  229,
+  229,
+  229,
+  229
+ ],
+ "corr_length_days": 5.702100823925634,
+ "s": 12.098861625892763,
+ "tau": 0.0003612992348785833,
+ "raw_autocorr_mean": [
+  0.5712975659831153,
+  0.20724078947170466,
+  0.026809957966110867,
+  0.01970798397727862,
+  -0.0526038542121527
+ ],
+ "raw_autocorr_members": [
+  [
+   0.8047545464897441,
+   0.4238728622308728,
+   0.11892434621769646,
+   0.009823546991099304,
+   -0.1598836513127236
+  ],
+  [
+   0.7800268541047419,
+   0.42122612910584223,
+   0.14287920120775968,
+   0.02338992865160718,
+   -0.11558996148090188
+  ],
+  [
+   0.82073923967662,
+   0.4527370139343432,
+   0.14593559129721426,
+   0.02188175583806389,
+   -0.16308231900045977
+  ],
+  [
+   0.8239368938928148,
+   0.4690497192737583,
+   0.153086894878354,
+   -0.013430664565612102,
+   -0.14484863637506867
+  ],
+  [
+   0.5707201572449805,
+   0.12958368817405094,
+   0.009560580729294051,
+   0.11834857109343472,
+   0.06390451791252108
+  ],
+  [
+   0.616135866460465,
+   0.17683004554899684,
+   -0.03618225088780855,
+   -0.012047866546878635,
+   0.0009349670480230448
+  ],
+  [
+   0.4325056445559863,
+   -0.0804661095415602,
+   -0.14954961019462687,
+   0.1288950438009759,
+   0.024379455195508288
+  ],
+  [
+   0.49849924617363245,
+   0.049904263316506936,
+   -0.13189474800001474,
+   -0.008815571912422262,
+   0.055028317592746
+  ],
+  [
+   0.5057706276619588,
+   0.06780947906163838,
+   -0.03655541588910766,
+   0.024127394431378395,
+   0.08904813243582606
+  ],
+  [
+   0.30146923631504197,
+   0.1339529140495274,
+   0.0643502635644401,
+   -0.13547700731141904,
+   -0.14136262215158737
+  ],
+  [
+   0.49712978647678563,
+   0.1875295520149899,
+   0.07804522892010375,
+   0.1006508623132956,
+   -0.09119280294113942
+  ],
+  [
+   0.2038826927446121,
+   0.054859916491489365,
+   -0.03688058624997402,
+   -0.020850185056179523,
+   -0.04858164746857604
+  ]
+ ],
+ "whitened_autocorr_mean": [
+  0.26140810417665056,
+  -0.04082891688344167,
+  -0.13817359964386658,
+  -0.012669750306042615,
+  0.005903936884559182
+ ],
+ "whitened_autocorr_members": [
+  [
+   0.6162521228572826,
+   0.1456119256916208,
+   -0.17234653699249677,
+   -0.024333327543412733,
+   -0.05134480950405171
+  ],
+  [
+   0.5350019267906134,
+   0.12143239906171685,
+   -0.12189458050330433,
+   -0.00978913011275982,
+   -0.008156228657108544
+  ],
+  [
+   0.6536982032435709,
+   0.17906902535735966,
+   -0.1643853409355652,
+   -0.025436182316815974,
+   -0.06035600686966006
+  ],
+  [
+   0.6407706153989362,
+   0.21089200431348712,
+   -0.1427637800069823,
+   -0.07061915744870342,
+   -0.05835494386445728
+  ],
+  [
+   0.1936429133006637,
+   -0.17816373962422208,
+   -0.11482735883194774,
+   0.06875912076183889,
+   0.11965773662529411
+  ],
+  [
+   0.2757186150007819,
+   -0.10892957939653786,
+   -0.17692850430700843,
+   -0.06701564000226709,
+   -0.05199801319651424
+  ],
+  [
+   0.09923715070698015,
+   -0.28384843375977387,
+   -0.2238326217051262,
+   0.10227042135994578,
+   0.07136162278957855
+  ],
+  [
+   0.0968321937906943,
+   -0.18217532832759198,
+   -0.21111181163781567,
+   -0.007721356469920764,
+   0.12995080846829218
+  ],
+  [
+   0.1614261019311921,
+   -0.21799816432769306,
+   -0.10025797531876222,
+   0.025580754435076757,
+   0.1097167728758935
+  ],
+  [
+   -0.09780119153728599,
+   -0.06528454809957225,
+   -0.006018620639321585,
+   -0.13018103778359744,
+   -0.0927718237088623
+  ],
+  [
+   0.07569598504913069,
+   -0.09277927589890822,
+   -0.06358055014165681,
+   0.09865052342687956,
+   -0.006763355524808479
+  ],
+  [
+   -0.11357738641275254,
+   -0.01777328759118506,
+   -0.16013551470641157,
+   -0.11220199197877517,
+   -0.030094516818885544
+  ]
+ ],
+ "whitened_variance_mean": 0.6204464599706632,
+ "whitened_variance_members": [
+  0.050018947030030965,
+  0.05065300499796357,
+  0.046488431526260234,
+  0.04551667100400876,
+  1.1277643216016606,
+  1.0908762462073183,
+  0.4121888288585529,
+  0.6720823396739045,
+  0.5308434602995329,
+  2.1433120724027366,
+  0.11248574881320099,
+  1.163127447232787
+ ],
+ "diag_scaled_variance_mean": 0.6020313830232876,
+ "diag_scaled_variance_members": [
+  0.07935909278647864,
+  0.07682387013685468,
+  0.07641861281674053,
+  0.07518665467343337,
+  1.1964693962923927,
+  1.258433672033464,
+  0.3732204834971855,
+  0.6333141611599189,
+  0.536033468097489,
+  1.829937907987763,
+  0.1116074663413538,
+  0.9775718104563769
+ ]
+}
diff --git a/paper/data/bayes/duplication_check.json b/paper/data/bayes/duplication_check.json
new file mode 100644
index 0000000..fcdcc7c
--- /dev/null
+++ b/paper/data/bayes/duplication_check.json
@@ -0,0 +1,46 @@
+{
+ "script": "scripts/check_ensemble_duplication.py",
+ "generator": "codameter.uq_bayes._build_bayes (seed 55, cadence 4); gibbs seed 0",
+ "codameter_version": "0.4.0",
+ "git_commit": "c0f91f1f5d72ab3d7b4ed4be9294e7b023a372aa",
+ "generated_utc": "2026-09-13T18:58:17+00:00",
+ "independent_data_expectation": "half-width scales as 1/sqrt(multiplicity)",
+ "rows": [
+  {
+   "multiplicity": 1,
+   "n_members": 12,
+   "median_halfwidth95_pct": 0.06251369482525337,
+   "median_sigma_cd_pct": 0.23755447948266895,
+   "s": 12.098861625892763,
+   "tau": 0.0003612992348785833,
+   "corr_length_days": 5.702100823925634,
+   "n_eff": 28.950925940431706,
+   "prior_precision_share": 0.7999045705950358,
+   "mu_mean_max_abs_change_pct": 0.0
+  },
+  {
+   "multiplicity": 2,
+   "n_members": 24,
+   "median_halfwidth95_pct": 0.05210912104304287,
+   "median_sigma_cd_pct": 0.23238751439063607,
+   "s": 11.807507293383788,
+   "tau": 0.0003863481244818083,
+   "corr_length_days": 5.179057960014449,
+   "n_eff": 26.313545207912476,
+   "prior_precision_share": 0.48961323405350315,
+   "mu_mean_max_abs_change_pct": 0.048943782029892566
+  },
+  {
+   "multiplicity": 4,
+   "n_members": 48,
+   "median_halfwidth95_pct": 0.039821612435499684,
+   "median_sigma_cd_pct": 0.2298511903925661,
+   "s": 11.670097966056039,
+   "tau": 0.00039183490050232606,
+   "corr_length_days": 4.9184731488293805,
+   "n_eff": 25.691616949519986,
+   "prior_precision_share": 0.2563514708073079,
+   "mu_mean_max_abs_change_pct": 0.07290830579498478
+  }
+ ]
+}
diff --git a/paper/data/calibration/README.md b/paper/data/calibration/README.md
new file mode 100644
index 0000000..702721e
--- /dev/null
+++ b/paper/data/calibration/README.md
@@ -0,0 +1,28 @@
+# Coverage calibration runs
+
+Produced by `python -m codameter.calibration` (see its module docstring). Each
+JSON holds `settings`, `seeds`, per-realisation `results` and the aggregate
+`summary` that `paper/build_calibration_table.py` turns into
+`paper/calibration_table.tex`. The table builder reads `locked_*.json` only.
+
+| File | Invocation | Notes |
+|---|---|---|
+| `locked_clean_n200.json` | `--n 200 --start-seed 2000 --scenario clean --jobs 6` | 2026-09-13, iteration-3 rerun with the held-out-half coverage, the two-chain split R-hat and the corrected correlation-length fit. Every in-sample statistic (member and posterior coverages, s, tau, bias, RMSE, prior shares) is bit-identical to the 2026-09-10 run it replaces; only `corr_length_days` and `n_eff` changed with the fit. |
+| `locked_shared_source_n200.json` | `--scenario shared_source`, same n and seeds, `--jobs 8` | 2026-09-13 rerun, same properties as the clean one (in-sample statistics bit-identical to the 2026-09-10 run) |
+| `locked_clock_drift_n200.json` | `--scenario clock_drift`, same n and seeds, `--jobs 8` | same |
+| `pilot_*_n20.json` | `--n 20 --start-seed 1000` | pilots used to fix the acceptance margin before the locked runs; not used by the table |
+
+Environment for the locked runs: single-threaded BLAS
+(`OMP_NUM_THREADS=OPENBLAS_NUM_THREADS=MKL_NUM_THREADS=1`), six to eight
+worker processes, wall time one to two hours per scenario on a 10-core laptop
+depending on what else it is doing.
+
+Provenance caveat: `git_commit` in a JSON is the HEAD when the run finished.
+The clean rerun was produced from the working tree of the P1 branch before its
+first commit, so its `git_commit` names the base commit (the P0 merge,
+c0f91f1); the shared-source and clock-drift reruns ran after the P1 code was
+committed and name later P1 commits (1345a47, 64e439c) that differ from the
+code that ran only in docstrings and the plan record. The code that produced
+all three is the one committed with these files (issue #39). A dirty-tree
+flag and a source digest are added to sidecars in P3 (issue #41) and belong
+in this record too.
diff --git a/paper/data/calibration/locked_clean_n200.json b/paper/data/calibration/locked_clean_n200.json
index 5389a7d..e16d486 100644
--- a/paper/data/calibration/locked_clean_n200.json
+++ b/paper/data/calibration/locked_clean_n200.json
@@ -1,9 +1,9 @@
 {
  "codameter_version": "0.4.0",
- "git_commit": "b426c4e660e50d5bbc705d8541269fd97b97c2ee",
- "started_utc": "2026-09-10T19:54:30+00:00",
- "finished_utc": "2026-09-10T20:52:14+00:00",
- "wall_seconds": 3463.596305,
+ "git_commit": "c0f91f1f5d72ab3d7b4ed4be9294e7b023a372aa",
+ "started_utc": "2026-09-13T16:51:31+00:00",
+ "finished_utc": "2026-09-13T18:52:09+00:00",
+ "wall_seconds": 7238.448291,
  "settings": {
   "scenario": "clean",
   "years": 2.5,
@@ -291,13 +291,13 @@
    "n": 200
   },
   "corr_length_days": {
-   "mean": 30.14387295108152,
-   "se": 0.8627435290075752,
+   "mean": 6.105257846302825,
+   "se": 0.03304128596934826,
    "n": 200
   },
   "n_eff": {
-   "mean": 32.31681393789955,
-   "se": 0.6417892519935303,
+   "mean": 44.52062479302683,
+   "se": 1.058975348676535,
    "n": 200
   },
   "missing_fraction": {
@@ -320,8 +320,40 @@
    "se": 1.0968623191806546e-06,
    "n": 200
   },
+  "heldout_member_coverage68": {
+   "mean": 0.7894978165938863,
+   "se": 0.00775966865834404,
+   "n": 200
+  },
+  "heldout_member_coverage95": {
+   "mean": 0.937197962154294,
+   "se": 0.004070236397404517,
+   "n": 200
+  },
+  "heldout_s": {
+   "mean": 11.55471262394824,
+   "se": 0.12195849702088998,
+   "n": 200
+  },
+  "rhat_tau2": {
+   "mean": 1.006184609350363,
+   "se": 0.0005155572134665688,
+   "n": 200
+  },
+  "rhat_s2": {
+   "mean": 1.0016097913375828,
+   "se": 0.00030737966682286205,
+   "n": 200
+  },
+  "rhat_lambda": {
+   "mean": 1.0218332127986485,
+   "se": 0.0018733977765706083,
+   "n": 200
+  },
   "member_coverage95_within_margin": true,
-  "member_coverage68_within_margin": false
+  "member_coverage68_within_margin": false,
+  "heldout_member_coverage95_within_margin": true,
+  "rhat_max": 1.0218332127986485
  },
  "results": [
   {
@@ -329,6 +361,7 @@
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.7958515283842795,
    "member_coverage95": 0.9552401746724891,
    "member_rmse": 0.0020429772046196082,
@@ -343,18 +376,33 @@
    "max_abs_err": 0.00242435083668182,
    "tau": 8.994563135910393e-05,
    "s": 11.074832091572507,
-   "corr_length_days": 25.102638023627126,
-   "n_eff": 38.03460166498179,
+   "corr_length_days": 6.981982143015812,
+   "n_eff": 62.49116350432305,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.37998106491927547,
    "prior_weight_s2": 6.114919917821163e-14,
-   "prior_weight_lambda": 3.482610737636895e-05
+   "prior_weight_lambda": 3.482610737636895e-05,
+   "heldout_member_coverage68": 0.8580786026200873,
+   "heldout_member_coverage95": 0.9774381368267832,
+   "heldout_s": 10.37317330674667,
+   "heldout_fit_members": [
+    1,
+    3,
+    7,
+    8,
+    9,
+    11
+   ],
+   "rhat_tau2": 0.9980535452136835,
+   "rhat_s2": 1.0029247601428504,
+   "rhat_lambda": 1.033736943124199
   },
   {
    "seed": 2001,
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.8093158660844251,
    "member_coverage95": 0.9566957787481805,
    "member_rmse": 0.0021932378793292216,
@@ -369,18 +417,33 @@
    "max_abs_err": 0.002431160741592585,
    "tau": 0.00038543415760045724,
    "s": 11.415633787345671,
-   "corr_length_days": 61.04967386879167,
-   "n_eff": 22.893616826815506,
+   "corr_length_days": 6.578525021386284,
+   "n_eff": 23.594648232907748,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.01219930932969702,
    "prior_weight_s2": 5.787432999202523e-14,
-   "prior_weight_lambda": 1.272086002300974e-05
+   "prior_weight_lambda": 1.272086002300974e-05,
+   "heldout_member_coverage68": 0.9170305676855895,
+   "heldout_member_coverage95": 0.9934497816593887,
+   "heldout_s": 11.411937118546623,
+   "heldout_fit_members": [
+    1,
+    3,
+    4,
+    5,
+    6,
+    9
+   ],
+   "rhat_tau2": 1.0048799676695315,
+   "rhat_s2": 1.0021897958743762,
+   "rhat_lambda": 1.010748887940618
   },
   {
    "seed": 2002,
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.7998544395924309,
    "member_coverage95": 0.9541484716157205,
    "member_rmse": 0.002296177164237327,
@@ -395,18 +458,33 @@
    "max_abs_err": 0.003781621514167738,
    "tau": 0.0002858779210332495,
    "s": 11.588697235888741,
-   "corr_length_days": 26.555177785480737,
-   "n_eff": 25.55955706126277,
+   "corr_length_days": 5.903973231875855,
+   "n_eff": 36.27486871589296,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.02303059437145119,
    "prior_weight_s2": 5.604548705043736e-14,
-   "prior_weight_lambda": 1.1411537364658345e-05
+   "prior_weight_lambda": 1.1411537364658345e-05,
+   "heldout_member_coverage68": 0.33551673944687044,
+   "heldout_member_coverage95": 0.6251819505094615,
+   "heldout_s": 6.707537638621036,
+   "heldout_fit_members": [
+    0,
+    1,
+    2,
+    3,
+    8,
+    10
+   ],
+   "rhat_tau2": 0.9987447504073745,
+   "rhat_s2": 1.0127121070055232,
+   "rhat_lambda": 1.0677170511834058
   },
   {
    "seed": 2003,
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.8180494905385735,
    "member_coverage95": 0.9588791848617176,
    "member_rmse": 0.0023043164825205975,
@@ -421,18 +499,33 @@
    "max_abs_err": 0.0017674590520714625,
    "tau": 0.00014735612483408913,
    "s": 12.025588180242503,
-   "corr_length_days": 30.11439112028414,
-   "n_eff": 38.201128932213464,
+   "corr_length_days": 6.758163807018681,
+   "n_eff": 56.72253592408903,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.11687578428664913,
    "prior_weight_s2": 5.1914405014592215e-14,
-   "prior_weight_lambda": 2.6441183720338543e-05
+   "prior_weight_lambda": 2.6441183720338543e-05,
+   "heldout_member_coverage68": 0.7139737991266376,
+   "heldout_member_coverage95": 0.9024745269286754,
+   "heldout_s": 9.266086511167645,
+   "heldout_fit_members": [
+    1,
+    3,
+    5,
+    6,
+    7,
+    10
+   ],
+   "rhat_tau2": 1.0111313188409694,
+   "rhat_s2": 0.9993093286733491,
+   "rhat_lambda": 1.0110065227433607
   },
   {
    "seed": 2004,
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.8027656477438136,
    "member_coverage95": 0.9512372634643377,
    "member_rmse": 0.0022505759706761214,
@@ -447,18 +540,33 @@
    "max_abs_err": 0.0029147914206257572,
    "tau": 0.00033675027107214474,
    "s": 11.453955963115959,
-   "corr_length_days": 37.155718033362035,
-   "n_eff": 23.280508966968718,
+   "corr_length_days": 6.780765188706867,
+   "n_eff": 27.908245477927725,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.014812366631525147,
    "prior_weight_s2": 5.719591247798182e-14,
-   "prior_weight_lambda": 2.678344534048347e-05
+   "prior_weight_lambda": 2.678344534048347e-05,
+   "heldout_member_coverage68": 0.9497816593886463,
+   "heldout_member_coverage95": 0.9978165938864629,
+   "heldout_s": 14.482923934211481,
+   "heldout_fit_members": [
+    2,
+    4,
+    5,
+    6,
+    9,
+    11
+   ],
+   "rhat_tau2": 1.0229837363258063,
+   "rhat_s2": 1.0018324508690852,
+   "rhat_lambda": 1.0005739948889665
   },
   {
    "seed": 2005,
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.8293304221251819,
    "member_coverage95": 0.9581513828238719,
    "member_rmse": 0.0025042831259372133,
@@ -473,18 +581,33 @@
    "max_abs_err": 0.0023753408513045317,
    "tau": 0.000472081099110869,
    "s": 12.321436470313797,
-   "corr_length_days": 37.13141807517663,
-   "n_eff": 19.305986590123215,
+   "corr_length_days": 6.220551976699213,
+   "n_eff": 20.884669298672847,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.00792394749000607,
    "prior_weight_s2": 4.9541669697431786e-14,
-   "prior_weight_lambda": 1.8047051430297987e-05
+   "prior_weight_lambda": 1.8047051430297987e-05,
+   "heldout_member_coverage68": 0.6542940320232896,
+   "heldout_member_coverage95": 0.8828238719068413,
+   "heldout_s": 11.974265950837104,
+   "heldout_fit_members": [
+    0,
+    2,
+    3,
+    4,
+    10,
+    11
+   ],
+   "rhat_tau2": 1.0071362825697674,
+   "rhat_s2": 1.0017904699513192,
+   "rhat_lambda": 1.0073358130820251
   },
   {
    "seed": 2006,
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.8111353711790393,
    "member_coverage95": 0.9599708879184862,
    "member_rmse": 0.0024656008947137177,
@@ -499,18 +622,33 @@
    "max_abs_err": 0.0024539809637212327,
    "tau": 0.0004645638984748826,
    "s": 11.621587277182456,
-   "corr_length_days": 33.89799030948579,
-   "n_eff": 16.888796925366286,
+   "corr_length_days": 5.565457999469819,
+   "n_eff": 19.6172128120537,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.007678234675567885,
    "prior_weight_s2": 5.5788890099326624e-14,
-   "prior_weight_lambda": 1.6447989451074896e-05
+   "prior_weight_lambda": 1.6447989451074896e-05,
+   "heldout_member_coverage68": 0.846433770014556,
+   "heldout_member_coverage95": 0.9745269286754003,
+   "heldout_s": 9.842004845114309,
+   "heldout_fit_members": [
+    1,
+    3,
+    5,
+    7,
+    9,
+    10
+   ],
+   "rhat_tau2": 1.0018662750887242,
+   "rhat_s2": 0.9985218482288363,
+   "rhat_lambda": 1.0228214594734444
   },
   {
    "seed": 2007,
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.8104075691411936,
    "member_coverage95": 0.9570596797671034,
    "member_rmse": 0.0023886558608840263,
@@ -525,18 +663,33 @@
    "max_abs_err": 0.0030388753835325993,
    "tau": 0.00022365672734799057,
    "s": 12.215173523975006,
-   "corr_length_days": 33.20400448281352,
-   "n_eff": 36.48570863619896,
+   "corr_length_days": 5.988347314571001,
+   "n_eff": 47.458416784625776,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.04311834139626083,
    "prior_weight_s2": 5.040111129256685e-14,
-   "prior_weight_lambda": 1.3970486458058348e-05
+   "prior_weight_lambda": 1.3970486458058348e-05,
+   "heldout_member_coverage68": 0.7976710334788938,
+   "heldout_member_coverage95": 0.9417758369723436,
+   "heldout_s": 12.795831334727193,
+   "heldout_fit_members": [
+    0,
+    3,
+    4,
+    7,
+    8,
+    11
+   ],
+   "rhat_tau2": 1.0020105477271566,
+   "rhat_s2": 0.9998749715453189,
+   "rhat_lambda": 1.0167456637586603
   },
   {
    "seed": 2008,
    "scenario": "clean",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.8220524017467249,
    "member_coverage95": 0.9621542940320232,
    "member_rmse": 0.0023020158950433846,
@@ -551,18 +704,33 @@
    "max_abs_err": 0.0020847633751079997,
    "tau": 0.0004188329190099956,
    "s": 11.777534184996062,
-   "corr_length_days": 28.9369437775835,
-   "n_eff": 19.04749543927452,
+   "corr_length_days": 6.008738617868476,
+   "n_eff": 22.78915868057231,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.009739407550246406,
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 }
diff --git a/paper/data/calibration/locked_clock_drift_n200.json b/paper/data/calibration/locked_clock_drift_n200.json
index d639fd9..1ec4833 100644
--- a/paper/data/calibration/locked_clock_drift_n200.json
+++ b/paper/data/calibration/locked_clock_drift_n200.json
@@ -1,9 +1,9 @@
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@@ -291,13 +291,13 @@
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@@ -655,18 +868,33 @@
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@@ -681,18 +909,33 @@
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@@ -707,18 +950,33 @@
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@@ -5361,18 +8289,33 @@
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@@ -5387,18 +8330,33 @@
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@@ -5413,18 +8371,33 @@
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@@ -5517,12 +8535,26 @@
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 }
diff --git a/paper/data/calibration/locked_shared_source_n200.json b/paper/data/calibration/locked_shared_source_n200.json
index 88e6a17..8bf7bea 100644
--- a/paper/data/calibration/locked_shared_source_n200.json
+++ b/paper/data/calibration/locked_shared_source_n200.json
@@ -1,9 +1,9 @@
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@@ -291,13 +291,13 @@
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@@ -320,8 +320,40 @@
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@@ -329,6 +361,7 @@
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@@ -343,18 +376,33 @@
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@@ -369,18 +417,33 @@
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@@ -395,18 +458,33 @@
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@@ -421,18 +499,33 @@
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@@ -447,18 +540,33 @@
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    "member_rmse": 0.0037979887468451465,
@@ -5465,18 +8453,33 @@
    "max_abs_err": 0.0043320111169856314,
    "tau": 0.0006242517674443822,
    "s": 13.99457055376076,
-   "corr_length_days": 17.93711757676317,
-   "n_eff": 19.075768552949576,
+   "corr_length_days": 6.681142783254337,
+   "n_eff": 22.831792008165586,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.004383238405285592,
    "prior_weight_s2": 3.837047197008905e-14,
-   "prior_weight_lambda": 1.0205116762598975e-05
+   "prior_weight_lambda": 1.0205116762598975e-05,
+   "heldout_member_coverage68": 0.9170305676855895,
+   "heldout_member_coverage95": 0.9905385735080058,
+   "heldout_s": 16.261884043340725,
+   "heldout_fit_members": [
+    0,
+    5,
+    6,
+    9,
+    10,
+    11
+   ],
+   "rhat_tau2": 1.003489812420351,
+   "rhat_s2": 1.0002693751158847,
+   "rhat_lambda": 1.0131554362092414
   },
   {
    "seed": 2198,
    "scenario": "shared_source",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.7783842794759825,
    "member_coverage95": 0.9497816593886463,
    "member_rmse": 0.003247733471680635,
@@ -5491,18 +8494,33 @@
    "max_abs_err": 0.00346037976300617,
    "tau": 0.00010436818145620916,
    "s": 12.022211303683275,
-   "corr_length_days": 18.245340823814608,
-   "n_eff": 38.89879562086831,
+   "corr_length_days": 5.818821203408968,
+   "n_eff": 73.56813891432246,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.38188342763170163,
    "prior_weight_s2": 5.1868581821460274e-14,
-   "prior_weight_lambda": 1.207471828331953e-05
+   "prior_weight_lambda": 1.207471828331953e-05,
+   "heldout_member_coverage68": 0.7794759825327511,
+   "heldout_member_coverage95": 0.9359534206695779,
+   "heldout_s": 11.283038407473086,
+   "heldout_fit_members": [
+    1,
+    2,
+    4,
+    5,
+    7,
+    8
+   ],
+   "rhat_tau2": 1.0052569804901472,
+   "rhat_s2": 1.0018711109132747,
+   "rhat_lambda": 1.02829900047563
   },
   {
    "seed": 2199,
    "scenario": "shared_source",
    "ok": true,
    "n_epochs": 229,
+   "n_member_epochs": 2748,
    "member_coverage68": 0.7987627365356623,
    "member_coverage95": 0.9537845705967977,
    "member_rmse": 0.0035812745750307532,
@@ -5517,12 +8535,26 @@
    "max_abs_err": 0.0036031897301615433,
    "tau": 0.000532166659375895,
    "s": 13.108684517332374,
-   "corr_length_days": 24.85035067397985,
-   "n_eff": 21.495167462304526,
+   "corr_length_days": 6.380426671581534,
+   "n_eff": 26.251649046854368,
    "missing_fraction": 0.0,
    "prior_weight_tau2": 0.005975739884732249,
    "prior_weight_s2": 4.383051353715831e-14,
-   "prior_weight_lambda": 7.363311864410508e-06
+   "prior_weight_lambda": 7.363311864410508e-06,
+   "heldout_member_coverage68": 0.7743813682678311,
+   "heldout_member_coverage95": 0.9301310043668122,
+   "heldout_s": 14.219848989096173,
+   "heldout_fit_members": [
+    1,
+    2,
+    6,
+    7,
+    8,
+    11
+   ],
+   "rhat_tau2": 0.9990806674390916,
+   "rhat_s2": 1.0020113747693622,
+   "rhat_lambda": 1.007306465000464
   }
  ]
 }
diff --git a/paper/manuscript_marine.qmd b/paper/manuscript_marine.qmd
index 43fea18..b9863a2 100644
--- a/paper/manuscript_marine.qmd
+++ b/paper/manuscript_marine.qmd
@@ -193,12 +193,13 @@ release; an evaluation of agents against them is not part of this paper.
 # Synthetic framework {#sec:methods}
 
 We build each synthetic reference coda wave as a band-limited random-phase
-wavefield modulated by a physically grounded coda envelope. We model the envelope
-from the exact single-scattering
-solution of the two-dimensional radiative transfer equation for isotropic
-scattering [@Sato1993; @Paasschens1997], which underlies coda-envelope modelling
-of scattering and intrinsic attenuation [@Margerin1998]. The energy density at
-source--receiver distance $r$ and lapse time $t$ is
+wavefield modulated by a coda envelope taken from radiative transfer. The
+envelope is the closed-form solution of the two-dimensional radiative
+transfer equation for isotropic scattering [@Sato1993; @Paasschens1997],
+which sums all scattering orders and underlies coda-envelope modelling of
+scattering and intrinsic attenuation [@Margerin1998]; the synthetic is not
+a wavefield simulation, only random phases under that envelope. The energy
+density at source--receiver distance $r$ and lapse time $t$ is
 
 \begin{linenomath*}
 \begin{equation}
@@ -231,8 +232,12 @@ series is produced by generating this stretched coda with a prescribed
 ground-truth $\dvv(t)$ and additive band-limited noise at a controlled
 signal-to-noise ratio. The concept has been demonstrated using full waveform
 modeling in several previous studies [@Obermann2013; @Obermann2016; @Yuan2021], so
-we do not repeat that full-waveform modeling here. Because the imposed $\dvv(t)$ is known, every departure of
-a recovered series from it is an artefact of the processing, not of the data.
+we do not repeat that full-waveform modeling here. Because the imposed
+$\dvv(t)$ is known, every departure of a recovered series from it is due to
+the processing or to the additive noise at the prescribed signal-to-noise
+ratio, never to an unknown Earth; the noise-limited part is what the
+coherence floor of Section\ \ref{sec:bayes} describes, and the rest is the
+processing.
 
 
 We use seven \dvv\ estimators that were implemented in ``noisepy``
@@ -316,10 +321,32 @@ All \dvv\ quantities are fractions of velocity; figures show percent.}
 \toprule
 \textbf{Quantity} & \textbf{Estimate of} & \textbf{Datum and support} \\
 \midrule
-Recovery RMS (Sections~\ref{sec:results}--\ref{sec:multiverse}) & Root mean
-square of (recovered $-$ imposed) \dvv\ for one configuration on one waveform
-realisation & Raw recovered series, no baseline alignment; epochs the pipeline
-produced; fixed reference from the first 60\% of the record \\ \hline
+Recovery RMS, per-choice experiments (Section~\ref{sec:results} except
+Section~\ref{sec:param_ref}) & Root mean square of (recovered $-$ imposed)
+\dvv\ for one configuration on one waveform realisation & Raw recovered
+series, no baseline alignment; epochs the pipeline produced; the reference
+is the noise-free generating coda, a best case no field pipeline can reach
+(Figs.~\ref{fig:methods}, \ref{fig:stack-coherence},
+\ref{fig:params}a, b, d, \ref{fig:branches}, \ref{fig:artifacts}), the
+noise-free stack of a 60-day zero-change record (Fig.~\ref{fig:window-envelope}),
+or, in Fig.~\ref{fig:params}c, the first 0.8 yr of the record \\ \hline
+Recovery RMS, reference schemes (Section~\ref{sec:param_ref}) & Same &
+The five named schemes of Fig.~\ref{fig:reference-schemes}: the earliest or
+latest 15\% before the eruption, the whole pre-eruption record, a 60-day
+trailing stack, and the joint inversion \\ \hline
+Recovery RMS, sweeps and ensemble (Sections~\ref{sec:multiverse} and
+\ref{sec:bayes}) & Same, on shared daily correlations & Fixed reference from
+the first 60\% of the record; the one-at-a-time sweep also reports the RMS
+on the epochs every configuration produced (common support) with the
+availability of each configuration, over three paired noise realisations
+\\ \hline
+Estimator defaults & The settings held fixed while a choice is varied & MWCS
+and WCC: 6-s sub-windows at 3-s step; DTW and WTDTW: strain penalty
+$\gamma=0.3$, maximum lag 0.8 s; stretching: trial stretch range
+$\pm6\,\%$ on a 161-point grid with parabolic peak refinement ($\pm5\,\%$
+in the one-at-a-time sweep; $\pm3\,\%$ on 81 points inside the joint
+inversion); WTS: $\pm6\,\%$ on 121 points; coherence gate 0.6 on the
+stretching coherence of the same band, window, stack and reference \\ \hline
 Within-measurement $\sigma_k(t)$ & Standard error of one dilation estimate from
 finite coda coherence, eq.~\ref{eq:weaver} & Per epoch and configuration;
 depends on coherence, band, window; a lower bound (Section~\ref{sec:bayes}) \\ \hline
@@ -396,7 +423,9 @@ Section~\ref{sec:params_freq} \\ \hline
 Coda window & $\sim\!0.01\,\%$ (adapted to band) &
 $\sim\!3.9\,\%$ (fixed, wrong band) & Section~\ref{sec:param_window} \\ \hline
 Reference scheme & $\sim\!0.03\,\%$ (whole record, earliest period, or joint
-inversion) & $\sim\!0.15$--$0.16\,\%$ (end-of-record fixed, or moving) &
+inversion) & $\sim\!0.15$--$0.16\,\%$ (end-of-record fixed, or an uncumulated
+trailing reference: an ablation of re-baselining without the trend
+reconstruction that published moving-reference workflows apply) &
 Section~\ref{sec:param_ref} \\ \hline
 Stack length & $\sim\!0.020\,\%$ (7--10-day, workable deployment) &
 $\sim\!0.044\,\%$ (1-day, same deployment) & Section~\ref{sec:param_substack} \\
@@ -709,9 +738,11 @@ reference nor cluster-based reference selection.
 \end{figure}
 
 **Scale of effect:** which *period* a fixed reference is drawn from can cost as
-much as switching to a moving reference altogether ($\sim\!0.15$--$0.16\,\%$ RMS
-either way); a reference from the quietest available period, of any length,
-recovers the trend to $\sim\!0.03\,\%$.
+much as an uncumulated trailing reference, the ablation of re-baselining
+without trend reconstruction ($\sim\!0.15$--$0.16\,\%$ RMS either way); a
+reference from the quietest available period, of any length, recovers the
+trend to $\sim\!0.03\,\%$. A published moving-reference workflow that
+cumulates or stitches its increments is not priced here.
 
 ## Substacking {#sec:param_substack}
 
@@ -750,12 +781,19 @@ tradeoff, and the reason "longer is always better" is wrong even once the
 coherence gate is satisfied. For the poor deployment, RMS is still falling at
 60 days ($\sim\!0.067\,\%$, down from $\sim\!0.74\,\%$ at 1 day): the noise
 floor dominates over the whole tested range, and the smearing penalty never
-gets the chance to show up. The signed error in the recovered step amplitude
-is negative (an under-estimate) at every stack length for the poor deployment,
-and for the workable deployment up to about 45 days, past which it crosses
-zero and the step is over-estimated. A recovered step is therefore a lower
-bound on the true drop only in the noise-limited regime; the sign of the error
-depends on the deployment and the stack length, and both should be reported.
+gets the chance to show up. We measure the recovered step as the median of
+the 120 days after the event minus the median of the 120 days before,
+computed the same way on the recovered series and on the truth (where it is
+$-0.26\,\%$); a minimum over the post-event window, the definition used in
+an earlier draft, picks the noisiest epoch and is biased towards a deeper
+drop as the series gets noisier. With the median definition the recovered
+step is shallower than the truth at every stack length and for both
+deployments, and the under-estimate grows with the stack length: for the
+workable deployment from $0.002\,\%$ at 2 days to $0.014\,\%$ at 60 days,
+for the poor deployment from $0.005$ to $0.066\,\%$, both small against the
+step itself. The smearing that a longer stack applies to a step is
+therefore visible in the step amplitude as well as in the RMS, and the
+direction of the error is towards under-estimating the drop.
 
 \begin{figure}
   \centering
@@ -763,9 +801,12 @@ depends on the deployment and the stack length, and both should be reported.
   \caption{Substacking on the earthquake synthetic, at two deployment
   qualities. (a) Median stretching correlation coefficient versus stack
   length; the dashed line is codameter's own CC-gate threshold
-  (Section~\ref{sec:results}). (b) RMS error and the absolute bias in the
+  (Section~\ref{sec:results}). (b) RMS error and the absolute error of the
   recovered coseismic-step amplitude, both against the known truth, log
-  scale.}
+  scale; the step amplitude is the median of the 120 days after the event
+  minus the median of the 120 days before, on the recovered series and on
+  the truth alike, and the signed errors (all positive, a shallower step)
+  are in the figure's sidecar.}
   \label{fig:stack-coherence}
 \end{figure}
 
@@ -864,8 +905,7 @@ genuinely different \dvv\ without either being wrong. Two regimes bound the
 choice (Fig.\ \ref{fig:branches}). When a change is *localized* to the volume one
 branch samples, symmetrizing or averaging the branches --- the common default ---
 dilutes it toward zero, while the branch that carries the change recovers it
-(Fig.\ \ref{fig:branches}a); here preferring the branch of greatest change is
-a researcher's judgement.
+(Fig.\ \ref{fig:branches}a).
 When instead both branches share the *same* change,
 their difference is measurement noise, and selecting the branch of greatest
 change over-reports it --- a max-of-two-estimators selection bias that grows as
@@ -873,12 +913,18 @@ SNR falls (Fig.\ \ref{fig:branches}b). Choosing the branch of greatest change
 after seeing the data is therefore a selection rule that Fig.\ \ref{fig:branches}b
 shows to be biased, and the coherence of each branch is estimated from the same
 observations, so selecting on coherence reduces but does not remove that bias.
-The rule we adopt is fixed before the data are seen: measure both branches and
-report both; combine them by their mean unless independent physical
+The rule we recommend is fixed before the data are seen: measure each
+branch, report both, combine them by their mean unless independent physical
 information (source-side illumination, a change known to be confined to one
-side) designates a branch beforehand; and carry the between-branch difference as
-an explicit term of the measurement covariance $C_d$ (Section\ \ref{sec:bayes})
-rather than discarding it by averaging.
+side) designates a branch beforehand, and carry the between-branch
+difference as an explicit term of the measurement covariance rather than
+discarding it by averaging. The pipeline used in the rest of this paper does
+not yet implement that rule: its stretching estimator fits one stretch
+factor jointly over the two branches of the coda window, which is neither
+a per-branch measurement nor a selection, and the covariance $C_d$ of
+Section\ \ref{sec:bayes} carries no branch term. Fig.\ \ref{fig:branches}
+is therefore an argument for the rule, not a demonstration of it, and the
+per-branch measurement is deferred.
 
 \begin{figure}
   \centering
@@ -928,8 +974,10 @@ The scenario is a single representative station pair monitoring a shallow volcan
 edifice, in the style of the permanent broadband deployments used at effusive/dome
 volcanoes such as Piton de la Fournaise [@Brenguier2008]: a coda band matched to
 shallow depths (0.4--1.0$\,$Hz), a coda window past the direct arrival (10--30$\,$s),
-and daily correlations sampled every 3 days over 2.5 years at a per-day
-correlation-coefficient SNR of 7, typical of a continuously operating station.
+and daily correlations over 2.5 years at a per-day correlation-coefficient
+SNR of 7, typical of a continuously operating station; every pipeline
+stacks and references on the daily grid, and only every third day of its
+output is retained for the figures and the statistics.
 The synthetic ground truth combines an annual seasonal \dvv\ cycle (as from
 near-surface thermoelastic/hydrologic effects), a slow pre-eruptive inflation
 ramp, and a sharp co-eruptive velocity drop with partial recovery. This single-pair
@@ -942,67 +990,89 @@ involves them all. We now estimate the combined effects of these parametric choi
 band matched to the target depth, a coda window well past the direct arrival, a
 10-day stack, a long stable reference, coherence gating; the cross-cutting rules
 of @Brenguier2014 [@Weaver2011; @Clarke2011] as distilled in our survey), we change
-one parameter at a time to a deviation from best practice documented in the literature
- and measure the resulting error against the known truth (Fig.\ \ref{fig:deviations}). The ranking is unambiguous: relative
-to a best-practice RMS error of $\sim\!0.03\,\%$, the two-dimensionally-unwrapped
-WCS estimator is catastrophic here ($\sim\!50\times$ worse), a wrapped-phase MWCS
-inflates the error by roughly an order of magnitude ($\sim\!12\times$), and DTW by
-$\sim\!6\times$; among the non-estimator choices the uncumulated trailing
-reference is worst ($\sim\!5\times$, and most distorts the recovered drop; it
-is an ablation of re-baselining without trend reconstruction, not a surveyed
-workflow, Section\ \ref{sec:param_ref}), while stack length, coda window and
-frequency band deviations change the error by factors between $0.7$ and
-$2.5$. Two of them score below the baseline: the $0.8$--$2$ Hz band
-($0.022\,\%$) and the $4$--$14$ s window ($0.027\,\%$) against the
-baseline's $0.032\,\%$, so the best-practice baseline is not the optimum of
-this scenario. Turning the coherence gate off leaves the error unchanged
-here. The joint-inversion reference stays closest to the fixed-reference
-baseline among the reference-scheme deviations.
+one parameter at a time to a deviation from best practice documented in the
+literature and measure the resulting error against the known truth on three
+paired noise realisations, on the epochs that every configuration produced
+(Fig.\ \ref{fig:deviations}; Table\ \ref{tab:estimands}). The ranking is
+unambiguous and stable across realisations: relative to a best-practice RMS
+error of $0.033\,\%$ ($0.031$ to $0.035$ over the three realisations), the
+two-dimensionally-unwrapped WCS estimator is catastrophic here
+($46\times$ worse), a wrapped-phase MWCS inflates the error by an order of
+magnitude ($12\times$), and DTW by $6\times$; among the non-estimator
+choices the uncumulated trailing reference is worst ($5\times$, with the
+largest step error; it is an ablation of re-baselining without trend
+reconstruction, not a surveyed workflow, Section\ \ref{sec:param_ref}, and
+it produces $96\,\%$ of the epochs, the rest being its warm-up), while stack
+length, coda window and frequency band deviations change the error by
+factors between $0.7$ and $2.3$. Two of them score below the baseline: the
+$0.8$--$2$ Hz band ($0.023\,\%$) and the $4$--$14$ s window ($0.027\,\%$),
+so the best-practice baseline is not the optimum of this scenario. Turning
+the coherence gate off leaves the error unchanged, because no epoch of this
+scenario falls below the gate. The joint-inversion reference, run with
+10-day blocks to match the stack length, sits at $1.7\times$ the baseline;
+it has no per-epoch coherence, so the gate does not apply to it, and the
+estimator axis does not combine with it because the inversion is itself a
+stretching measurement between block stacks.
 
 \begin{figure}
   \centering
   \includegraphics[width=\textwidth]{demo_10_deviations.png}
   \caption{One-at-a-time deviations from a best-practice baseline, ranked by
-  their RMS error against the truth (a, log scale; RMS mixes bias and
-  scatter) and by how they distort the recovered co-eruptive drop (b,
-  symlog). Bars are coloured red when the error exceeds three times the
-  baseline (dashed line). "Uncumulated trailing" is the moving reference
-  without trend reconstruction of Section\ \ref{sec:param_ref}.}
+  their RMS error against the truth on the epochs every configuration
+  produced (a, log scale; RMS mixes bias and scatter) and by the error of the
+  recovered co-eruptive step (b, symlog; post-event median minus pre-event
+  median, recovered minus true). Bars are means over three paired noise
+  realisations and whiskers span their range. Bars are coloured red when the
+  error exceeds three times the baseline (dashed line). "Uncumulated
+  trailing" is the moving reference without trend reconstruction of
+  Section\ \ref{sec:param_ref}; the percentage after it is the fraction of
+  epochs it produced.}
   \label{fig:deviations}
 \end{figure}
 
-We test the compounding effects of these choices through 108 reasonable workflows selecting
- three estimators, two frequency bands, three coda windows, three stacking
-lengths and two reference schemes on a synthetic "volcano" dv/v time series
-that includes a seasonal oscillation, a slow pre-eruptive inflation ramp, and a
-sharp co-eruptive drop with partial exponential recovery (Fig.\ \ref{fig:multiverse}a).
-The per-day standard deviation across the 108 pipelines varies by a factor of
-$\sim\!4$--5 over the time series (from $\sim\!0.4\,\%$ to $\sim\!1.7\,\%$), and is
-widest exactly at the sharp co-eruptive drop; the RMS error against the known
-truth spans over two orders of magnitude across pipelines ($\sim\!0.02$--$2.8\,\%$).
-
-Attributing the variance of the outcome to each axis with a first-order (main-effect) sensitivity index
-(Fig.\ \ref{fig:multiverse}b) shows that, for this dataset, the **coda window**
-controls the RMS error most, with the estimator second and the stack length
-third; for the recovered drop amplitude the order changes to **stack length**
-first, window second, and estimator third. The first-order indices sum to
-well under one in both cases ($\sim\!0.66$ for RMS, $\sim\!0.63$ for the
-drop), so a large part of the spread is *interaction* between choices
-compounding. The appropriate object is therefore not a single curve
-but a distribution of \dvv\ over the processing choices.
+We test the compounding effects of these choices through the full factorial
+of three estimators, two frequency bands, three coda windows, three stacking
+lengths and two reference schemes, 108 workflows, on a synthetic "volcano"
+dv/v time series that includes a seasonal oscillation, a slow pre-eruptive
+inflation ramp, and a sharp co-eruptive drop with partial exponential
+recovery (Fig.\ \ref{fig:multiverse}a). Twelve of the 108 return no epoch
+at all: MWCS with the 4--14 s coda window, at every stack length and
+reference, because that window holds two of the 6-s sub-windows and the
+delay-versus-lapse fit needs at least three. The statistics below are over
+the 96 pipelines that return a series. Their per-epoch standard deviation
+varies by a factor of $\sim\!4$ over the time series (from $0.39$ to
+$1.72\,\%$), and is widest exactly at the sharp co-eruptive drop; the RMS
+error against the known truth spans more than two orders of magnitude
+across pipelines ($0.020$ to $2.84\,\%$).
+
+Attributing the variance of the outcome to each axis with a first-order
+(main-effect) sensitivity index (Fig.\ \ref{fig:multiverse}b) shows that,
+for this dataset, the **coda window** controls the RMS error most (index
+$0.27$), with the estimator ($0.19$) and the stack length ($0.17$) next and
+the band and the reference scheme below $0.03$. For the recovered step, the
+reference scheme leads ($0.13$) with the estimator ($0.06$) and the window
+($0.06$) next; the stack length has no first-order effect on the step as
+measured by post- and pre-event medians, which the smearing of a stack
+shorter than the 120-day windows barely moves. The first-order indices sum
+to $0.65$ for the RMS and to $0.28$ for the step, so a large part of the
+spread, and most of it for the step, is *interaction* between choices
+compounding. The appropriate object is therefore not a single curve but a
+distribution of \dvv\ over the processing choices.
 
 
 \begin{figure}
   \centering
   \includegraphics[width=\textwidth]{demo_11_multiverse.png}
-  \caption{The full multiverse. (a) 108 reasonable pipelines on one dataset,
-  each coloured by its RMS error against the truth (a fraction of velocity) on
-  a colourblind-safe scale (bright accurate, dark biased), with the median
-  across pipelines (purple) and the truth (black); the axis is clipped at
-  $\pm0.8\,\%$, and the number of pipelines that leave it and the extent of
-  the 10--90\% inter-pipeline band, which exceeds the axis range, are printed
-  on the panel. (b) First-order variance attribution of the RMS error and of
-  the recovered drop to each processing axis.}
+  \caption{The full multiverse. (a) The 96 of 108 pipelines that return a
+  series on one dataset, each coloured by its RMS error against the truth (a
+  fraction of velocity) on a colourblind-safe scale (bright accurate, dark
+  biased), with the median across pipelines (purple) and the truth (black);
+  the axis is clipped at $\pm0.8\,\%$, and the number of pipelines that
+  return no epoch, the number that leave the axis and the extent of the
+  10--90\% inter-pipeline band, which exceeds the axis range, are printed on
+  the panel. (b) First-order variance attribution of the RMS error and of
+  the recovered step (post- minus pre-event median) to each processing axis,
+  over the 96 pipelines.}
   \label{fig:multiverse}
 \end{figure}
 
@@ -1025,7 +1095,7 @@ follow the literature survey (Appendix~\ref{app:survey}).}
 \textbf{Choice} & \textbf{Best practice} & \textbf{Common deviation} &
 \textbf{Consequence} \\
 \midrule
-Estimator & Stretching family (TS/WTS/WCC), robust at low SNR and large \dvv\ \citep{Mikesell2015,Yuan2021} & Wrapped-phase MWCS \citep{Clarke2011} without 2-D
+Estimator & Stretching family (TS/WTS/WCC): accurate at large \dvv\ on our synthetics (Section~\ref{sec:methods-fig}); its noise robustness relative to the warping methods depends on the setting \citep{Mikesell2015,Yuan2021} & Wrapped-phase MWCS \citep{Clarke2011} without 2-D
 unwrapping \citep{Mao2020} & Cycle-skips at large \dvv; error inflated
 $\sim\!10\times$ or catastrophic \\ \hline
 Frequency band & Matched to the target depth: $\sim\!0.1$--2\,Hz (volcano, crust),
@@ -1085,7 +1155,18 @@ The likelihood treats residuals as conditionally independent across
 configurations and epochs. Shared input waveforms do not ensure this
 assumption. Fitting all member outputs jointly is not the same operation as
 marginalising a discrete mixture of alternative pipelines. The posterior is
-therefore conditional on this working likelihood. We use a
+therefore conditional on this working likelihood. One consequence can be
+measured directly: duplicating every member of the ensemble, which the
+working likelihood counts as new data, shrinks the median half-width of the
+$95\,\%$ credible band on $\mu$ on the realisation of
+Fig.\ \ref{fig:bayes} from $0.063$ to $0.052\,\%$ (a factor 0.83, where
+independent data would give 0.71), and quadrupling it to $0.040\,\%$ (0.64
+against 0.50), because the smoothness prior with its fitted $\lambda$
+supplies about $80\,\%$ of the per-epoch precision of $\mu$ at the
+posterior mean; the single-member scale $\sigma_{C_d}$ moves by less than
+$4\,\%$ under the same duplication. The credible band on
+$\mu$ is thus set more by the assumed smoothness than by the members, which
+is one reason its coverage has to be tested rather than assumed. We use a
 second-difference smoothness prior of precision $\lambda$ on the latent
 true series $\mu(t)$, built on the physical time grid so that a gap in the
 record is a gap in the prior. Here $\beta_k$ is configuration $k$'s constant
@@ -1096,15 +1177,21 @@ Every configuration is run through the same pipeline code as the rest of the
 paper, so the estimator, band, window, stack length in days, reference scheme
 and coherence gate all take effect; an epoch a configuration does not produce
 (reference warm-up, a gated coherence) is simply missing and carries no
-information. The hyper-priors on $\tau^2$, $s^2$ and $\lambda$ are conjugate
-inverse-gamma and gamma distributions whose scales are small against the data
-terms. Codameter reports the prior scale term divided by the conditional
-posterior rate, evaluated at posterior means. The ratio is about 0.09 for
-$\tau^2$ in the clean scenario and below 0.01 for $s^2$ and $\lambda$
-(Table\ \ref{tab:calibration}). This diagnostic does not measure the total
-influence of the prior or establish sampler convergence. A conjugate Gibbs sampler,
-implemented in codameter with no external sampler dependency and with a banded
-solve for the smoothness update, returns the joint posterior.
+information; so is an epoch whose peak stretching coherence falls below
+0.5, where the floor of eq.\ \ref{eq:weaver} is undefined. The hyper-priors
+are conjugate: $\tau^2$ and $s^2$ follow inverse-gamma distributions with
+shape 2 and scale $10^{-8}$, and the smoothness precision $\lambda$ a gamma
+distribution with shape 2 and rate $10^{-10}$; the scales are small against
+the data terms, and codameter reports the prior scale term divided by the
+conditional posterior rate, evaluated at posterior means. The ratio is about
+0.09 for $\tau^2$ in the clean scenario and below 0.01 for $s^2$ and
+$\lambda$ (Table\ \ref{tab:calibration}). This diagnostic does not measure
+the total influence of the prior. A conjugate Gibbs sampler, implemented in
+codameter with no external sampler dependency and with a banded solve for
+the smoothness update, returns the joint posterior from one chain of 1200
+sweeps, the first 400 discarded and every second retained thereafter; the
+sampler seed is the realisation seed, and the calibration runs below add a
+second chain from another seed to check convergence.
 
 The model yields two distinct objects, and conflating them is a common
 error (Fig.\ \ref{fig:bayes}; Table\ \ref{tab:estimands}). The posterior of
@@ -1121,14 +1208,29 @@ with $\sigma_{\mathrm{tot}}^2(t) = s^2\,\overline{\sigma_k^2(t)} +
 \max\!\big[\operatorname{Var}_k(m_k(t)-\beta_k) - s^2\,\overline{\sigma_k^2(t)},\,0\big]$,
 the calibrated floor plus whatever spread across configurations exceeds it
 (so that the floor is not counted twice), and $R_{ij}=e^{-|t_i-t_j|/L}$ for a
-correlation length $L$ estimated from the ensemble residuals. $C_d$ is
+correlation length $L$ fitted through the origin to the leading lags of the
+residual autocorrelation, those above 0.1. $C_d$ is
 constructed from the fitted model, not sampled. It targets the error of one
 measurement drawn from the ensemble, not of $\mu$. The between-configuration
 offset scale $\tau$ does not identify an error shared by all configurations.
 Pointwise coverage tests only the diagonal scale; it does not validate $R$
-or the rank-one term. A downstream inversion needs the error covariance of
-its actual input estimate. Neither using this $C_d$ for the ensemble mean
-nor interpreting its time axes as frequency-band axes is justified here.
+or the rank-one term. What can be checked is what $R$ leaves behind:
+whitening each member's residual about $\mu$ by the Cholesky factor of
+$C_d$ on its observed epochs should give white residuals of unit
+variance. On the realisation of Fig.\ \ref{fig:bayes} the raw
+residuals are correlated at 0.57 over one epoch (4 days) and 0.21 over
+two, the signature of consecutive 10-day trailing stacks sharing their
+days; with $L=5.7$ days the whitened residuals retain a lag-one correlation
+of 0.26 and have a variance of 0.62, so the single exponential captures
+most but not all of the stacking-induced correlation, and the residual
+scatter about $\mu$ is below the single-member scale (which is what the
+$68\,\%$ overcoverage below also says). An earlier fit of $L$ over 40 lags
+with an intercept returned 39 days on this realisation, several times the
+short-lag decay, and its whitened residuals had a variance of 3 with
+negative correlation at two and three epochs; that fit is withdrawn. A
+downstream inversion needs the error covariance of its actual input
+estimate. Neither using this $C_d$ for the ensemble mean nor interpreting
+its time axes as frequency-band axes is justified here.
 
 Two properties of the fit deserve to be stated plainly. First, $s\approx 12$
 on this synthetic: the residual scatter of the members about the ensemble mean
@@ -1138,22 +1240,33 @@ The floor is a lower bound, and the rescale is what makes it usable. Second,
 once $s$ is fitted on those residuals, the calibrated floor absorbs nearly all
 of the between-configuration spread, and the excess term of eq.\ \ref{eq:cd} is
 non-zero only at the epochs where the configurations disagree more than they
-usually do (Fig.\ \ref{fig:bayes}c). The assumed temporal correlation
-($L\approx 39$ days on the realisation shown, 30 days on average over the
-200 realisations of Table\ \ref{tab:calibration}, at a 4-day cadence) and
-the common-mode term collapse the effective number of independent epochs
-from 229 to a few tens.
+usually do (Fig.\ \ref{fig:bayes}c). The fitted temporal correlation
+($L=5.7$ days on the realisation shown, $6.1$ days on average over the 200
+realisations of Table\ \ref{tab:calibration}, at a 4-day cadence) and,
+above all, the common-mode term $\tau$ collapse the effective number of
+independent epochs from 229 to 29 on the realisation shown and 45 on
+average.
 
 Whether these intervals mean what they say is a question one realisation
 cannot answer, so we repeat the whole measurement on independent
-realisations of the same scenario (Table\ \ref{tab:calibration}; the driver
-is \texttt{codameter.calibration}). Three coverages answer three different
+realisations of the same scenario (Table\ \ref{tab:calibration}). Three
+coverages answer three different
 questions. The fraction of member epochs whose error against the truth lies
 within $1.96\,\sigma_{C_d}$ is 0.956 on 200 realisations, within the margin of $\pm 0.03$ fixed
 before the run. This supports the $95\,\%$ pointwise interval on this
 scenario, not calibration of the entire covariance. At the $68\,\%$ level
 it covers 0.81 and fails the same margin. One Gaussian scale therefore does
-not calibrate both interval levels. The $95\,\%$ credible band on
+not calibrate both interval levels. That coverage is also in-sample: $s$
+and the excess spread are fitted on the members they score. Fitting $C_d$
+on a random half of the twelve members and scoring the other half gives
+$0.937\pm0.004$ at the $95\,\%$ level, still within the margin, and $0.79$
+at $68\,\%$. Two Gibbs chains from different seeds give split
+$\hat R$ values of $1.006$, $1.002$ and $1.022$ for $\tau^2$, $s^2$ and
+$\lambda$ on average on the clean scenario; $\lambda$ exceeds $1.05$ in
+22, 40 and 27 of the 200 realisations of the clean, shared-source and
+clock-drift scenarios (largest $1.19$, $1.90$ and $1.81$), and excluding
+those realisations changes no coverage of Table\ \ref{tab:calibration} by
+more than $0.004$. The $95\,\%$ credible band on
 $\mu$ contains the truth at only 0.59 of the epochs: the ensemble mean
 inherits the biases its members share (the stacking that rounds the drop, the
 estimator biases at low coherence), and no amount of averaging over
@@ -1214,8 +1327,9 @@ Section\ \ref{sec:artifacts}.
 The remaining sections present a framework rather than new synthetics: they set
 out how the covariance of Section\ \ref{sec:bayes} propagates down the inference
 chain, and ground each step in what the monitoring literature does and does not
-yet report. The executable stages are in development in the open codameter package
-(Section\ \ref{sec:discussion}).
+yet report. The depth stage is implemented in the open codameter package as
+a linear inversion that consumes a per-band covariance; it is not evaluated
+in this paper (Section\ \ref{sec:discussion}).
 
 The field has converged on one physical rule for depth --- *depth is set by the
 frequency band and the coda lapse time, it is not assumed* [@Obermann2013;
@@ -1244,11 +1358,14 @@ This covariance must describe the band estimates actually supplied. The
 temporal $C_d$ in Section\ \ref{sec:bayes} does not supply its cross-band
 entries. Given such a covariance, the Bayesian solution under a
 smoothness prior returns a depth profile $\delta V_S/V_S(z)$ together with its
-posterior covariance $C_m(z)$, implemented in codameter. The bands
-must sit where the kernels resolve: too low and the kernel leaks into the
-half-space, too high and the coda is incoherent (Section\ \ref{sec:params_freq}). The
-width of $C_m(z)$ --- not the profile alone --- is the deliverable, and it
-inherits the temporal correlation and common-mode structure of $C_d$.
+posterior covariance $C_m(z)$; codameter implements this inversion, with a
+diagonal or a full band covariance as supplied, and we do not evaluate it
+here. The bands must sit where the kernels resolve: too low and the kernel
+leaks into the half-space, too high and the coda is incoherent
+(Section\ \ref{sec:params_freq}). What the stage should report is the width
+of $C_m(z)$ together with the profile, and that width inherits whatever
+correlation the supplied per-band covariance carries: a diagonal covariance
+gives a width that understates the effect of errors the bands share.
 
 One assumption is usually left implicit: that a \dvv\ change is a shear-velocity
 change alone. In partially saturated ground it is not. Filling or draining pore
@@ -1264,10 +1381,10 @@ substitution for the modulus and a porosity--saturation relation for the density
 own prior uncertainty on porosity, fluid modulus, and the saturation path.
 Hydrological and cryospheric targets, where saturation varies strongly
 [@Clements2018; @James2019], are precisely where neglecting the density term
-biases the inferred velocity change and, downstream, the stress. The framework carries
-$\delta\rho/\rho$ as a second inverted field with its own kernel and reports how
-much of the surface \dvv\ each explains; the executable version is a documented
-extension (Section\ \ref{sec:discussion}).
+biases the inferred velocity change and, downstream, the stress. Carrying
+$\delta\rho/\rho$ as a second inverted field with its own kernel, so that
+the inversion reports how much of the surface \dvv\ each field explains, is
+a natural extension of the linear stage; codameter does not implement it.
 
 \begin{table}
 \footnotesize
@@ -1323,11 +1440,9 @@ trailing 90-day mean to the daily series (at least 45 finite days in the
 window), compare demeaned --- the two products reference different epochs,
 and a constant offset is bookkeeping, not error --- and exclude the first 150
 days of each station's series as reference burn-in. The comparison is
-computed by a script archived with the paper
-(\texttt{scripts/compare\_gate1.py}) from the daily products and the
-published series, with the join, smoothing and mask stated in its output
-(\texttt{paper/data/gate1/comparison.json}); Table\ \ref{tab:gate1} lists the
-result. Under the matched rule CI.LJR reaches $r=0.985$ on 579 days with an
+computed by a script archived with the paper from the daily products and
+the published series, with the join, smoothing and mask stated in its
+output; Table\ \ref{tab:gate1} lists the result. Under the matched rule CI.LJR reaches $r=0.985$ on 579 days with an
 amplitude slope of 1.07 (published on codameter); CI.ARV reaches $r=0.905$ on
 357 days, the 2018 data gaps reducing the overlap, but with a slope of 2.15,
 so the published product has twice the amplitude of ours there; CI.RXH
@@ -1342,8 +1457,8 @@ stated mask.
 \begin{table}
 \footnotesize
 \caption{Comparison of codameter single-station \dvv\ (2--4\,Hz, 2018--2019)
-with the published \citet{Clements2023} product, from
-\texttt{scripts/compare\_gate1.py}. Matched: trailing 90-day mean, 150-day
+with the published \citet{Clements2023} product, under three stated
+rules. Matched: trailing 90-day mean, 150-day
 burn-in. Centred: centred 45-day mean, no burn-in (the rule behind the
 annotation on Fig.~\ref{fig:realdata-validation}). Slope is the OLS slope of
 the published product on codameter; RMS is the RMS difference after removing
@@ -1378,9 +1493,8 @@ CI.RXH & centred & 554 & 0.620 & 0.035 & 0.52 \\
   0.62 for LJR, ARV and RXH from the archived products), not to the matched
   rule quoted in the text. The error bars drawn here predate the Weaver-floor
   correction of the present revision and are too large by a factor of 3.1 at
-  2--4\,Hz (the archived columns have since been rescaled by
-  \texttt{scripts/correct\_gate1\_within\_error.py}; the externally produced
-  figure has not been regenerated).}
+  2--4\,Hz (the archived columns have since been rescaled; the externally
+  produced figure has not been regenerated).}
   \label{fig:realdata-validation}
 \end{figure}
 
@@ -1436,13 +1550,18 @@ correlation coefficient is reported alongside the recovered series.
 
 The experiments above share one finding: on these synthetics, with one
 waveform realisation held fixed, the processing choice moves both the
-recovered \dvv\ and its stated uncertainty by more than the measurement noise
-does, by two orders of magnitude in RMS across the 108-pipeline multiverse and
-by a factor $\sqrt{N}$ in the reported network error bar. Whether processing
+recovered \dvv\ and its stated uncertainty across a range far wider than
+the noise-limited error of the best configuration: the RMS error spans
+$0.02$ to $2.8\,\%$ over the 96 pipelines of the 108-pipeline factorial
+that return a series, against $0.033\,\%$ for the best-practice baseline,
+and the reported network error bar changes by a factor $\sqrt{N}$ with the
+quantity a study names. Whether processing
 also dominates the variability between real deployments is a question these
-experiments cannot answer, because they hold the observed waveform fixed; the
-repeated-realisation calibration of Section\ \ref{sec:bayes} is the first step
-toward it. The problem is consequential but tractable. We suggest the
+experiments cannot answer, because they hold the observed waveform fixed;
+the repeated-realisation calibration of Section\ \ref{sec:bayes} redraws
+only the additive noise on one fixed coda, so it varies the noise-limited
+part of the error and not the wavefield, and is a first step toward that
+question rather than an answer to it. The problem is consequential but tractable. We suggest the
 following responses.
 
 **Report the choices.** At minimum, a \dvv\ study should state the estimator and
@@ -1503,10 +1622,12 @@ conditional on it. Every configuration transforms the same waveforms, so an
 error they all share (a source change, a contaminated reference, a clock
 drift measured on one branch) leaves no trace in their spread: on the
 shared-source scenario of Table\ \ref{tab:calibration} the ensemble agrees with
-itself, the error of its mean doubles, and $C_d$ cannot see it. Configurations in different bands sample
-different depths and may not estimate the same physical quantity, so the
-configuration axis should be marginalised only over pipelines that target
-one estimand. And the coherence floor of @Weaver2011 is a lower bound: on our
+itself, the error of its mean doubles, and $C_d$ cannot see it.
+Configurations in different bands sample different depths and may not
+estimate the same physical quantity in the field, so the configuration axis
+should be marginalised only over pipelines that target one estimand; the
+two bands of our ensemble see one imposed \dvv\ on the synthetic, which is
+why they can be combined there. And the coherence floor of @Weaver2011 is a lower bound: on our
 synthetic the residual scatter about the ensemble mean is an order of
 magnitude above it, which the fitted rescale $s$ reports rather than hides.
 The pointwise tests in Table\ \ref{tab:calibration} support the $95\,\%$
@@ -1519,8 +1640,8 @@ valid downstream intervals.
 this paper are released in the open codameter package; one driver regenerates
 every generated figure together with a numerical sidecar holding every plotted
 array and the run's provenance, and the package is unit-tested. The three
-real-data figures were produced by the cloud run and are archived, not
-regenerated (Section\ \ref{sec:deployment}). An executable record turns an undocumented
+real-data figures were produced by the cloud run and are committed to the
+repository as produced, not regenerated (Section\ \ref{sec:deployment}). An executable record turns an undocumented
 choice into a versioned, inspectable one, and lets a reader re-run a study's
 pipeline on the truth-known synthetic to see its bias before trusting it on data.
 
@@ -1567,7 +1688,8 @@ Ambient-noise \dvv\ monitoring rests on a chain of processing choices that are
 made ad hoc and reported incompletely. Using a truth-known synthetic and the full
 estimator suite of an open toolbox, we have shown that these choices change the
 RMS error of the recovered \dvv\ by more than two orders of magnitude
-(0.02 to $2.8\,\%$) across 108 pipelines on one synthetic volcano scenario
+(0.02 to $2.8\,\%$) across the 96 pipelines of a 108-pipeline factorial
+that return a series, on one synthetic volcano scenario,
 and, more consequentially, change the number reported as its uncertainty by
 a factor of $\sim\!\sqrt{N}$ depending on whether a study calls $1\sigma$
 the standard error of the network mean or the between-pair standard
@@ -1753,23 +1875,22 @@ under-reporting; the verified rate is the one among the 82 full-text rows.
 
 All synthetics, estimators, and generated figures in this paper are implemented
 in the open-source Python package codameter (MIT license), openly available at
-<https://github.com/Denolle-Lab/codameter>; each generated figure's sidecar
-records its generating commit and numerical arrays. The figures and manuscript
-can originate from different revisions. \texttt{python -m codameter.figures}
-regenerates every generated figure with a \texttt{.npz} sidecar of its plotted
-arrays and a \texttt{.json} sidecar of its provenance;
-\texttt{python -m codameter.calibration} reproduces
-Table\ \ref{tab:calibration} (\texttt{paper/data/calibration/});
-\texttt{scripts/compare\_gate1.py} reproduces Table\ \ref{tab:gate1} from the
-daily products under \texttt{paper/data/gate1/} and the published
-\citet{Clements2023} series archived there. The daily products and the three
-real-data figures were produced by the noisepy-dvv-cloud Gate 1 run from
-public Southern California Earthquake Data Center waveforms; the products are
-available locally during this analysis but are not tracked in the repository.
-The exact Gate 1 run commit, run configuration and redistribution archive
-remain to be supplied; their current provenance limits are recorded in
-\texttt{paper/data/gate1/README.md}. A versioned archive is planned but
-has not yet been deposited.
+<https://github.com/Denolle-Lab/codameter>; each generated figure carries a
+numerical sidecar with its plotted arrays and its generating commit, so the
+figures and the manuscript can originate from different revisions and be
+told apart. The repository documents how one command regenerates every
+generated figure, how the repeated-realisation calibration of
+Table\ \ref{tab:calibration} is rerun (its settings and seeds are stored
+with each archived run), and how Table\ \ref{tab:gate1} is recomputed from
+the daily products and the published \citet{Clements2023} series archived
+with the paper. The daily products and the three real-data figures were
+produced by the noisepy-dvv-cloud Gate 1 run from public Southern
+California Earthquake Data Center waveforms; the products are available
+locally during this analysis but are not tracked in the repository. The
+exact Gate 1 run commit, run configuration and redistribution archive
+remain to be supplied; their current provenance limits are recorded with
+the archived products. A versioned archive is planned but has not yet been
+deposited.
 
 # Acknowledgements {.unnumbered}
 
diff --git a/paper/manuscript_marine.tex b/paper/manuscript_marine.tex
index 21093a5..03fb6df 100644
--- a/paper/manuscript_marine.tex
+++ b/paper/manuscript_marine.tex
@@ -251,7 +251,7 @@
 \title{The reproducibility cost of ad-hoc processing choices in
 ambient-noise seismic velocity-change monitoring}
 \author{M. A. Denolle}
-\date{2026-09-13}
+\date{2026-09-14}
 \begin{document}
 \maketitle
 \begin{abstract}
@@ -453,13 +453,14 @@ \section{Introduction}\label{sec:intro}
 \section{Synthetic framework}\label{sec:methods}
 
 We build each synthetic reference coda wave as a band-limited
-random-phase wavefield modulated by a physically grounded coda envelope.
-We model the envelope from the exact single-scattering solution of the
+random-phase wavefield modulated by a coda envelope taken from radiative
+transfer. The envelope is the closed-form solution of the
 two-dimensional radiative transfer equation for isotropic scattering
-\citep{Sato1993, Paasschens1997}, which underlies coda-envelope
-modelling of scattering and intrinsic attenuation \citep{Margerin1998}.
-The energy density at source--receiver distance \(r\) and lapse time
-\(t\) is
+\citep{Sato1993, Paasschens1997}, which sums all scattering orders and
+underlies coda-envelope modelling of scattering and intrinsic
+attenuation \citep{Margerin1998}; the synthetic is not a wavefield
+simulation, only random phases under that envelope. The energy density
+at source--receiver distance \(r\) and lapse time \(t\) is
 
 \begin{linenomath*}
 \begin{equation}
@@ -498,8 +499,10 @@ \section{Synthetic framework}\label{sec:methods}
 using full waveform modeling in several previous studies
 \citep{Obermann2013, Obermann2016, Yuan2021}, so we do not repeat that
 full-waveform modeling here. Because the imposed \(\dvv(t)\) is known,
-every departure of a recovered series from it is an artefact of the
-processing, not of the data.
+every departure of a recovered series from it is due to the processing
+or to the additive noise at the prescribed signal-to-noise ratio, never
+to an unknown Earth; the noise-limited part is what the coherence floor
+of Section~\ref{sec:bayes} describes, and the rest is the processing.
 
 We use seven \dvv~estimators that were implemented in \texttt{noisepy}
 \citep{Jiang2020}: trace stretching (TS, \citet{lobkis03}), windowed
@@ -582,10 +585,32 @@ \section{Synthetic framework}\label{sec:methods}
 \toprule
 \textbf{Quantity} & \textbf{Estimate of} & \textbf{Datum and support} \\
 \midrule
-Recovery RMS (Sections~\ref{sec:results}--\ref{sec:multiverse}) & Root mean
-square of (recovered $-$ imposed) \dvv\ for one configuration on one waveform
-realisation & Raw recovered series, no baseline alignment; epochs the pipeline
-produced; fixed reference from the first 60\% of the record \\ \hline
+Recovery RMS, per-choice experiments (Section~\ref{sec:results} except
+Section~\ref{sec:param_ref}) & Root mean square of (recovered $-$ imposed)
+\dvv\ for one configuration on one waveform realisation & Raw recovered
+series, no baseline alignment; epochs the pipeline produced; the reference
+is the noise-free generating coda, a best case no field pipeline can reach
+(Figs.~\ref{fig:methods}, \ref{fig:stack-coherence},
+\ref{fig:params}a, b, d, \ref{fig:branches}, \ref{fig:artifacts}), the
+noise-free stack of a 60-day zero-change record (Fig.~\ref{fig:window-envelope}),
+or, in Fig.~\ref{fig:params}c, the first 0.8 yr of the record \\ \hline
+Recovery RMS, reference schemes (Section~\ref{sec:param_ref}) & Same &
+The five named schemes of Fig.~\ref{fig:reference-schemes}: the earliest or
+latest 15\% before the eruption, the whole pre-eruption record, a 60-day
+trailing stack, and the joint inversion \\ \hline
+Recovery RMS, sweeps and ensemble (Sections~\ref{sec:multiverse} and
+\ref{sec:bayes}) & Same, on shared daily correlations & Fixed reference from
+the first 60\% of the record; the one-at-a-time sweep also reports the RMS
+on the epochs every configuration produced (common support) with the
+availability of each configuration, over three paired noise realisations
+\\ \hline
+Estimator defaults & The settings held fixed while a choice is varied & MWCS
+and WCC: 6-s sub-windows at 3-s step; DTW and WTDTW: strain penalty
+$\gamma=0.3$, maximum lag 0.8 s; stretching: trial stretch range
+$\pm6\,\%$ on a 161-point grid with parabolic peak refinement ($\pm5\,\%$
+in the one-at-a-time sweep; $\pm3\,\%$ on 81 points inside the joint
+inversion); WTS: $\pm6\,\%$ on 121 points; coherence gate 0.6 on the
+stretching coherence of the same band, window, stack and reference \\ \hline
 Within-measurement $\sigma_k(t)$ & Standard error of one dilation estimate from
 finite coda coherence, eq.~\ref{eq:weaver} & Per epoch and configuration;
 depends on coherence, band, window; a lower bound (Section~\ref{sec:bayes}) \\ \hline
@@ -662,7 +687,9 @@ \section{\texorpdfstring{parameter-dependent \dvv~and its
 Coda window & $\sim\!0.01\,\%$ (adapted to band) &
 $\sim\!3.9\,\%$ (fixed, wrong band) & Section~\ref{sec:param_window} \\ \hline
 Reference scheme & $\sim\!0.03\,\%$ (whole record, earliest period, or joint
-inversion) & $\sim\!0.15$--$0.16\,\%$ (end-of-record fixed, or moving) &
+inversion) & $\sim\!0.15$--$0.16\,\%$ (end-of-record fixed, or an uncumulated
+trailing reference: an ablation of re-baselining without the trend
+reconstruction that published moving-reference workflows apply) &
 Section~\ref{sec:param_ref} \\ \hline
 Stack length & $\sim\!0.020\,\%$ (7--10-day, workable deployment) &
 $\sim\!0.044\,\%$ (1-day, same deployment) & Section~\ref{sec:param_substack} \\
@@ -1003,10 +1030,12 @@ \subsection{Reference}\label{sec:param_ref}
 \end{figure}
 
 \textbf{Scale of effect:} which \emph{period} a fixed reference is drawn
-from can cost as much as switching to a moving reference altogether
+from can cost as much as an uncumulated trailing reference, the ablation
+of re-baselining without trend reconstruction
 (\(\sim\!0.15\)--\(0.16\,\%\) RMS either way); a reference from the
 quietest available period, of any length, recovers the trend to
-\(\sim\!0.03\,\%\).
+\(\sim\!0.03\,\%\). A published moving-reference workflow that cumulates
+or stitches its increments is not priced here.
 
 \subsection{Substacking}\label{sec:param_substack}
 
@@ -1050,13 +1079,20 @@ \subsection{Substacking}\label{sec:param_substack}
 the poor deployment, RMS is still falling at 60 days
 (\(\sim\!0.067\,\%\), down from \(\sim\!0.74\,\%\) at 1 day): the noise
 floor dominates over the whole tested range, and the smearing penalty
-never gets the chance to show up. The signed error in the recovered step
-amplitude is negative (an under-estimate) at every stack length for the
-poor deployment, and for the workable deployment up to about 45 days,
-past which it crosses zero and the step is over-estimated. A recovered
-step is therefore a lower bound on the true drop only in the
-noise-limited regime; the sign of the error depends on the deployment
-and the stack length, and both should be reported.
+never gets the chance to show up. We measure the recovered step as the
+median of the 120 days after the event minus the median of the 120 days
+before, computed the same way on the recovered series and on the truth
+(where it is \(-0.26\,\%\)); a minimum over the post-event window, the
+definition used in an earlier draft, picks the noisiest epoch and is
+biased towards a deeper drop as the series gets noisier. With the median
+definition the recovered step is shallower than the truth at every stack
+length and for both deployments, and the under-estimate grows with the
+stack length: for the workable deployment from \(0.002\,\%\) at 2 days
+to \(0.014\,\%\) at 60 days, for the poor deployment from \(0.005\) to
+\(0.066\,\%\), both small against the step itself. The smearing that a
+longer stack applies to a step is therefore visible in the step
+amplitude as well as in the RMS, and the direction of the error is
+towards under-estimating the drop.
 
 \begin{figure}
   \centering
@@ -1064,9 +1100,12 @@ \subsection{Substacking}\label{sec:param_substack}
   \caption{Substacking on the earthquake synthetic, at two deployment
   qualities. (a) Median stretching correlation coefficient versus stack
   length; the dashed line is codameter's own CC-gate threshold
-  (Section~\ref{sec:results}). (b) RMS error and the absolute bias in the
+  (Section~\ref{sec:results}). (b) RMS error and the absolute error of the
   recovered coseismic-step amplitude, both against the known truth, log
-  scale.}
+  scale; the step amplitude is the median of the 120 days after the event
+  minus the median of the 120 days before, on the recovered series and on
+  the truth alike, and the signed errors (all positive, a shallower step)
+  are in the figure's sidecar.}
   \label{fig:stack-coherence}
 \end{figure}
 
@@ -1174,22 +1213,27 @@ \subsection{Causal and acausal branches}\label{sec:branches}
 (Fig.~\ref{fig:branches}). When a change is \emph{localized} to the
 volume one branch samples, symmetrizing or averaging the branches ---
 the common default --- dilutes it toward zero, while the branch that
-carries the change recovers it (Fig.~\ref{fig:branches}a); here
-preferring the branch of greatest change is a researcher's judgement.
-When instead both branches share the \emph{same} change, their
-difference is measurement noise, and selecting the branch of greatest
-change over-reports it --- a max-of-two-estimators selection bias that
-grows as SNR falls (Fig.~\ref{fig:branches}b). Choosing the branch of
-greatest change after seeing the data is therefore a selection rule that
+carries the change recovers it (Fig.~\ref{fig:branches}a). When instead
+both branches share the \emph{same} change, their difference is
+measurement noise, and selecting the branch of greatest change
+over-reports it --- a max-of-two-estimators selection bias that grows as
+SNR falls (Fig.~\ref{fig:branches}b). Choosing the branch of greatest
+change after seeing the data is therefore a selection rule that
 Fig.~\ref{fig:branches}b shows to be biased, and the coherence of each
 branch is estimated from the same observations, so selecting on
-coherence reduces but does not remove that bias. The rule we adopt is
-fixed before the data are seen: measure both branches and report both;
+coherence reduces but does not remove that bias. The rule we recommend
+is fixed before the data are seen: measure each branch, report both,
 combine them by their mean unless independent physical information
 (source-side illumination, a change known to be confined to one side)
-designates a branch beforehand; and carry the between-branch difference
-as an explicit term of the measurement covariance \(C_d\)
-(Section~\ref{sec:bayes}) rather than discarding it by averaging.
+designates a branch beforehand, and carry the between-branch difference
+as an explicit term of the measurement covariance rather than discarding
+it by averaging. The pipeline used in the rest of this paper does not
+yet implement that rule: its stretching estimator fits one stretch
+factor jointly over the two branches of the coda window, which is
+neither a per-branch measurement nor a selection, and the covariance
+\(C_d\) of Section~\ref{sec:bayes} carries no branch term.
+Fig.~\ref{fig:branches} is therefore an argument for the rule, not a
+demonstration of it, and the per-branch measurement is deferred.
 
 \begin{figure}
   \centering
@@ -1242,15 +1286,16 @@ \section{The combined impact of processing
 deployments used at effusive/dome volcanoes such as Piton de la
 Fournaise \citep{Brenguier2008}: a coda band matched to shallow depths
 (0.4--1.0\(\,\)Hz), a coda window past the direct arrival
-(10--30\(\,\)s), and daily correlations sampled every 3 days over 2.5
-years at a per-day correlation-coefficient SNR of 7, typical of a
-continuously operating station. The synthetic ground truth combines an
-annual seasonal \dvv~cycle (as from near-surface
-thermoelastic/hydrologic effects), a slow pre-eruptive inflation ramp,
-and a sharp co-eruptive velocity drop with partial recovery. This
-single-pair scenario isolates the measurement-step choices from the
-network-aggregation choices already covered in
-Sections~\ref{sec:aggregation}--\ref{sec:uncertainty}.
+(10--30\(\,\)s), and daily correlations over 2.5 years at a per-day
+correlation-coefficient SNR of 7, typical of a continuously operating
+station; every pipeline stacks and references on the daily grid, and
+only every third day of its output is retained for the figures and the
+statistics. The synthetic ground truth combines an annual seasonal
+\dvv~cycle (as from near-surface thermoelastic/hydrologic effects), a
+slow pre-eruptive inflation ramp, and a sharp co-eruptive velocity drop
+with partial recovery. This single-pair scenario isolates the
+measurement-step choices from the network-aggregation choices already
+covered in Sections~\ref{sec:aggregation}--\ref{sec:uncertainty}.
 
 The previous sections only identified single choices, but the overall
 research workflow involves them all. We now estimate the combined
@@ -1262,71 +1307,90 @@ \section{The combined impact of processing
 \citetext{\citeyear{Brenguier2014}; \citealp{Weaver2011}; \citealp{Clarke2011}}
 as distilled in our survey), we change one parameter at a time to a
 deviation from best practice documented in the literature and measure
-the resulting error against the known truth (Fig.~\ref{fig:deviations}).
-The ranking is unambiguous: relative to a best-practice RMS error of
-\(\sim\!0.03\,\%\), the two-dimensionally-unwrapped WCS estimator is
-catastrophic here (\(\sim\!50\times\) worse), a wrapped-phase MWCS
-inflates the error by roughly an order of magnitude
-(\(\sim\!12\times\)), and DTW by \(\sim\!6\times\); among the
-non-estimator choices the uncumulated trailing reference is worst
-(\(\sim\!5\times\), and most distorts the recovered drop; it is an
+the resulting error against the known truth on three paired noise
+realisations, on the epochs that every configuration produced
+(Fig.~\ref{fig:deviations}; Table~\ref{tab:estimands}). The ranking is
+unambiguous and stable across realisations: relative to a best-practice
+RMS error of \(0.033\,\%\) (\(0.031\) to \(0.035\) over the three
+realisations), the two-dimensionally-unwrapped WCS estimator is
+catastrophic here (\(46\times\) worse), a wrapped-phase MWCS inflates
+the error by an order of magnitude (\(12\times\)), and DTW by
+\(6\times\); among the non-estimator choices the uncumulated trailing
+reference is worst (\(5\times\), with the largest step error; it is an
 ablation of re-baselining without trend reconstruction, not a surveyed
-workflow, Section~\ref{sec:param_ref}), while stack length, coda window
-and frequency band deviations change the error by factors between
-\(0.7\) and \(2.5\). Two of them score below the baseline: the
-\(0.8\)--\(2\) Hz band (\(0.022\,\%\)) and the \(4\)--\(14\) s window
-(\(0.027\,\%\)) against the baseline's \(0.032\,\%\), so the
-best-practice baseline is not the optimum of this scenario. Turning the
-coherence gate off leaves the error unchanged here. The joint-inversion
-reference stays closest to the fixed-reference baseline among the
-reference-scheme deviations.
+workflow, Section~\ref{sec:param_ref}, and it produces \(96\,\%\) of the
+epochs, the rest being its warm-up), while stack length, coda window and
+frequency band deviations change the error by factors between \(0.7\)
+and \(2.3\). Two of them score below the baseline: the \(0.8\)--\(2\) Hz
+band (\(0.023\,\%\)) and the \(4\)--\(14\) s window (\(0.027\,\%\)), so
+the best-practice baseline is not the optimum of this scenario. Turning
+the coherence gate off leaves the error unchanged, because no epoch of
+this scenario falls below the gate. The joint-inversion reference, run
+with 10-day blocks to match the stack length, sits at \(1.7\times\) the
+baseline; it has no per-epoch coherence, so the gate does not apply to
+it, and the estimator axis does not combine with it because the
+inversion is itself a stretching measurement between block stacks.
 
 \begin{figure}
   \centering
   \includegraphics[width=\textwidth]{demo_10_deviations.png}
   \caption{One-at-a-time deviations from a best-practice baseline, ranked by
-  their RMS error against the truth (a, log scale; RMS mixes bias and
-  scatter) and by how they distort the recovered co-eruptive drop (b,
-  symlog). Bars are coloured red when the error exceeds three times the
-  baseline (dashed line). "Uncumulated trailing" is the moving reference
-  without trend reconstruction of Section\ \ref{sec:param_ref}.}
+  their RMS error against the truth on the epochs every configuration
+  produced (a, log scale; RMS mixes bias and scatter) and by the error of the
+  recovered co-eruptive step (b, symlog; post-event median minus pre-event
+  median, recovered minus true). Bars are means over three paired noise
+  realisations and whiskers span their range. Bars are coloured red when the
+  error exceeds three times the baseline (dashed line). "Uncumulated
+  trailing" is the moving reference without trend reconstruction of
+  Section\ \ref{sec:param_ref}; the percentage after it is the fraction of
+  epochs it produced.}
   \label{fig:deviations}
 \end{figure}
 
-We test the compounding effects of these choices through 108 reasonable
-workflows selecting three estimators, two frequency bands, three coda
-windows, three stacking lengths and two reference schemes on a synthetic
-``volcano'' dv/v time series that includes a seasonal oscillation, a
-slow pre-eruptive inflation ramp, and a sharp co-eruptive drop with
-partial exponential recovery (Fig.~\ref{fig:multiverse}a). The per-day
-standard deviation across the 108 pipelines varies by a factor of
-\(\sim\!4\)--5 over the time series (from \(\sim\!0.4\,\%\) to
-\(\sim\!1.7\,\%\)), and is widest exactly at the sharp co-eruptive drop;
-the RMS error against the known truth spans over two orders of magnitude
-across pipelines (\(\sim\!0.02\)--\(2.8\,\%\)).
+We test the compounding effects of these choices through the full
+factorial of three estimators, two frequency bands, three coda windows,
+three stacking lengths and two reference schemes, 108 workflows, on a
+synthetic ``volcano'' dv/v time series that includes a seasonal
+oscillation, a slow pre-eruptive inflation ramp, and a sharp co-eruptive
+drop with partial exponential recovery (Fig.~\ref{fig:multiverse}a).
+Twelve of the 108 return no epoch at all: MWCS with the 4--14 s coda
+window, at every stack length and reference, because that window holds
+two of the 6-s sub-windows and the delay-versus-lapse fit needs at least
+three. The statistics below are over the 96 pipelines that return a
+series. Their per-epoch standard deviation varies by a factor of
+\(\sim\!4\) over the time series (from \(0.39\) to \(1.72\,\%\)), and is
+widest exactly at the sharp co-eruptive drop; the RMS error against the
+known truth spans more than two orders of magnitude across pipelines
+(\(0.020\) to \(2.84\,\%\)).
 
 Attributing the variance of the outcome to each axis with a first-order
 (main-effect) sensitivity index (Fig.~\ref{fig:multiverse}b) shows that,
-for this dataset, the \textbf{coda window} controls the RMS error most,
-with the estimator second and the stack length third; for the recovered
-drop amplitude the order changes to \textbf{stack length} first, window
-second, and estimator third. The first-order indices sum to well under
-one in both cases (\(\sim\!0.66\) for RMS, \(\sim\!0.63\) for the drop),
-so a large part of the spread is \emph{interaction} between choices
-compounding. The appropriate object is therefore not a single curve but
-a distribution of \dvv~over the processing choices.
+for this dataset, the \textbf{coda window} controls the RMS error most
+(index \(0.27\)), with the estimator (\(0.19\)) and the stack length
+(\(0.17\)) next and the band and the reference scheme below \(0.03\).
+For the recovered step, the reference scheme leads (\(0.13\)) with the
+estimator (\(0.06\)) and the window (\(0.06\)) next; the stack length
+has no first-order effect on the step as measured by post- and pre-event
+medians, which the smearing of a stack shorter than the 120-day windows
+barely moves. The first-order indices sum to \(0.65\) for the RMS and to
+\(0.28\) for the step, so a large part of the spread, and most of it for
+the step, is \emph{interaction} between choices compounding. The
+appropriate object is therefore not a single curve but a distribution of
+\dvv~over the processing choices.
 
 \begin{figure}
   \centering
   \includegraphics[width=\textwidth]{demo_11_multiverse.png}
-  \caption{The full multiverse. (a) 108 reasonable pipelines on one dataset,
-  each coloured by its RMS error against the truth (a fraction of velocity) on
-  a colourblind-safe scale (bright accurate, dark biased), with the median
-  across pipelines (purple) and the truth (black); the axis is clipped at
-  $\pm0.8\,\%$, and the number of pipelines that leave it and the extent of
-  the 10--90\% inter-pipeline band, which exceeds the axis range, are printed
-  on the panel. (b) First-order variance attribution of the RMS error and of
-  the recovered drop to each processing axis.}
+  \caption{The full multiverse. (a) The 96 of 108 pipelines that return a
+  series on one dataset, each coloured by its RMS error against the truth (a
+  fraction of velocity) on a colourblind-safe scale (bright accurate, dark
+  biased), with the median across pipelines (purple) and the truth (black);
+  the axis is clipped at $\pm0.8\,\%$, and the number of pipelines that
+  return no epoch, the number that leave the axis and the extent of the
+  10--90\% inter-pipeline band, which exceeds the axis range, are printed on
+  the panel. (b) First-order variance attribution of the RMS error and of
+  the recovered step (post- minus pre-event median) to each processing axis,
+  over the 96 pipelines.}
   \label{fig:multiverse}
 \end{figure}
 
@@ -1349,7 +1413,7 @@ \section{The combined impact of processing
 \textbf{Choice} & \textbf{Best practice} & \textbf{Common deviation} &
 \textbf{Consequence} \\
 \midrule
-Estimator & Stretching family (TS/WTS/WCC), robust at low SNR and large \dvv\ \citep{Mikesell2015,Yuan2021} & Wrapped-phase MWCS \citep{Clarke2011} without 2-D
+Estimator & Stretching family (TS/WTS/WCC): accurate at large \dvv\ on our synthetics (Section~\ref{sec:methods-fig}); its noise robustness relative to the warping methods depends on the setting \citep{Mikesell2015,Yuan2021} & Wrapped-phase MWCS \citep{Clarke2011} without 2-D
 unwrapping \citep{Mao2020} & Cycle-skips at large \dvv; error inflated
 $\sim\!10\times$ or catastrophic \\ \hline
 Frequency band & Matched to the target depth: $\sim\!0.1$--2\,Hz (volcano, crust),
@@ -1410,28 +1474,46 @@ \section{A Bayesian measurement model and its data
 not ensure this assumption. Fitting all member outputs jointly is not
 the same operation as marginalising a discrete mixture of alternative
 pipelines. The posterior is therefore conditional on this working
-likelihood. We use a second-difference smoothness prior of precision
-\(\lambda\) on the latent true series \(\mu(t)\), built on the physical
-time grid so that a gap in the record is a gap in the prior. Here
-\(\beta_k\) is configuration \(k\)'s constant offset (the systematic
-offset between, say, MWCS and stretching), \(\tau\) its scale across the
-ensemble, and \(s\) rescales the coherence floor of eq.~\ref{eq:weaver}
-so that the data report whether that floor is calibrated. Every
-configuration is run through the same pipeline code as the rest of the
-paper, so the estimator, band, window, stack length in days, reference
-scheme and coherence gate all take effect; an epoch a configuration does
-not produce (reference warm-up, a gated coherence) is simply missing and
-carries no information. The hyper-priors on \(\tau^2\), \(s^2\) and
-\(\lambda\) are conjugate inverse-gamma and gamma distributions whose
-scales are small against the data terms. Codameter reports the prior
-scale term divided by the conditional posterior rate, evaluated at
-posterior means. The ratio is about 0.09 for \(\tau^2\) in the clean
-scenario and below 0.01 for \(s^2\) and \(\lambda\)
-(Table~\ref{tab:calibration}). This diagnostic does not measure the
-total influence of the prior or establish sampler convergence. A
-conjugate Gibbs sampler, implemented in codameter with no external
-sampler dependency and with a banded solve for the smoothness update,
-returns the joint posterior.
+likelihood. One consequence can be measured directly: duplicating every
+member of the ensemble, which the working likelihood counts as new data,
+shrinks the median half-width of the \(95\,\%\) credible band on \(\mu\)
+on the realisation of Fig.~\ref{fig:bayes} from \(0.063\) to
+\(0.052\,\%\) (a factor 0.83, where independent data would give 0.71),
+and quadrupling it to \(0.040\,\%\) (0.64 against 0.50), because the
+smoothness prior with its fitted \(\lambda\) supplies about \(80\,\%\)
+of the per-epoch precision of \(\mu\) at the posterior mean; the
+single-member scale \(\sigma_{C_d}\) moves by less than \(4\,\%\) under
+the same duplication. The credible band on \(\mu\) is thus set more by
+the assumed smoothness than by the members, which is one reason its
+coverage has to be tested rather than assumed. We use a
+second-difference smoothness prior of precision \(\lambda\) on the
+latent true series \(\mu(t)\), built on the physical time grid so that a
+gap in the record is a gap in the prior. Here \(\beta_k\) is
+configuration \(k\)'s constant offset (the systematic offset between,
+say, MWCS and stretching), \(\tau\) its scale across the ensemble, and
+\(s\) rescales the coherence floor of eq.~\ref{eq:weaver} so that the
+data report whether that floor is calibrated. Every configuration is run
+through the same pipeline code as the rest of the paper, so the
+estimator, band, window, stack length in days, reference scheme and
+coherence gate all take effect; an epoch a configuration does not
+produce (reference warm-up, a gated coherence) is simply missing and
+carries no information; so is an epoch whose peak stretching coherence
+falls below 0.5, where the floor of eq.~\ref{eq:weaver} is undefined.
+The hyper-priors are conjugate: \(\tau^2\) and \(s^2\) follow
+inverse-gamma distributions with shape 2 and scale \(10^{-8}\), and the
+smoothness precision \(\lambda\) a gamma distribution with shape 2 and
+rate \(10^{-10}\); the scales are small against the data terms, and
+codameter reports the prior scale term divided by the conditional
+posterior rate, evaluated at posterior means. The ratio is about 0.09
+for \(\tau^2\) in the clean scenario and below 0.01 for \(s^2\) and
+\(\lambda\) (Table~\ref{tab:calibration}). This diagnostic does not
+measure the total influence of the prior. A conjugate Gibbs sampler,
+implemented in codameter with no external sampler dependency and with a
+banded solve for the smoothness update, returns the joint posterior from
+one chain of 1200 sweeps, the first 400 discarded and every second
+retained thereafter; the sampler seed is the realisation seed, and the
+calibration runs below add a second chain from another seed to check
+convergence.
 
 The model yields two distinct objects, and conflating them is a common
 error (Fig.~\ref{fig:bayes}; Table~\ref{tab:estimands}). The posterior
@@ -1448,16 +1530,31 @@ \section{A Bayesian measurement model and its data
 \max\!\big[\operatorname{Var}_k(m_k(t)-\beta_k) - s^2\,\overline{\sigma_k^2(t)},\,0\big]\),
 the calibrated floor plus whatever spread across configurations exceeds
 it (so that the floor is not counted twice), and
-\(R_{ij}=e^{-|t_i-t_j|/L}\) for a correlation length \(L\) estimated
-from the ensemble residuals. \(C_d\) is constructed from the fitted
-model, not sampled. It targets the error of one measurement drawn from
-the ensemble, not of \(\mu\). The between-configuration offset scale
+\(R_{ij}=e^{-|t_i-t_j|/L}\) for a correlation length \(L\) fitted
+through the origin to the leading lags of the residual autocorrelation,
+those above 0.1. \(C_d\) is constructed from the fitted model, not
+sampled. It targets the error of one measurement drawn from the
+ensemble, not of \(\mu\). The between-configuration offset scale
 \(\tau\) does not identify an error shared by all configurations.
 Pointwise coverage tests only the diagonal scale; it does not validate
-\(R\) or the rank-one term. A downstream inversion needs the error
-covariance of its actual input estimate. Neither using this \(C_d\) for
-the ensemble mean nor interpreting its time axes as frequency-band axes
-is justified here.
+\(R\) or the rank-one term. What can be checked is what \(R\) leaves
+behind: whitening each member's residual about \(\mu\) by the Cholesky
+factor of \(C_d\) on its observed epochs should give white residuals of
+unit variance. On the realisation of Fig.~\ref{fig:bayes} the raw
+residuals are correlated at 0.57 over one epoch (4 days) and 0.21 over
+two, the signature of consecutive 10-day trailing stacks sharing their
+days; with \(L=5.7\) days the whitened residuals retain a lag-one
+correlation of 0.26 and have a variance of 0.62, so the single
+exponential captures most but not all of the stacking-induced
+correlation, and the residual scatter about \(\mu\) is below the
+single-member scale (which is what the \(68\,\%\) overcoverage below
+also says). An earlier fit of \(L\) over 40 lags with an intercept
+returned 39 days on this realisation, several times the short-lag decay,
+and its whitened residuals had a variance of 3 with negative correlation
+at two and three epochs; that fit is withdrawn. A downstream inversion
+needs the error covariance of its actual input estimate. Neither using
+this \(C_d\) for the ensemble mean nor interpreting its time axes as
+frequency-band axes is justified here.
 
 Two properties of the fit deserve to be stated plainly. First,
 \(s\approx 12\) on this synthetic: the residual scatter of the members
@@ -1468,31 +1565,42 @@ \section{A Bayesian measurement model and its data
 residuals, the calibrated floor absorbs nearly all of the
 between-configuration spread, and the excess term of eq.~\ref{eq:cd} is
 non-zero only at the epochs where the configurations disagree more than
-they usually do (Fig.~\ref{fig:bayes}c). The assumed temporal
-correlation (\(L\approx 39\) days on the realisation shown, 30 days on
-average over the 200 realisations of Table~\ref{tab:calibration}, at a
-4-day cadence) and the common-mode term collapse the effective number of
-independent epochs from 229 to a few tens.
+they usually do (Fig.~\ref{fig:bayes}c). The fitted temporal correlation
+(\(L=5.7\) days on the realisation shown, \(6.1\) days on average over
+the 200 realisations of Table~\ref{tab:calibration}, at a 4-day cadence)
+and, above all, the common-mode term \(\tau\) collapse the effective
+number of independent epochs from 229 to 29 on the realisation shown and
+45 on average.
 
 Whether these intervals mean what they say is a question one realisation
 cannot answer, so we repeat the whole measurement on independent
-realisations of the same scenario (Table~\ref{tab:calibration}; the
-driver is \texttt{codameter.calibration}). Three coverages answer three
-different questions. The fraction of member epochs whose error against
-the truth lies within \(1.96\,\sigma_{C_d}\) is 0.956 on 200
-realisations, within the margin of \(\pm 0.03\) fixed before the run.
-This supports the \(95\,\%\) pointwise interval on this scenario, not
-calibration of the entire covariance. At the \(68\,\%\) level it covers
-0.81 and fails the same margin. One Gaussian scale therefore does not
-calibrate both interval levels. The \(95\,\%\) credible band on \(\mu\)
-contains the truth at only 0.59 of the epochs: the ensemble mean
-inherits the biases its members share (the stacking that rounds the
-drop, the estimator biases at low coherence), and no amount of averaging
-over configurations removes them, which is what the posterior's
-precision cannot know. Comparing \(\mu\) with \(\pm 2\sigma_{C_d}\)
-mixes the ensemble mean with a single-member scale and yields nearly
-complete coverage here; it does not validate the uncertainty of the
-combined estimate. The other two scenarios of
+realisations of the same scenario (Table~\ref{tab:calibration}). Three
+coverages answer three different questions. The fraction of member
+epochs whose error against the truth lies within \(1.96\,\sigma_{C_d}\)
+is 0.956 on 200 realisations, within the margin of \(\pm 0.03\) fixed
+before the run. This supports the \(95\,\%\) pointwise interval on this
+scenario, not calibration of the entire covariance. At the \(68\,\%\)
+level it covers 0.81 and fails the same margin. One Gaussian scale
+therefore does not calibrate both interval levels. That coverage is also
+in-sample: \(s\) and the excess spread are fitted on the members they
+score. Fitting \(C_d\) on a random half of the twelve members and
+scoring the other half gives \(0.937\pm0.004\) at the \(95\,\%\) level,
+still within the margin, and \(0.79\) at \(68\,\%\). Two Gibbs chains
+from different seeds give split \(\hat R\) values of \(1.006\),
+\(1.002\) and \(1.022\) for \(\tau^2\), \(s^2\) and \(\lambda\) on
+average on the clean scenario; \(\lambda\) exceeds \(1.05\) in 22, 40
+and 27 of the 200 realisations of the clean, shared-source and
+clock-drift scenarios (largest \(1.19\), \(1.90\) and \(1.81\)), and
+excluding those realisations changes no coverage of
+Table~\ref{tab:calibration} by more than \(0.004\). The \(95\,\%\)
+credible band on \(\mu\) contains the truth at only 0.59 of the epochs:
+the ensemble mean inherits the biases its members share (the stacking
+that rounds the drop, the estimator biases at low coherence), and no
+amount of averaging over configurations removes them, which is what the
+posterior's precision cannot know. Comparing \(\mu\) with
+\(\pm 2\sigma_{C_d}\) mixes the ensemble mean with a single-member scale
+and yields nearly complete coverage here; it does not validate the
+uncertainty of the combined estimate. The other two scenarios of
 Table~\ref{tab:calibration} inject artefacts that every configuration
 sees identically. A station clock drift changes no coverage by more than
 0.015 and adds no shared bias (Table~\ref{tab:calibration}), because a
@@ -1548,8 +1656,9 @@ \section{\texorpdfstring{Propagating \dvv~errors at depth
 The remaining sections present a framework rather than new synthetics:
 they set out how the covariance of Section~\ref{sec:bayes} propagates
 down the inference chain, and ground each step in what the monitoring
-literature does and does not yet report. The executable stages are in
-development in the open codameter package
+literature does and does not yet report. The depth stage is implemented
+in the open codameter package as a linear inversion that consumes a
+per-band covariance; it is not evaluated in this paper
 (Section~\ref{sec:discussion}).
 
 The field has converged on one physical rule for depth --- \emph{depth
@@ -1581,12 +1690,15 @@ \section{\texorpdfstring{Propagating \dvv~errors at depth
 Section~\ref{sec:bayes} does not supply its cross-band entries. Given
 such a covariance, the Bayesian solution under a smoothness prior
 returns a depth profile \(\delta V_S/V_S(z)\) together with its
-posterior covariance \(C_m(z)\), implemented in codameter. The bands
-must sit where the kernels resolve: too low and the kernel leaks into
-the half-space, too high and the coda is incoherent
-(Section~\ref{sec:params_freq}). The width of \(C_m(z)\) --- not the
-profile alone --- is the deliverable, and it inherits the temporal
-correlation and common-mode structure of \(C_d\).
+posterior covariance \(C_m(z)\); codameter implements this inversion,
+with a diagonal or a full band covariance as supplied, and we do not
+evaluate it here. The bands must sit where the kernels resolve: too low
+and the kernel leaks into the half-space, too high and the coda is
+incoherent (Section~\ref{sec:params_freq}). What the stage should report
+is the width of \(C_m(z)\) together with the profile, and that width
+inherits whatever correlation the supplied per-band covariance carries:
+a diagonal covariance gives a width that understates the effect of
+errors the bands share.
 
 One assumption is usually left implicit: that a \dvv~change is a
 shear-velocity change alone. In partially saturated ground it is not.
@@ -1603,10 +1715,10 @@ \section{\texorpdfstring{Propagating \dvv~errors at depth
 the saturation path. Hydrological and cryospheric targets, where
 saturation varies strongly \citep{Clements2018, James2019}, are
 precisely where neglecting the density term biases the inferred velocity
-change and, downstream, the stress. The framework carries
-\(\delta\rho/\rho\) as a second inverted field with its own kernel and
-reports how much of the surface \dvv~each explains; the executable
-version is a documented extension (Section~\ref{sec:discussion}).
+change and, downstream, the stress. Carrying \(\delta\rho/\rho\) as a
+second inverted field with its own kernel, so that the inversion reports
+how much of the surface \dvv~each field explains, is a natural extension
+of the linear stage; codameter does not implement it.
 
 \begin{table}
 \footnotesize
@@ -1665,26 +1777,25 @@ \section{Real-data comparison and deployment}\label{sec:deployment}
 window), compare demeaned --- the two products reference different
 epochs, and a constant offset is bookkeeping, not error --- and exclude
 the first 150 days of each station's series as reference burn-in. The
-comparison is computed by a script archived with the paper
-(\texttt{scripts/compare\_gate1.py}) from the daily products and the
-published series, with the join, smoothing and mask stated in its output
-(\texttt{paper/data/gate1/comparison.json}); Table~\ref{tab:gate1} lists
-the result. Under the matched rule CI.LJR reaches \(r=0.985\) on 579
-days with an amplitude slope of 1.07 (published on codameter); CI.ARV
-reaches \(r=0.905\) on 357 days, the 2018 data gaps reducing the
-overlap, but with a slope of 2.15, so the published product has twice
-the amplitude of ours there; CI.RXH reaches \(r=0.829\) on 446 days with
-a slope of 0.81 on a station whose recovered \dvv~is nearly flat.
-Correlation measures the shape of the annual cycle after smoothing; it
-does not validate the amplitude (the ARV slope) or the error bars, which
-the published product does not carry, and the earlier draft's quoted 681
+comparison is computed by a script archived with the paper from the
+daily products and the published series, with the join, smoothing and
+mask stated in its output; Table~\ref{tab:gate1} lists the result. Under
+the matched rule CI.LJR reaches \(r=0.985\) on 579 days with an
+amplitude slope of 1.07 (published on codameter); CI.ARV reaches
+\(r=0.905\) on 357 days, the 2018 data gaps reducing the overlap, but
+with a slope of 2.15, so the published product has twice the amplitude
+of ours there; CI.RXH reaches \(r=0.829\) on 446 days with a slope of
+0.81 on a station whose recovered \dvv~is nearly flat. Correlation
+measures the shape of the annual cycle after smoothing; it does not
+validate the amplitude (the ARV slope) or the error bars, which the
+published product does not carry, and the earlier draft's quoted 681
 days was the raw daily overlap, not the count under the stated mask.
 
 \begin{table}
 \footnotesize
 \caption{Comparison of codameter single-station \dvv\ (2--4\,Hz, 2018--2019)
-with the published \citet{Clements2023} product, from
-\texttt{scripts/compare\_gate1.py}. Matched: trailing 90-day mean, 150-day
+with the published \citet{Clements2023} product, under three stated
+rules. Matched: trailing 90-day mean, 150-day
 burn-in. Centred: centred 45-day mean, no burn-in (the rule behind the
 annotation on Fig.~\ref{fig:realdata-validation}). Slope is the OLS slope of
 the published product on codameter; RMS is the RMS difference after removing
@@ -1718,9 +1829,8 @@ \section{Real-data comparison and deployment}\label{sec:deployment}
   0.62 for LJR, ARV and RXH from the archived products), not to the matched
   rule quoted in the text. The error bars drawn here predate the Weaver-floor
   correction of the present revision and are too large by a factor of 3.1 at
-  2--4\,Hz (the archived columns have since been rescaled by
-  \texttt{scripts/correct\_gate1\_within\_error.py}; the externally produced
-  figure has not been regenerated).}
+  2--4\,Hz (the archived columns have since been rescaled; the externally
+  produced figure has not been regenerated).}
   \label{fig:realdata-validation}
 \end{figure}
 
@@ -1776,13 +1886,18 @@ \section{Discussion}\label{sec:discussion}
 
 The experiments above share one finding: on these synthetics, with one
 waveform realisation held fixed, the processing choice moves both the
-recovered \dvv~and its stated uncertainty by more than the measurement
-noise does, by two orders of magnitude in RMS across the 108-pipeline
-multiverse and by a factor \(\sqrt{N}\) in the reported network error
-bar. Whether processing also dominates the variability between real
-deployments is a question these experiments cannot answer, because they
-hold the observed waveform fixed; the repeated-realisation calibration
-of Section~\ref{sec:bayes} is the first step toward it. The problem is
+recovered \dvv~and its stated uncertainty across a range far wider than
+the noise-limited error of the best configuration: the RMS error spans
+\(0.02\) to \(2.8\,\%\) over the 96 pipelines of the 108-pipeline
+factorial that return a series, against \(0.033\,\%\) for the
+best-practice baseline, and the reported network error bar changes by a
+factor \(\sqrt{N}\) with the quantity a study names. Whether processing
+also dominates the variability between real deployments is a question
+these experiments cannot answer, because they hold the observed waveform
+fixed; the repeated-realisation calibration of Section~\ref{sec:bayes}
+redraws only the additive noise on one fixed coda, so it varies the
+noise-limited part of the error and not the wavefield, and is a first
+step toward that question rather than an answer to it. The problem is
 consequential but tractable. We suggest the following responses.
 
 \textbf{Report the choices.} At minimum, a \dvv~study should state the
@@ -1846,14 +1961,16 @@ \section{Discussion}\label{sec:discussion}
 scenario of Table~\ref{tab:calibration} the ensemble agrees with itself,
 the error of its mean doubles, and \(C_d\) cannot see it. Configurations
 in different bands sample different depths and may not estimate the same
-physical quantity, so the configuration axis should be marginalised only
-over pipelines that target one estimand. And the coherence floor of
-\citet{Weaver2011} is a lower bound: on our synthetic the residual
-scatter about the ensemble mean is an order of magnitude above it, which
-the fitted rescale \(s\) reports rather than hides. The pointwise tests
-in Table~\ref{tab:calibration} support the \(95\,\%\) member intervals
-on the listed scenarios. They also expose \(68\,\%\) overcoverage and
-poor coverage of the combined estimate. They do not establish temporal
+physical quantity in the field, so the configuration axis should be
+marginalised only over pipelines that target one estimand; the two bands
+of our ensemble see one imposed \dvv~on the synthetic, which is why they
+can be combined there. And the coherence floor of \citet{Weaver2011} is
+a lower bound: on our synthetic the residual scatter about the ensemble
+mean is an order of magnitude above it, which the fitted rescale \(s\)
+reports rather than hides. The pointwise tests in
+Table~\ref{tab:calibration} support the \(95\,\%\) member intervals on
+the listed scenarios. They also expose \(68\,\%\) overcoverage and poor
+coverage of the combined estimate. They do not establish temporal
 covariance calibration, convergence across independent chains, or valid
 downstream intervals.
 
@@ -1862,11 +1979,11 @@ \section{Discussion}\label{sec:discussion}
 driver regenerates every generated figure together with a numerical
 sidecar holding every plotted array and the run's provenance, and the
 package is unit-tested. The three real-data figures were produced by the
-cloud run and are archived, not regenerated
-(Section~\ref{sec:deployment}). An executable record turns an
-undocumented choice into a versioned, inspectable one, and lets a reader
-re-run a study's pipeline on the truth-known synthetic to see its bias
-before trusting it on data.
+cloud run and are committed to the repository as produced, not
+regenerated (Section~\ref{sec:deployment}). An executable record turns
+an undocumented choice into a versioned, inspectable one, and lets a
+reader re-run a study's pipeline on the truth-known synthetic to see its
+bias before trusting it on data.
 
 \textbf{Validate against something you did not generate.} Every
 synthetic test in this paper passed before the discovery below, and that
@@ -1914,27 +2031,28 @@ \section{Conclusions}\label{sec:conclusions}
 that are made ad hoc and reported incompletely. Using a truth-known
 synthetic and the full estimator suite of an open toolbox, we have shown
 that these choices change the RMS error of the recovered \dvv~by more
-than two orders of magnitude (0.02 to \(2.8\,\%\)) across 108 pipelines
-on one synthetic volcano scenario and, more consequentially, change the
-number reported as its uncertainty by a factor of \(\sim\!\sqrt{N}\)
-depending on whether a study calls \(1\sigma\) the standard error of the
-network mean or the between-pair standard deviation, all without
-touching the data. The remedy is not a single mandated pipeline but
-transparency: report every choice and name the quantity each error bar
-estimates, sample the choices the physics does not fix, carry the
-resulting measurement covariance into the inference after validating
-what it is meant to cover, and release the pipeline as executable code.
-Repeated synthetic realisations support the proposed \(95\,\%\)
-pointwise intervals for the error of a single processing configuration,
-while the nominal \(68\,\%\) intervals overcover and the credible band
-on the ensemble mean undercovers (Table~\ref{tab:calibration}). The
-temporal correlation in \(C_d\) is untested, a cross-band covariance is
-not constructed, and an error shared by every configuration is
-demonstrably invisible to the ensemble. A depth inversion also needs
-kernel uncertainty and the covariance of the actual observations it
-consumes. Converting a depth profile to stress or strain is a further
-step this paper does not attempt. We offer codameter as one such record;
-its depth stage is an interface awaiting evaluation.
+than two orders of magnitude (0.02 to \(2.8\,\%\)) across the 96
+pipelines of a 108-pipeline factorial that return a series, on one
+synthetic volcano scenario, and, more consequentially, change the number
+reported as its uncertainty by a factor of \(\sim\!\sqrt{N}\) depending
+on whether a study calls \(1\sigma\) the standard error of the network
+mean or the between-pair standard deviation, all without touching the
+data. The remedy is not a single mandated pipeline but transparency:
+report every choice and name the quantity each error bar estimates,
+sample the choices the physics does not fix, carry the resulting
+measurement covariance into the inference after validating what it is
+meant to cover, and release the pipeline as executable code. Repeated
+synthetic realisations support the proposed \(95\,\%\) pointwise
+intervals for the error of a single processing configuration, while the
+nominal \(68\,\%\) intervals overcover and the credible band on the
+ensemble mean undercovers (Table~\ref{tab:calibration}). The temporal
+correlation in \(C_d\) is untested, a cross-band covariance is not
+constructed, and an error shared by every configuration is demonstrably
+invisible to the ensemble. A depth inversion also needs kernel
+uncertainty and the covariance of the actual observations it consumes.
+Converting a depth profile to stress or strain is a further step this
+paper does not attempt. We offer codameter as one such record; its depth
+stage is an interface awaiting evaluation.
 
 \appendix
 
@@ -2139,24 +2257,21 @@ \section*{Data availability}\label{data-availability}
 All synthetics, estimators, and generated figures in this paper are
 implemented in the open-source Python package codameter (MIT license),
 openly available at \url{https://github.com/Denolle-Lab/codameter}; each
-generated figure's sidecar records its generating commit and numerical
-arrays. The figures and manuscript can originate from different
-revisions. \texttt{python -m codameter.figures} regenerates every
-generated figure with a \texttt{.npz} sidecar of its plotted arrays and
-a \texttt{.json} sidecar of its provenance;
-\texttt{python -m codameter.calibration} reproduces
-Table~\ref{tab:calibration} (\texttt{paper/data/calibration/});
-\texttt{scripts/compare\_gate1.py} reproduces Table~\ref{tab:gate1} from
-the daily products under \texttt{paper/data/gate1/} and the published
-\citet{Clements2023} series archived there. The daily products and the
-three real-data figures were produced by the noisepy-dvv-cloud Gate 1
-run from public Southern California Earthquake Data Center waveforms;
-the products are available locally during this analysis but are not
-tracked in the repository. The exact Gate 1 run commit, run
-configuration and redistribution archive remain to be supplied; their
-current provenance limits are recorded in
-\texttt{paper/data/gate1/README.md}. A versioned archive is planned but
-has not yet been deposited.
+generated figure carries a numerical sidecar with its plotted arrays and
+its generating commit, so the figures and the manuscript can originate
+from different revisions and be told apart. The repository documents how
+one command regenerates every generated figure, how the
+repeated-realisation calibration of Table~\ref{tab:calibration} is rerun
+(its settings and seeds are stored with each archived run), and how
+Table~\ref{tab:gate1} is recomputed from the daily products and the
+published \citet{Clements2023} series archived with the paper. The daily
+products and the three real-data figures were produced by the
+noisepy-dvv-cloud Gate 1 run from public Southern California Earthquake
+Data Center waveforms; the products are available locally during this
+analysis but are not tracked in the repository. The exact Gate 1 run
+commit, run configuration and redistribution archive remain to be
+supplied; their current provenance limits are recorded with the archived
+products. A versioned archive is planned but has not yet been deposited.
 
 \section*{Acknowledgements}\label{acknowledgements}
 \addcontentsline{toc}{section}{Acknowledgements}
diff --git a/review/HUMAN_AI_COLLABORATION.md b/review/HUMAN_AI_COLLABORATION.md
index 606d4ee..c15ee8f 100644
--- a/review/HUMAN_AI_COLLABORATION.md
+++ b/review/HUMAN_AI_COLLABORATION.md
@@ -19,12 +19,18 @@ Agents involved: Astra (Codex/GPT-6), which produced the iteration-1 review, the
 11. **"Sorry, I meant GitHub issues."** Fable recommended one issue per work package plus separate issues for the inputs and decisions only the author can supply, all under one milestone, so that status lives in the issues and the plan stays stable.
 12. **"Yes, go for it. We will have a CLI multi-agent system tackle them; we may need to bundle them into individual PRs and have Copilot automatically review them before approval."** The author approved. Fable opened thirteen issues (#38 to #50) under the milestone "Iteration 3 revision": eight package issues P0 to P7 with ledger identifiers, acceptance criteria, file pointers and a working agreement (one pull request per issue, Copilot review requested, no hand edits to the ledger), and five author-input issues (Gate 1 provenance and rights, the Yuan et al. 2021 Table B3 ranking, the survey rows to verify, the Fig 8 decision, the step-error metric). Automatic Copilot review needs a repository ruleset that the author must enable; the repository has none.
 
+## Session of 2026-09-13 (Fable, then Opus after a session restart)
+
+13. **"PR51 is merged. Move on to P1?"** The author merged the P0 pull request and asked for P1. The agent branched `iter3/P1`, executed the package (daily-grid multiverse, robust step metric, gate probe, three-seed sweep, hyper-priors and chain settings stated, held-out coverage and split R-hat in the calibration driver, the depth and framework wording), and opened PR #52. Two of the plan's diagnostics found errors the plan had not anticipated: the correlation-length fit of the temporal covariance was wrong (39 days from an intercept fit over 40 lags, 5.7 days from the short-lag decay), and the credible band on the ensemble mean is about 80 percent set by the smoothness prior. Both were corrected or stated, not hidden. Where an author decision was pending (#50, the step metric), the agent proceeded under a stated default and recorded it in the issue.
+14. **"Back in here, keep working; some Copilot reviews came in."** The author asked the agent to continue and to handle the automatic Copilot reviews. The agent answered every Copilot thread on PRs #52, #53 and #54 with a fix and a reply (zero-variance rows in the autocorrelation, a stale docstring, the wavefield split among measuring rows, a false "one DOI each", a markdown code-span corruption in Appendix C that predated the branch, an untracked-file leak in the dirty flag, a literal tilde, an over-claim about sidecar fields, the tolerance scale of the sidecar check). It then went on to the next agent-ready packages without being asked package by package: P4 (survey hygiene, PR #53) and P3 part 1 (provenance, sidecar check, in-repo Gate 1 figure, paper workflow, PR #54). The locked calibration reruns were lost to a machine restart and rerun.
+
 ## Decisions that were the author's
 
 - The scope of the paper: depth propagation as an interface, the advisor as infrastructure, no cloud-scalability claim.
 - The rescaling of the archived field error bars.
 - The impact framing and the extension to engineering applications.
 - Tracking the revision through GitHub issues with one pull request per issue and Copilot review before approval.
+- Merging each package; the agent opens pull requests and answers reviews but does not merge.
 - Adjudication of every reviewer finding remains the author's; no finding was closed on the agent's say-so, and the iteration-2 verdicts came from independent subagents.
 
 ## What the agents did not do
diff --git a/review/REVISION_PLAN_ITER3.md b/review/REVISION_PLAN_ITER3.md
index 6296028..509a104 100644
--- a/review/REVISION_PLAN_ITER3.md
+++ b/review/REVISION_PLAN_ITER3.md
@@ -157,3 +157,4 @@ The submission decision should rest on a defensible measurement claim, transpare
 - 2026-09-11: Rewritten for Marine Denolle's observational priorities, with explicit measurement targets, diagnostic failure responses, provenance requirements, and evidence-based completion criteria. No experiments or implementation tasks are marked complete by this rewrite.
 - 2026-09-11: GitHub issues opened under milestone "Iteration 3 revision": P0 #38, P1 #39, P2 #40, P3 #41, P4 #42, P5 #43, P6 #44, P7 #45; author inputs #46 (Gate 1 provenance and rights, blocks P3), #47 (Yuan 2021 Table B3, blocks P1 and P4), #48 (survey rows and search rules, blocks P4), #49 (Fig 8 keep, trim or drop, blocks P0), #50 (step-error metric, blocks P1). Status is tracked in the issues; this file changes only by ticking boxes and appending to this record.
 - 2026-09-13: P0 executed on branch `iter3/P0` (commits 10a9db3, c66b409) for issue #38; every P0 item addressed except the Fig 8 keep/trim/drop decision (#49), where the composite was kept and made legible pending the decision. PDF rebuilt: 83 pages, no `??`, no `,%`, no `<<`; the Acknowledgements placeholder remains for P6.
+- 2026-09-13: P1 executed on branch `iter3/P1` (commits 6613570, 7b67e53, f62e01e) for issue #39; step-error metric taken as post- minus pre-event medians pending #50, the Yuan et al. (2021) regime left for #47. Two findings beyond the plan: the correlation-length fit was wrong (39 d from an intercept fit over 40 lags; 5.7 d from the short-lag decay; whitening check added) and the credible band on mu is about 80% prior-set (duplication check added). The shared_source and clock_drift locked reruns were still running when the PR opened and follow in the same PR.
diff --git a/scripts/check_cd_whitening.py b/scripts/check_cd_whitening.py
new file mode 100644
index 0000000..0d75a29
--- /dev/null
+++ b/scripts/check_cd_whitening.py
@@ -0,0 +1,109 @@
+"""Whiten the ensemble residuals with C_d and report what is left (audit UQ-04).
+
+C_d = D R D + tau^2 11^T (manuscript eq. cd) proposes a temporal correlation
+R with one exponential length L fitted from the residual autocorrelation.
+If that model is adequate, the residuals of each member about the posterior
+mean, whitened by the Cholesky factor of C_d on the member's observed
+epochs, should be close to white with unit variance. This script runs the
+manuscript's Bayesian demo (same seed and settings as Fig. 14, via
+codameter.uq_bayes._build_bayes) and writes the raw and whitened lag
+autocorrelations and the whitened variance to paper/data/bayes/cd_whitening.json.
+
+Run:  python scripts/check_cd_whitening.py
+"""
+
+from __future__ import annotations
+
+import json
+import subprocess
+from datetime import datetime, timezone
+from pathlib import Path
+
+import numpy as np
+
+HERE = Path(__file__).resolve().parent
+OUT = HERE.parent / "paper" / "data" / "bayes" / "cd_whitening.json"
+LAGS = (1, 2, 3, 5, 10)
+
+
+def _autocorr(x: np.ndarray, lag: int) -> float:
+    x = x - x.mean()
+    if x.size <= lag + 2:
+        return float("nan")
+    return float(np.corrcoef(x[:-lag], x[lag:])[0, 1])
+
+
+def whitening_report(res, run) -> dict:
+    members = np.asarray(run.members, float)
+    resid = members - res.mu_mean[None, :] - res.beta_mean[:, None]
+    Cd = np.asarray(res.Cd, float)
+    sd = np.sqrt(np.diag(Cd))
+    raw, white, var_white, var_diag, n_epochs = [], [], [], [], []
+    for k in range(resid.shape[0]):
+        ok = np.isfinite(resid[k])
+        if ok.sum() < 20:
+            continue
+        r = resid[k][ok]
+        L = np.linalg.cholesky(Cd[np.ix_(ok, ok)])
+        w = np.linalg.solve(L, r)
+        raw.append([_autocorr(r, lag) for lag in LAGS])
+        white.append([_autocorr(w, lag) for lag in LAGS])
+        var_white.append(float(np.var(w)))
+        var_diag.append(float(np.var(r / sd[ok])))  # scale only, no R
+        n_epochs.append(int(ok.sum()))
+    raw_a, white_a = np.array(raw), np.array(white)
+    return {
+        "lags_epochs": list(LAGS),
+        "cadence_days": float(np.median(np.diff(run.times_days))),
+        "n_members": int(len(var_white)),
+        "n_epochs_per_member": n_epochs,
+        "corr_length_days": float(res.corr_length_days),
+        "s": float(res.s),
+        "tau": float(res.tau),
+        "raw_autocorr_mean": [float(v) for v in np.nanmean(raw_a, axis=0)],
+        "raw_autocorr_members": raw_a.tolist(),
+        "whitened_autocorr_mean": [float(v) for v in np.nanmean(white_a, axis=0)],
+        "whitened_autocorr_members": white_a.tolist(),
+        "whitened_variance_mean": float(np.mean(var_white)),
+        "whitened_variance_members": var_white,
+        "diag_scaled_variance_mean": float(np.mean(var_diag)),
+        "diag_scaled_variance_members": var_diag,
+    }
+
+
+def main() -> int:
+    from codameter import __version__
+    from codameter.uq_bayes import _build_bayes
+
+    res, run = _build_bayes()
+    report = whitening_report(res, run)
+    try:
+        commit = subprocess.run(
+            ["git", "rev-parse", "HEAD"],
+            capture_output=True,
+            text=True,
+            check=True,
+            cwd=Path(__file__).resolve().parent.parent,
+        ).stdout.strip()
+    except Exception:  # noqa: BLE001
+        commit = None
+    payload = {
+        "script": "scripts/check_cd_whitening.py",
+        "generator": "codameter.uq_bayes._build_bayes (seed 55, cadence 4)",
+        "codameter_version": __version__,
+        "git_commit": commit,
+        "generated_utc": datetime.now(timezone.utc).isoformat(timespec="seconds"),
+        **report,
+    }
+    OUT.parent.mkdir(parents=True, exist_ok=True)
+    OUT.write_text(json.dumps(payload, indent=1))
+    print(f"raw autocorr      {np.round(report['raw_autocorr_mean'], 3)}")
+    print(f"whitened autocorr {np.round(report['whitened_autocorr_mean'], 3)}")
+    print(f"whitened variance {report['whitened_variance_mean']:.3f}")
+    print(f"diag-scaled var   {report['diag_scaled_variance_mean']:.3f}")
+    print(f"wrote {OUT}")
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/scripts/check_ensemble_duplication.py b/scripts/check_ensemble_duplication.py
new file mode 100644
index 0000000..fb890a5
--- /dev/null
+++ b/scripts/check_ensemble_duplication.py
@@ -0,0 +1,107 @@
+"""What duplicating the ensemble does to the posterior band and to C_d (audit UQ-03).
+
+The working likelihood of the Bayesian measurement model treats member
+residuals as independent, so a duplicated member counts as new data. This
+script runs the manuscript's Bayesian demo (seed 55, cadence 4, as Fig. 14)
+on the ensemble as measured, on the ensemble with every member duplicated,
+and with every member quadrupled, and reports the median 95 percent
+half-width of the credible band on mu, the median of the C_d diagonal, the
+fitted s and tau, and the share of the precision of mu that the smoothness
+prior supplies at the posterior mean. Writes paper/data/bayes/duplication_check.json.
+
+Run:  python scripts/check_ensemble_duplication.py
+"""
+
+from __future__ import annotations
+
+import json
+import subprocess
+from datetime import datetime, timezone
+from pathlib import Path
+
+import numpy as np
+
+OUT = Path(__file__).resolve().parent.parent / "paper" / "data" / "bayes"
+
+
+def prior_share(res, run) -> float:
+    """Median over epochs of lam * diag(D^T D) / (data precision + lam * diag(D^T D))."""
+    from codameter.uq_bayes import second_difference_operator
+
+    obs = (
+        np.isfinite(run.members)
+        & np.isfinite(run.within_sigma)
+        & (run.within_sigma > 0)
+    )
+    sig = np.where(obs, run.within_sigma, 1.0)
+    w = np.where(obs, 1.0 / (res.s**2 * sig**2), 0.0)
+    prec_data = w.sum(axis=0)
+    lam = float(np.mean(res.samples_hyper["lambda"]))
+    D = second_difference_operator(run.times_days)
+    prec_prior = lam * (D.T @ D).diagonal()
+    return float(np.median(prec_prior / (prec_prior + prec_data)))
+
+
+def main() -> int:
+    from codameter import __version__
+    from codameter.uq_bayes import _build_bayes, gibbs_dvv
+
+    res0, run = _build_bayes()
+    kw = dict(n_iter=1200, burn=400, thin=2, seed=0)
+    rows = []
+    for mult in (1, 2, 4):
+        M = np.vstack([run.members] * mult)
+        S = np.vstack([run.within_sigma] * mult)
+        res = gibbs_dvv(M, S, run.times_days, **kw)
+        run_m = type(run)(list(run.labels) * mult, M, S, run.times_days, run.truth)
+        rows.append(
+            {
+                "multiplicity": mult,
+                "n_members": int(M.shape[0]),
+                "median_halfwidth95_pct": float(
+                    np.median(res.mu_hi - res.mu_lo) / 2 * 100
+                ),
+                "median_sigma_cd_pct": float(np.median(np.sqrt(np.diag(res.Cd))) * 100),
+                "s": float(res.s),
+                "tau": float(res.tau),
+                "corr_length_days": float(res.corr_length_days),
+                "n_eff": float(res.n_eff),
+                "prior_precision_share": prior_share(res, run_m),
+                "mu_mean_max_abs_change_pct": float(
+                    np.max(np.abs(res.mu_mean - res0.mu_mean)) * 100
+                ),
+            }
+        )
+    try:
+        commit = subprocess.run(
+            ["git", "rev-parse", "HEAD"],
+            capture_output=True,
+            text=True,
+            check=True,
+            cwd=Path(__file__).resolve().parent.parent,
+        ).stdout.strip()
+    except Exception:  # noqa: BLE001
+        commit = None
+    payload = {
+        "script": "scripts/check_ensemble_duplication.py",
+        "generator": "codameter.uq_bayes._build_bayes (seed 55, cadence 4); gibbs seed 0",
+        "codameter_version": __version__,
+        "git_commit": commit,
+        "generated_utc": datetime.now(timezone.utc).isoformat(timespec="seconds"),
+        "independent_data_expectation": "half-width scales as 1/sqrt(multiplicity)",
+        "rows": rows,
+    }
+    OUT.mkdir(parents=True, exist_ok=True)
+    (OUT / "duplication_check.json").write_text(json.dumps(payload, indent=1))
+    for r in rows:
+        print(
+            f"x{r['multiplicity']}: half-width {r['median_halfwidth95_pct']:.4f}% "
+            f"sigma_Cd {r['median_sigma_cd_pct']:.4f}% s {r['s']:.2f} "
+            f"prior share {r['prior_precision_share']:.2f}"
+        )
+    print(f"wrote {OUT / 'duplication_check.json'}")
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/src/codameter/calibration.py b/src/codameter/calibration.py
index ff63097..f6fe7d8 100644
--- a/src/codameter/calibration.py
+++ b/src/codameter/calibration.py
@@ -21,6 +21,16 @@
     because the manuscript used to quote it, but it mixes the ensemble mean
     with a single-measurement scale and over-covers by construction.
 
+``heldout_member_coverage68/95``
+    The same member coverage, but ``Cd`` is fitted on a random half of the
+    members (six of twelve, drawn per realisation) and scored on the other
+    half. The in-sample coverage above scores the members that ``s`` and the
+    excess spread were fitted on; this one does not.
+``rhat_tau2, rhat_s2, rhat_lambda``
+    Split R-hat (:func:`codameter.uq_bayes.split_rhat`) of the scale
+    hyper-parameters over two Gibbs chains started from different seeds on
+    the same ensemble, each split in halves.
+
 Also reported: interval width, bias, RMSE of ``mu`` and of the members, the
 shared bias ``mean(mu - truth)``, the prior shares, and failures. Aggregate
 values are means over realisations with standard errors across them
@@ -129,25 +139,74 @@ def run_realization(
     burn: int = 400,
     thin: int = 2,
 ) -> dict[str, Any]:
-    """One realisation end to end; never raises (failures are recorded)."""
-    from .uq_bayes import bayes_dvv_from_ccfs
+    """One realisation end to end; never raises (failures are recorded).
 
+    A realisation redraws the additive noise (and, for ``shared_source``, the
+    late-coda source term) on one fixed generating coda; the truth and the
+    ensemble configurations are the same in every realisation.
+    """
     out: dict[str, Any] = {"seed": int(seed), "scenario": scenario, "ok": False}
     try:
+        from .uq_bayes import (
+            default_prior,
+            gibbs_dvv,
+            run_processing_ensemble,
+            split_rhat,
+        )
+
         s, days, truth, ccfs = make_realization(seed, scenario, years=years, snr=snr)
-        res, run = bayes_dvv_from_ccfs(
-            ccfs,
-            s.t,
-            s.fs,
-            truth=truth,
-            days=days,
-            cadence=cadence,
+        run = run_processing_ensemble(
+            ccfs, s.t, s.fs, default_prior(), cadence=cadence, truth=truth, days=days
+        )
+        res = gibbs_dvv(
+            run.members,
+            run.within_sigma,
+            run.times_days,
+            seed=seed,
+            n_iter=n_iter,
+            burn=burn,
+            thin=thin,
+        )
+        # Second chain from another seed on the same ensemble: split R-hat.
+        res2 = gibbs_dvv(
+            run.members,
+            run.within_sigma,
+            run.times_days,
+            seed=int(seed) + 1_000_003,
             n_iter=n_iter,
             burn=burn,
             thin=thin,
+        )
+        rhat = {
+            key: split_rhat(
+                np.vstack([res.samples_hyper[key], res2.samples_hyper[key]])
+            )
+            for key in ("tau2", "s2", "lambda")
+        }
+        # Held-out check: fit Cd on a random half of the members, score the rest.
+        K = run.members.shape[0]
+        perm = np.random.default_rng(int(seed)).permutation(K)
+        fit_idx, score_idx = np.sort(perm[: K // 2]), np.sort(perm[K // 2 :])
+        res_half = gibbs_dvv(
+            run.members[fit_idx],
+            run.within_sigma[fit_idx],
+            run.times_days,
             seed=seed,
+            n_iter=n_iter,
+            burn=burn,
+            thin=thin,
         )
         tr = np.asarray(run.truth, float)
+        sd_half = np.sqrt(np.diag(res_half.Cd))
+        held_err = run.members[score_idx] - tr[None, :]
+        held_obs = (
+            np.isfinite(held_err)
+            & np.isfinite(run.within_sigma[score_idx])
+            & (run.within_sigma[score_idx] > 0)
+            & np.isfinite(sd_half[None, :])
+        )
+        held_abs = np.abs(held_err[held_obs])
+        held_sd = np.broadcast_to(sd_half, held_err.shape)[held_obs]
         err = res.mu_mean - tr
         sd = np.sqrt(np.diag(res.Cd))
         member_err = run.members - tr[None, :]
@@ -187,6 +246,17 @@ def run_realization(
             prior_weight_tau2=float((res.prior_weight or {}).get("tau2", np.nan)),
             prior_weight_s2=float((res.prior_weight or {}).get("s2", np.nan)),
             prior_weight_lambda=float((res.prior_weight or {}).get("lambda", np.nan)),
+            heldout_member_coverage68=(
+                float(np.mean(held_abs <= Z68 * held_sd)) if held_obs.any() else np.nan
+            ),
+            heldout_member_coverage95=(
+                float(np.mean(held_abs <= Z95 * held_sd)) if held_obs.any() else np.nan
+            ),
+            heldout_s=float(res_half.s),
+            heldout_fit_members=[int(i) for i in fit_idx],
+            rhat_tau2=float(rhat["tau2"]),
+            rhat_s2=float(rhat["s2"]),
+            rhat_lambda=float(rhat["lambda"]),
         )
     except Exception as exc:  # a failed realisation is a result, not a crash
         out.update(error=f"{type(exc).__name__}: {exc}")
@@ -244,6 +314,12 @@ def summarize(results, *, margin: float = COVERAGE_MARGIN) -> dict[str, Any]:
         "prior_weight_tau2",
         "prior_weight_s2",
         "prior_weight_lambda",
+        "heldout_member_coverage68",
+        "heldout_member_coverage95",
+        "heldout_s",
+        "rhat_tau2",
+        "rhat_s2",
+        "rhat_lambda",
     ):
         summary[key] = (
             _mean_se([r.get(key, np.nan) for r in ok]) if ok else _mean_se([])
@@ -256,6 +332,16 @@ def summarize(results, *, margin: float = COVERAGE_MARGIN) -> dict[str, Any]:
     summary["member_coverage68_within_margin"] = (
         bool(abs(c68 - 0.68) <= margin) if c68 is not None else None
     )
+    h95 = summary["heldout_member_coverage95"]["mean"]
+    summary["heldout_member_coverage95_within_margin"] = (
+        bool(abs(h95 - 0.95) <= margin) if h95 is not None else None
+    )
+    rh = [summary[f"rhat_{k}"]["mean"] for k in ("tau2", "s2", "lambda")]
+    summary["rhat_max"] = (
+        float(max(x for x in rh if x is not None))
+        if any(x is not None for x in rh)
+        else None
+    )
     return summary
 
 
@@ -350,8 +436,13 @@ def fmt(key):
         "n_eff",
         "prior_weight_tau2",
         "prior_weight_lambda",
+        "heldout_member_coverage95",
+        "heldout_s",
+        "rhat_tau2",
+        "rhat_s2",
+        "rhat_lambda",
     ):
-        print(f"  {key:<22} {fmt(key)}")
+        print(f"  {key:<26} {fmt(key)}")
     print(
         f"  member 95% within +-{summary['margin']:.0%}: "
         f"{summary['member_coverage95_within_margin']}"
diff --git a/src/codameter/deviations.py b/src/codameter/deviations.py
index b4d77aa..3a8fa12 100644
--- a/src/codameter/deviations.py
+++ b/src/codameter/deviations.py
@@ -26,6 +26,7 @@
 
 from __future__ import annotations
 
+import inspect
 from dataclasses import dataclass
 from itertools import product
 
@@ -44,6 +45,7 @@
     measure_inversion,
     measure_stretching,
     measure_stretching_trailing,
+    step_amplitude,
     volcano_truth,
 )
 
@@ -82,6 +84,9 @@
 }
 
 ERUPT_DAY = int(2.0 * YEAR_D)
+GATE_CC = (
+    0.6  # coherence gate: epochs with peak stretching CC at or below this are dropped
+)
 
 
 # ---------------------------------------------------------------------------
@@ -152,9 +157,14 @@ def run_pipeline(ccfs, t, fs, cfg, *, eps_max=0.05, return_cc=False, prefiltered
     ``cc`` is NaN wherever the configuration does not produce one (non-stretching
     estimators, the inversion reference, and warm-up epochs).
 
-    CC-gating (``cfg["gate"]``) applies to the fixed reference only, as it
-    always has; the moving-reference CC is returned for error modelling but
-    does not change ``valid``.
+    CC-gating (``cfg["gate"]``) applies to the fixed and the moving reference
+    and to every estimator: an epoch is kept only where the peak stretching
+    coherence at the same band, window, stack and reference exceeds
+    :data:`GATE_CC` (for a non-stretching estimator that coherence comes from
+    a stretching probe run on the same data). The joint-inversion reference
+    has no per-epoch coherence, so the gate leaves its ``valid`` unchanged.
+    (Before the 2026-09 revision the gate applied to the fixed reference
+    with the stretching estimator only.)
 
     With ``prefiltered=True``, ``ccfs`` is taken as already band-passed at
     ``cfg["band"]`` and the estimator skips its internal band-pass. Callers
@@ -212,17 +222,47 @@ def run_pipeline(ccfs, t, fs, cfg, *, eps_max=0.05, return_cc=False, prefiltered
                 name, stacked, t, band=band, fs=fs, window=window, **extra
             )
     elif ref == "inversion":  # Brenguier et al. (2014) joint inversion (stretching)
+        if name != "stretching (TS)":
+            raise ValueError(
+                "reference='inversion' is a stretching-based joint inversion; "
+                f"it cannot be combined with estimator={name!r}"
+            )
+        # The stack axis sets the block length, so a 10-day stack means
+        # 10-day blocks here as it means 10-day trailing stacks elsewhere.
         dvv = measure_inversion(
-            ccfs, t, band=band, fs=fs, window=window, prefiltered=prefiltered
+            ccfs,
+            t,
+            band=band,
+            fs=fs,
+            window=window,
+            block_days=int(k),
+            prefiltered=prefiltered,
         )
     else:
         raise ValueError(ref)
 
     dvv = np.asarray(dvv, float)
     valid = np.isfinite(dvv)
-    if cfg.get("gate") and ref == "fixed" and cc is not None:
-        keep = cc > 0.6
-        valid &= keep
+    if cfg.get("gate") and ref in ("fixed", "moving"):
+        # The gate is a property of the data at this band, window, stack and
+        # reference, read from the stretching coherence; estimators without a
+        # coherence of their own are gated by the same probe (as in
+        # uq_bayes.run_processing_ensemble). The joint inversion has no
+        # per-epoch coherence, so ``gate`` has no effect on it.
+        if cc is None:
+            probe = dict(cfg, estimator="stretching (TS)")
+            _, _, cc_probe = run_pipeline(
+                ccfs,
+                t,
+                fs,
+                probe,
+                eps_max=eps_max,
+                return_cc=True,
+                prefiltered=prefiltered,
+            )
+        else:
+            cc_probe = np.asarray(cc, float)
+        valid &= np.isfinite(cc_probe) & (cc_probe > GATE_CC)
     if return_cc:
         cc_arr = np.full(dvv.shape, np.nan) if cc is None else np.asarray(cc, float)
         return dvv, valid, cc_arr
@@ -233,12 +273,13 @@ def run_pipeline(ccfs, t, fs, cfg, *, eps_max=0.05, return_cc=False, prefiltered
 # Metrics against the known truth.
 # ---------------------------------------------------------------------------
 def _drop_amplitude(dvv, days, valid, eq_day=ERUPT_DAY, span=120):
-    """Recovered co-eruptive drop: min dv/v in [eq, eq+span] minus pre-eq level."""
-    pre = (days < eq_day) & (days > eq_day - 120) & valid
-    post = (days >= eq_day) & (days < eq_day + span) & valid
-    if pre.sum() < 3 or post.sum() < 3:
-        return np.nan
-    return np.nanmin(dvv[post]) - np.nanmedian(dvv[pre])
+    """Recovered co-eruptive drop: post-window median minus pre-window median.
+
+    Delegates to :func:`codameter.synthetic_demo.step_amplitude`; before the
+    2026-09 revision this took the minimum over the post-event window, whose
+    extreme-value bias grows with the noise (review finding S-RE.3).
+    """
+    return step_amplitude(dvv, days, valid, eq_day, span=span)
 
 
 def metrics(dvv, truth, days, valid):
@@ -261,11 +302,29 @@ def metrics(dvv, truth, days, valid):
 # ---------------------------------------------------------------------------
 @dataclass
 class OATRow:
+    """One row of the one-at-a-time sweep.
+
+    ``rms`` and ``drop_err`` are means over the paired seeds; ``rms_lo`` /
+    ``rms_hi`` and ``drop_lo`` / ``drop_hi`` are the min and max over seeds.
+    ``rms_common`` is the RMS on the epochs every row of the sweep produced
+    (the common support), ``availability`` the fraction of epochs this row
+    produced on its own support, both averaged over seeds.
+    """
+
     axis: str
     option: str
     is_best: bool
     rms: float
     drop_err: float
+    rms_lo: float = np.nan
+    rms_hi: float = np.nan
+    drop_lo: float = np.nan
+    drop_hi: float = np.nan
+    rms_common: float = np.nan
+    rms_common_lo: float = np.nan
+    rms_common_hi: float = np.nan
+    availability: float = np.nan
+    n_seeds: int = 1
 
 
 def _label(axis, opt):
@@ -274,29 +333,94 @@ def _label(axis, opt):
     return str(opt)
 
 
-def oat_effects(*, years=3.0, snr=7.0, seed=55):
-    """One-at-a-time: flip each axis off best practice, measure the damage."""
+OAT_SEEDS = (55, 56, 57)
+
+
+def _nanstat(values, fn) -> float:
+    """``fn`` over the finite entries of ``values``; NaN when there are none."""
+    v = np.asarray(values, float)
+    v = v[np.isfinite(v)]
+    return float(fn(v)) if v.size else float("nan")
+
+
+def _oat_configs():
+    """(axis label, option label, is_best, cfg) for the baseline and every deviation."""
+    out = [("baseline", "best practice", True, dict(BASELINE))]
+    for axis, (lbl, opts, best) in DEVIATIONS.items():
+        for opt in opts:
+            out.append(
+                (lbl, _label(axis, opt), opt in best, dict(BASELINE, **{axis: opt}))
+            )
+    return out
+
+
+def _oat_one_seed(*, years, snr, seed):
+    """Run every OAT configuration on one noise realisation; return per-row metrics."""
     s = Synth()
     days = _days(years)
     truth = volcano_truth(days)
     ccfs = daily_ccfs(s.t, [s.ref], [truth], fs=s.fs, snr=snr, seed=seed)
+    series, valids = [], []
+    for _, _, _, cfg in _oat_configs():
+        dvv, valid = run_pipeline(ccfs, s.t, s.fs, cfg)
+        series.append(np.asarray(dvv, float))
+        valids.append(valid & np.isfinite(dvv))
+    common = np.logical_and.reduce(valids)
+    rows = []
+    for dvv, valid in zip(series, valids, strict=True):
+        m = metrics(dvv, truth, days, valid)
+        m["rms_common"] = (
+            float(np.sqrt(np.mean((dvv[common] - truth[common]) ** 2)))
+            if common.sum() > 10
+            else np.nan
+        )
+        m["availability"] = float(valid.mean())
+        rows.append(m)
+    return rows, dict(days=days, truth=truth, ccfs=ccfs, s=s, common=common)
+
 
+def oat_effects(*, years=3.0, snr=7.0, seed=55, seeds=None):
+    """One-at-a-time: flip each axis off best practice, measure the damage.
+
+    ``seeds`` (default :data:`OAT_SEEDS`) are paired noise realisations: every
+    configuration runs on the same realisation, and the row statistics are the
+    mean, min and max over seeds. Pass ``seeds=(seed,)`` for a single
+    realisation. The returned context is that of the first seed.
+    """
+    seeds = tuple(seeds) if seeds is not None else OAT_SEEDS
+    if not seeds:
+        seeds = (seed,)
+    per_seed, ctx = [], None
+    for sd in seeds:
+        rows_sd, ctx_sd = _oat_one_seed(years=years, snr=snr, seed=sd)
+        per_seed.append(rows_sd)
+        ctx = ctx if ctx is not None else ctx_sd
     rows: list[OATRow] = []
-    # Baseline first.
-    dvv, valid = run_pipeline(ccfs, s.t, s.fs, BASELINE)
-    base = metrics(dvv, truth, days, valid)
-    rows.append(
-        OATRow("baseline", "best practice", True, base["rms"], base["drop_err"])
-    )
-    for axis, (lbl, opts, best) in DEVIATIONS.items():
-        for opt in opts:
-            cfg = dict(BASELINE, **{axis: opt})
-            dvv, valid = run_pipeline(ccfs, s.t, s.fs, cfg)
-            m = metrics(dvv, truth, days, valid)
-            rows.append(
-                OATRow(lbl, _label(axis, opt), opt in best, m["rms"], m["drop_err"])
+    for i, (lbl, opt, is_best, _) in enumerate(_oat_configs()):
+        rms = np.array([r[i]["rms"] for r in per_seed], float)
+        rmsc = np.array([r[i]["rms_common"] for r in per_seed], float)
+        drop = np.array([r[i]["drop_err"] for r in per_seed], float)
+        avail = np.array([r[i]["availability"] for r in per_seed], float)
+        rows.append(
+            OATRow(
+                lbl,
+                opt,
+                is_best,
+                _nanstat(rms, np.mean),
+                _nanstat(drop, np.mean),
+                rms_lo=_nanstat(rms, np.min),
+                rms_hi=_nanstat(rms, np.max),
+                drop_lo=_nanstat(drop, np.min),
+                drop_hi=_nanstat(drop, np.max),
+                rms_common=_nanstat(rmsc, np.mean),
+                rms_common_lo=_nanstat(rmsc, np.min),
+                rms_common_hi=_nanstat(rmsc, np.max),
+                availability=_nanstat(avail, np.mean),
+                n_seeds=len(seeds),
             )
-    return rows, dict(days=days, truth=truth, ccfs=ccfs, s=s)
+        )
+    assert ctx is not None
+    return rows, ctx
 
 
 # ---------------------------------------------------------------------------
@@ -332,10 +456,18 @@ def _sobol_first_order(labels_per_axis, values):
 def multiverse(*, years=2.5, cadence=3, snr=7.0, seed=55, axes=None):
     """Run the full factorial of choices on one dataset; attribute the variance.
 
-    ``cadence`` sub-samples the daily CCFs (a moving reference reruns the
-    estimator per epoch, so the cadence keeps the factorial tractable). Returns
-    the per-pipeline recovered curves, their RMS-vs-truth, the recovered drop,
-    and the first-order variance attribution over the axes.
+    Every pipeline stacks and references on the daily CCF grid; only the
+    *output* is decimated by ``cadence``, so a 10-day stack is ten days and a
+    45-day moving reference is 45 days at any cadence. (Before the 2026-09
+    revision the CCFs were decimated first, which stretched every stack and
+    reference by the cadence; audit UQ-05.) The RMS against the truth and the
+    recovered drop are computed on the decimated epochs the pipeline produced.
+    Pipelines that return no epoch at all are listed in ``empty`` with the
+    reason and counted in ``n_empty``; the variance attribution uses the
+    ``n_valid`` pipelines with a finite RMS (more than ten produced epochs).
+    A pipeline that produces between one and ten epochs is in neither group
+    and is counted in ``n_sparse``, so ``n_valid + n_sparse + n_empty`` is
+    ``n_pipelines``.
     """
     axes = axes or MULTIVERSE_AXES
     s = Synth()
@@ -343,46 +475,94 @@ def multiverse(*, years=2.5, cadence=3, snr=7.0, seed=55, axes=None):
     truth_full = volcano_truth(days_full)
     ccfs_full = daily_ccfs(s.t, [s.ref], [truth_full], fs=s.fs, snr=snr, seed=seed)
     idx = np.arange(0, len(days_full), cadence)
-    days, truth, ccfs = days_full[idx], truth_full[idx], ccfs_full[idx]
-    eq = np.argmin(np.abs(days - ERUPT_DAY))
+    days, truth = days_full[idx], truth_full[idx]
 
     keys = list(axes)
     combos = list(product(*(axes[k] for k in keys)))
-    curves, rms, drop = [], [], []
+    curves, rms, drop, empty = [], [], [], []
     per_axis_labels = {k: [] for k in keys}
     for combo in combos:
         cfg = dict(BASELINE, gate=False, **dict(zip(keys, combo, strict=True)))
-        dvv, valid = run_pipeline(ccfs, s.t, s.fs, cfg, eps_max=0.06)
+        dvv_full, valid_full = run_pipeline(ccfs_full, s.t, s.fs, cfg, eps_max=0.06)
+        dvv, valid = np.asarray(dvv_full, float)[idx], np.asarray(valid_full)[idx]
         curve = np.where(valid, dvv, np.nan)
         curves.append(curve)
         v = valid & np.isfinite(dvv)
+        if not np.any(valid_full & np.isfinite(dvv_full)):
+            empty.append(
+                {
+                    "config": {
+                        k: _label(k, lvl) for k, lvl in zip(keys, combo, strict=True)
+                    },
+                    "reason": _empty_reason(cfg),
+                }
+            )
         rms.append(
             float(np.sqrt(np.mean((dvv[v] - truth[v]) ** 2)))
             if v.sum() > 10
             else np.nan
         )
-        drop.append(_drop_amplitude(dvv, days, valid, eq_day=days[eq]))
+        # The event day itself, not the nearest decimated epoch: with an
+        # output cadence that skips the event day the nearest epoch can fall
+        # before it and would count a pre-event epoch as post-event.
+        drop.append(_drop_amplitude(dvv, days, valid, eq_day=ERUPT_DAY))
         for k, lvl in zip(keys, combo, strict=True):
             per_axis_labels[k].append(_label(k, lvl))
 
+    rms_arr = np.array(rms)
     return {
         "days": days,
         "truth": truth,
         "curves": np.array(curves),
-        "rms": np.array(rms),
+        "rms": rms_arr,
         "drop": np.array(drop),
         "sobol_rms": _sobol_first_order(per_axis_labels, rms),
         "sobol_drop": _sobol_first_order(per_axis_labels, drop),
         "n_pipelines": len(combos),
+        "n_valid": int(np.isfinite(rms_arr).sum()),
+        "n_empty": len(empty),
+        "n_sparse": int(len(combos) - np.isfinite(rms_arr).sum() - len(empty)),
+        "empty": empty,
+        "cadence": int(cadence),
         "axes": keys,
     }
 
 
+def _empty_reason(cfg) -> str:
+    """Why a pipeline configuration can return no epoch (the known cases)."""
+    if cfg["estimator"] == "MWCS":
+        from .synthetic_demo import measure_mwcs
+
+        sig = inspect.signature(measure_mwcs)
+        sub = sig.parameters["subwin_s"].default
+        step = sig.parameters["step_s"].default
+        w0, w1 = cfg["window"]
+        n_sub = len(np.arange(w0 + sub / 2, w1 - sub / 2, step))
+        if n_sub < 3:
+            return (
+                f"MWCS needs at least three sub-windows for the delay-versus-lapse "
+                f"fit; the {w0:g}-{w1:g} s window holds {n_sub} at {sub:g} s length "
+                f"and {step:g} s step"
+            )
+    return "no valid epoch"
+
+
 # ---------------------------------------------------------------------------
 # Figures.
 # ---------------------------------------------------------------------------
+def _rms_field(r):
+    """Common-support RMS when the sweep computed it, else the own-support RMS."""
+    return r.rms_common if np.isfinite(r.rms_common) else r.rms
+
+
 def fig_deviation_ranking(rows=None):
-    """Bar chart: RMS error and recovered-drop error of each deviation vs best."""
+    """Bar chart: RMS error and recovered-drop error of each deviation vs best.
+
+    Bars are the common-support RMS (epochs every configuration produced),
+    averaged over the paired seeds; the whiskers span the min and max over
+    seeds. Rows that produced fewer epochs than the others carry their
+    availability in the label.
+    """
     import matplotlib.pyplot as plt
 
     if rows is None:
@@ -392,41 +572,82 @@ def fig_deviation_ranking(rows=None):
     items += [
         r for r in rows if r.axis == "Reference scheme" and r.option == "inversion"
     ]
-    items.sort(key=lambda r: -(r.rms if np.isfinite(r.rms) else 0))
+    items.sort(key=lambda r: -(_rms_field(r) if np.isfinite(_rms_field(r)) else 0))
     # display names: "moving" is the uncumulated trailing reference of the text
     shown = {"moving": "uncumulated trailing", "False": "off"}
-    labels = [f"{r.axis}: {shown.get(r.option, r.option)}" for r in items]
-    rms = [r.rms * PCT for r in items]
+    labels = []
+    for r in items:
+        axis = "Reference" if r.axis == "Reference scheme" else r.axis
+        lab = f"{axis}: {shown.get(r.option, r.option)}"
+        if np.isfinite(r.availability) and r.availability < 0.99:
+            lab += f" ({r.availability:.0%})"
+        labels.append(lab)
+    rms = np.array([_rms_field(r) * PCT for r in items])
+    base_rms = _rms_field(base)
+    lo = np.array(
+        [
+            (r.rms_common_lo if np.isfinite(r.rms_common) else r.rms_lo) * PCT
+            for r in items
+        ]
+    )
+    hi = np.array(
+        [
+            (r.rms_common_hi if np.isfinite(r.rms_common) else r.rms_hi) * PCT
+            for r in items
+        ]
+    )
     fig, ax = plt.subplots(
         1, 2, figsize=(7.9, 4.6), gridspec_kw={"width_ratios": [1.35, 1]}
     )
     y = np.arange(len(items))
-    cols = [C["volcano"] if r.rms > 3 * base.rms else C["bad"] for r in items]
+    cols = [C["volcano"] if _rms_field(r) > 3 * base_rms else C["bad"] for r in items]
     ax[0].barh(y, rms, color=cols, log=True)
+    if np.isfinite(lo).all() and np.isfinite(hi).all():
+        ax[0].errorbar(
+            rms,
+            y,
+            xerr=[np.maximum(rms - lo, 0), np.maximum(hi - rms, 0)],
+            fmt="none",
+            ecolor="0.2",
+            elinewidth=0.9,
+            capsize=2,
+        )
     ax[0].axvline(
-        base.rms * PCT,
+        base_rms * PCT,
         color=C["truth"],
         ls="--",
         lw=1.2,
-        label=f"best practice ({base.rms * PCT:.3f}%)",
+        label=f"best practice ({base_rms * PCT:.3f}%)",
     )
     ax[0].set(
         yticks=y,
         xlabel="RMS error vs truth (dv/v, %, log)",
-        title="(a) RMS error of each deviation",
+        title="(a) RMS error, common support",
     )
     ax[0].set_yticklabels(labels, fontsize=10.5)
     ax[0].invert_yaxis()
     ax[0].legend(fontsize=10.5, frameon=False, loc="lower right")
-    drop = [r.drop_err * PCT for r in items]
+    drop = np.array([r.drop_err * PCT for r in items])
     ax[1].barh(y, drop, color=cols)
+    dlo = np.array([r.drop_lo * PCT for r in items])
+    dhi = np.array([r.drop_hi * PCT for r in items])
+    if np.isfinite(dlo).all() and np.isfinite(dhi).all():
+        ax[1].errorbar(
+            drop,
+            y,
+            xerr=[np.maximum(drop - dlo, 0), np.maximum(dhi - drop, 0)],
+            fmt="none",
+            ecolor="0.2",
+            elinewidth=0.9,
+            capsize=2,
+        )
     ax[1].axvline(0, color=C["truth"], lw=1)
     ax[1].set_xscale("symlog", linthresh=0.01)
     ax[1].set(
         yticks=y,
         yticklabels=[],
-        xlabel="drop error (%, symlog)",
-        title="(b) Distortion of the drop",
+        xlabel="step error (%, symlog)",
+        title="(b) Error of the drop",
     )
     ax[1].invert_yaxis()
     _boost_fonts(ax[0], ax[1], tick=10.5, label=12, title=13)
@@ -469,7 +690,10 @@ def fig_multiverse_full(mv=None):
     # the point -- the colourbar flags them) but would otherwise swamp the
     # signal and make the panel unreadable.
     ax[0].set_ylim((-0.8, 0.8))
-    n_off = int(np.sum(np.nanmax(np.abs(curves * PCT), axis=1) > 0.8))
+    has_output = np.any(np.isfinite(curves), axis=1)
+    n_off = int(np.sum(np.nanmax(np.abs(curves[has_output] * PCT), axis=1) > 0.8))
+    n_with_output = int(has_output.sum())  # finite RMS or too few epochs for one
+    n_empty = mv.get("n_empty", int((~has_output).sum()))
     ax[0].set(
         xlabel="time (years)",
         ylabel="dv/v (%)",
@@ -478,12 +702,14 @@ def fig_multiverse_full(mv=None):
     ax[0].text(
         0.02,
         0.97,
-        f"{n_off} of {mv['n_pipelines']} pipelines leave the axis range;\n"
+        f"{n_empty} of {mv['n_pipelines']} pipelines return no epoch\n"
+        f"{n_off} of the {n_with_output} others leave the axis range\n"
         f"10–90% band across pipelines: {band_lo:+.1f} to {band_hi:+.1f}%",
         transform=ax[0].transAxes,
-        fontsize=9,
+        fontsize=8.5,
         va="top",
-        color="0.25",
+        color="0.2",
+        bbox=dict(boxstyle="round,pad=0.25", fc="white", ec="0.7", alpha=0.9),
     )
     ax[0].legend(
         fontsize=10,
diff --git a/src/codameter/figures.py b/src/codameter/figures.py
index 3ef3b09..c794dbd 100644
--- a/src/codameter/figures.py
+++ b/src/codameter/figures.py
@@ -256,7 +256,12 @@ def generators() -> dict[str, tuple[str, Generator]]:
     for name, builder in sd.FIGURES.items():
 
         def _gen(b=builder):
-            return b(), {}, {}
+            # A builder may attach extra sidecar content to the figure object:
+            # ``fig.codameter_arrays`` (name -> array) and ``fig.codameter_meta``.
+            fig = b()
+            arrays = dict(getattr(fig, "codameter_arrays", {}) or {})
+            meta = dict(getattr(fig, "codameter_meta", {}) or {})
+            return fig, arrays, meta
 
         gens[name] = (f"codameter.synthetic_demo.{builder.__name__}", _gen)
     gens["demo_10_deviations"] = (
diff --git a/src/codameter/synthetic_demo.py b/src/codameter/synthetic_demo.py
index 224a990..7aa088d 100644
--- a/src/codameter/synthetic_demo.py
+++ b/src/codameter/synthetic_demo.py
@@ -1170,6 +1170,30 @@ def _days(years: float = 3.0) -> np.ndarray:
     return np.arange(0, int(years * YEAR_D))
 
 
+def step_amplitude(x, days, valid, eq_day, span: int = 120) -> float:
+    """Amplitude of a step at ``eq_day``: post-window median minus pre-window median.
+
+    Both windows are ``span`` days long and use only ``valid`` epochs. The
+    median is robust to the noise-driven extremes that a minimum over the
+    post-event window would pick (an extreme-value bias that grows as the
+    series gets noisier); applied identically to a recovered series and to
+    the truth, it gives a signed step error that is unbiased for noise alone.
+    A step followed by an exponential recovery, as in
+    :func:`earthquake_truth` and :func:`volcano_truth`, has a post-window
+    median above its minimum, so the amplitude is that of the smoothed step,
+    not of the instantaneous drop. NaN when either window has fewer than
+    three valid epochs.
+    """
+    days = np.asarray(days)
+    x = np.asarray(x, float)
+    valid = np.asarray(valid, bool) & np.isfinite(x)
+    pre = (days < eq_day) & (days >= eq_day - span) & valid
+    post = (days >= eq_day) & (days < eq_day + span) & valid
+    if pre.sum() < 3 or post.sum() < 3:
+        return float("nan")
+    return float(np.median(x[post]) - np.median(x[pre]))
+
+
 def _seasonal(days: np.ndarray, amp: float, phase_d: float = 0.0) -> np.ndarray:
     return amp * np.sin(2 * np.pi * (days - phase_d) / YEAR_D)
 
@@ -2341,17 +2365,19 @@ def fig_stack_coherence(seed: int = 143):
     cc_threshold = 0.6
 
     def _step_bias(dvv, valid):
-        pre = (days < eq) & (days > eq - 120) & valid
-        post = (days >= eq) & (days < eq + 120) & valid
-        if pre.sum() < 3 or post.sum() < 3:
-            return np.nan
-        rec_drop = np.nanmin(dvv[post]) - np.nanmedian(dvv[pre])
-        true_drop = np.nanmin(truth[post]) - np.nanmedian(truth[pre])
+        # Signed error of the recovered step: negative means the recovered
+        # drop is deeper than the true drop (over-estimated), positive means
+        # shallower (under-estimated). Both amplitudes use the same robust
+        # definition (:func:`step_amplitude`), so the comparison is unbiased
+        # by the noise-driven extreme values a minimum would pick.
+        rec_drop = step_amplitude(dvv, days, valid, eq)
+        true_drop = step_amplitude(truth, days, np.ones_like(days, bool), eq)
         return float(rec_drop - true_drop)
 
     import matplotlib.pyplot as plt
 
     fig, (axA, axB) = plt.subplots(1, 2, figsize=(11.0, 5.0))
+    extra: dict[str, np.ndarray] = {"stack_days": stack_days.astype(float)}
     for snr, col, lab in [
         (0.5, C["bad"], "SNR 0.5 (poor)"),
         (4.0, C["earthquake"], "SNR 4 (workable)"),
@@ -2371,6 +2397,10 @@ def _step_bias(dvv, valid):
             med_cc.append(float(np.nanmedian(cc[v])))
             rms.append(float(np.sqrt(np.mean((rec[v] - truth[v]) ** 2))) * PCT)
             bias.append(_step_bias(rec, v) * PCT)
+        key = f"snr{snr:g}"
+        extra[f"{key}/median_cc"] = np.asarray(med_cc, float)
+        extra[f"{key}/rms_pct"] = np.asarray(rms, float)
+        extra[f"{key}/signed_step_error_pct"] = np.asarray(bias, float)
         axA.plot(stack_days, med_cc, "o-", color=col, lw=2.2, ms=6, label=lab)
         axB.plot(stack_days, rms, "o-", color=col, lw=2.2, ms=6, label=f"{lab}: RMS")
         axB.plot(
@@ -2401,6 +2431,13 @@ def _step_bias(dvv, valid):
     leg.get_frame().set(facecolor="white", alpha=0.9, edgecolor="0.7")
     _boost_fonts(axA, axB, tick=16, label=18, title=20)
     fig.tight_layout()
+    fig.codameter_arrays = extra  # type: ignore[attr-defined]
+    fig.codameter_meta = {  # type: ignore[attr-defined]
+        "step_error": "recovered minus true step amplitude, each the median of "
+        "the 120 days after the event minus the median of the 120 days before "
+        "(synthetic_demo.step_amplitude); negative = recovered drop deeper "
+        "than the truth"
+    }
     return fig
 
 
diff --git a/src/codameter/uq_bayes.py b/src/codameter/uq_bayes.py
index 84438b4..1296932 100644
--- a/src/codameter/uq_bayes.py
+++ b/src/codameter/uq_bayes.py
@@ -44,6 +44,8 @@
     "run_processing_ensemble",
     "BayesResult",
     "gibbs_dvv",
+    "split_rhat",
+    "residual_autocorrelation",
     "bayes_dvv_from_ccfs",
 ]
 
@@ -260,36 +262,105 @@ class BayesResult:
     beta_mean: np.ndarray | None = None
     n_obs: np.ndarray | None = None
     prior_weight: dict[str, float] | None = None
+    #: Retained post-burn-in draws of the scale hyper-parameters, in sweep
+    #: order (``tau2``, ``s2``, ``lambda``), for convergence diagnostics.
+    samples_hyper: dict[str, np.ndarray] | None = None
 
 
-def _estimate_corr_length(residuals: np.ndarray, times_days: np.ndarray) -> float:
-    r"""Temporal correlation length from the mean residual autocorrelation.
+def split_rhat(chains) -> float:
+    r"""Split :math:`\hat R` of Gelman et al. (2013, Sec. 11.4) for one scalar.
 
-    Fit :math:`\rho(\Delta) \approx e^{-\Delta/L}` to the lag-autocorrelation of
-    the ensemble residuals (members minus the posterior mean), averaged over
-    configurations. Returns ``L`` in days.
+    ``chains`` is ``(n_chains, n_draws)``; every chain is split into halves
+    and the potential scale reduction is computed over the ``2 n_chains``
+    half-chains: :math:`\hat R = \sqrt{(W (n-1)/n + B/n) / W}` with ``W`` the
+    mean within-half variance and ``B/n`` the variance of the half means. Values
+    near 1 mean the halves agree; the usual acceptance is below 1.01 to 1.05.
+    Returns NaN when fewer than four draws per half are available or the
+    within variance is zero.
+    """
+    X = np.atleast_2d(np.asarray(chains, float))
+    n = X.shape[1] // 2
+    if n < 4:
+        return float("nan")
+    halves = np.concatenate([X[:, :n], X[:, n : 2 * n]], axis=0)
+    W = float(np.mean(np.var(halves, axis=1, ddof=1)))
+    B_over_n = float(np.var(np.mean(halves, axis=1), ddof=1))
+    if not np.isfinite(W) or W <= 0:
+        return float("nan")
+    return float(np.sqrt((W * (n - 1) / n + B_over_n) / W))
+
+
+#: Autocorrelation below this is treated as the noise floor of the estimate
+#: and excluded from the correlation-length fit.
+CORR_FIT_FLOOR = 0.1
+
+
+def residual_autocorrelation(residuals: np.ndarray, maxlag: int = 40) -> np.ndarray:
+    """Mean lag-autocorrelation of the rows of ``residuals`` (NaN-aware).
+
+    Each row is demeaned and normalised by its own variance; the lag products
+    are averaged over the observed pairs of each row, then over rows. Entry
+    ``k`` is the autocorrelation at ``k`` epochs; entry 0 is 1 when the
+    estimate is defined, and every entry is NaN when no row has a finite,
+    non-zero variance.
     """
     R = np.asarray(residuals, float)
     with warnings.catch_warnings():
         warnings.simplefilter("ignore", RuntimeWarning)  # all-NaN rows/lags
+        scale = np.nanmean(R**2, axis=1, keepdims=True)  # before demeaning
         R = R - np.nanmean(R, axis=1, keepdims=True)
-        K, T = R.shape
+        T = R.shape[1]
         var = np.nanmean(R**2, axis=1, keepdims=True)
-        maxlag = min(T - 1, 40)
-        rho = np.zeros(maxlag + 1)
+        # A row with zero or undefined variance (constant up to rounding, or
+        # too few valid epochs) has no autocorrelation: exclude it rather
+        # than count it as 0.
+        ok = np.isfinite(var) & (var > 0) & (var > 1e-12 * scale)
+        var = np.where(ok, var, np.nan)
+        maxlag = min(T - 1, maxlag)
+        rho = np.full(maxlag + 1, np.nan)
         for lag in range(maxlag + 1):
             prod = R[:, : T - lag] * R[:, lag:]
-            c = np.nanmean(prod, axis=1, keepdims=True) / (var + 1e-30)
+            c = np.nanmean(prod, axis=1, keepdims=True) / var
             rho[lag] = np.nanmean(c)
-    rho = np.clip(np.nan_to_num(rho, nan=1e-3), 1e-3, 1.0)
+    if np.isfinite(rho[0]):
+        rho[0] = 1.0
+    return rho
+
+
+def _estimate_corr_length(residuals: np.ndarray, times_days: np.ndarray) -> float:
+    r"""Temporal correlation length from the mean residual autocorrelation.
+
+    Fit :math:`\rho(\Delta) = e^{-\Delta/L}` through the origin to the
+    lag-autocorrelation of the ensemble residuals (members minus offset and
+    posterior mean), averaged over configurations, using only the leading
+    lags whose autocorrelation exceeds :data:`CORR_FIT_FLOOR`, each weighted
+    by its autocorrelation. Returns ``L`` in days, at least the cadence.
+
+    Before the 2026-09 revision the fit included an intercept and every lag
+    up to 40, so the noise floor of the long-lag autocorrelation (of order
+    0.05 to 0.1 for a dozen members over a few hundred epochs) flattened the
+    slope and returned correlation lengths several times longer than the
+    short-lag decay supports; whitening the residuals with the resulting
+    covariance left a variance of 3 and negative autocorrelation at two and
+    three epochs (audit UQ-04, ``scripts/check_cd_whitening.py``).
+    """
+    R = np.asarray(residuals, float)
+    T = R.shape[1]
+    rho = residual_autocorrelation(R)
     dt = float(np.median(np.diff(times_days))) if T > 1 else 1.0
-    lags_days = np.arange(maxlag + 1) * dt
-    # Linear fit of log(rho) vs lag (weight early, well-determined lags).
-    w = rho.copy()
-    A = np.vstack([lags_days, np.ones_like(lags_days)]).T
-    slope = np.linalg.lstsq(A * w[:, None], np.log(rho) * w, rcond=None)[0][0]
-    L = -1.0 / slope if slope < 0 else dt * maxlag
-    return float(np.clip(L, dt, dt * maxlag))
+    lead = []
+    for lag in range(1, rho.size):
+        if not np.isfinite(rho[lag]) or rho[lag] <= CORR_FIT_FLOOR:
+            break
+        lead.append(lag)
+    if not lead:
+        return float(dt)
+    lags_days = np.array(lead, float) * dt
+    r = np.clip(rho[lead], 1e-6, 1.0)
+    w = r  # weight the well-determined, large autocorrelations
+    slope = float(np.sum(w * lags_days * np.log(r)) / np.sum(w * lags_days**2))
+    L = -1.0 / slope if slope < 0 else dt * (rho.size - 1)
+    return float(np.clip(L, dt, dt * (rho.size - 1)))
 
 
 def _second_difference(T: int) -> np.ndarray:
@@ -419,7 +490,7 @@ def gibbs_dvv(
     s2 = 1.0
     lam = 1.0 / (np.var(Dsp @ mu) + 1e-12)
 
-    keep_mu, keep_tau, keep_s, keep_beta = [], [], [], []
+    keep_mu, keep_tau, keep_s, keep_beta, keep_lam = [], [], [], [], []
     for it in range(n_iter):
         # 1. mu | rest : Gaussian with precision Q = diag(prec_t) + lam*DtD.
         w = 1.0 / (s2 * S2)  # zero where unobserved
@@ -463,6 +534,7 @@ def gibbs_dvv(
             keep_tau.append(tau2)
             keep_s.append(s2)
             keep_beta.append(beta.copy())
+            keep_lam.append(lam)
 
     samples = np.array(keep_mu)
     mu_mean = samples.mean(axis=0)
@@ -521,6 +593,11 @@ def gibbs_dvv(
         beta_mean=beta_mean,
         n_obs=n_obs_t,
         prior_weight=prior_weight,
+        samples_hyper={
+            "tau2": np.asarray(keep_tau, float),
+            "s2": np.asarray(keep_s, float),
+            "lambda": np.asarray(keep_lam, float),
+        },
     )
 
 
diff --git a/src/codameter/uq_depth.py b/src/codameter/uq_depth.py
index 4fd24f8..d887329 100644
--- a/src/codameter/uq_depth.py
+++ b/src/codameter/uq_depth.py
@@ -179,10 +179,14 @@ def invert_depth_profile(
         \hat C_m = (G^\top C_d^{-1} G + C_{m0}^{-1})^{-1},\quad
         \hat m = \hat C_m G^\top C_d^{-1} d .
 
-    The **measurement** covariance ``cov_bands`` (:math:`C_d`) is exactly the
-    object produced by the measurement- and processing-uncertainty modules — so
-    band errors, their cross-band correlation, and the processing-choice spread
-    all flow into the depth uncertainty ``DepthProfilePosterior.std``.
+    The **measurement** covariance ``cov_bands`` (:math:`C_d`) is whatever the
+    caller supplies: a diagonal of per-band variances, or a full matrix with
+    cross-band correlation. The depth uncertainty ``DepthProfilePosterior.std``
+    inherits exactly the correlation that matrix carries and no more. No
+    routine in this package builds the cross-band covariance from the temporal
+    single-member covariance of :mod:`codameter.uq_bayes`; that construction,
+    and the evaluation of this stage on truth-known synthetics, are open
+    (manuscript Section 6; audit INV-01).
 
     Parameters
     ----------
diff --git a/src/codameter/uq_measurement.py b/src/codameter/uq_measurement.py
index 95562b0..6e952df 100644
--- a/src/codameter/uq_measurement.py
+++ b/src/codameter/uq_measurement.py
@@ -28,11 +28,14 @@
    a common reference injects a fully correlated *common-mode* term.
 
 The deliverable of this module is therefore not a scalar per epoch but a
-**measurement covariance** :math:`C_d`. That matrix is exactly the object the
-weighted-least-squares likelihood in :mod:`codameter.inverse.linear_fit`
-assumes (it currently uses ``W = diag(1/sigma^2)``, i.e. a *diagonal*
-:math:`C_d`). Feeding the full :math:`C_d` from here into that inversion closes
-the loop between the measurement and inference uncertainty budgets.
+**measurement covariance** :math:`C_d`. The weighted-least-squares
+likelihood in :mod:`codameter.inverse.linear_fit` uses a *diagonal* weight
+``W = diag(1/sigma^2)`` and does not consume the full matrix; the depth
+inversion in :mod:`codameter.uq_depth` accepts a per-band covariance but no
+routine in this package builds that cross-band covariance from the temporal
+:math:`C_d` produced here. The propagation of :math:`C_d` into an inference
+is therefore an interface, not a closed loop (manuscript Section 6; audit
+INV-01).
 
 References
 ----------
diff --git a/tests/test_calibration.py b/tests/test_calibration.py
index 3aec5ae..7bbdd75 100644
--- a/tests/test_calibration.py
+++ b/tests/test_calibration.py
@@ -38,7 +38,12 @@ def test_missing_members_do_not_count_as_coverage_misses(monkeypatch):
     members = np.array([[0.0, np.nan, 0.0], [3.0, np.nan, np.nan]])
     sigmas = np.ones_like(members)
     sigmas[0, 2] = np.nan
-    run = SimpleNamespace(truth=np.zeros(3), members=members, within_sigma=sigmas)
+    run = SimpleNamespace(
+        truth=np.zeros(3),
+        members=members,
+        within_sigma=sigmas,
+        times_days=np.arange(3.0),
+    )
     result = SimpleNamespace(
         mu_mean=np.zeros(3),
         Cd=np.eye(3),
@@ -49,6 +54,7 @@ def test_missing_members_do_not_count_as_coverage_misses(monkeypatch):
         corr_length_days=1.0,
         n_eff=3,
         prior_weight={},
+        samples_hyper={k: np.ones(10) for k in ("tau2", "s2", "lambda")},
     )
     monkeypatch.setattr(
         C,
@@ -60,13 +66,17 @@ def test_missing_members_do_not_count_as_coverage_misses(monkeypatch):
             np.zeros((3, 5)),
         ),
     )
-    monkeypatch.setattr(uq_bayes, "bayes_dvv_from_ccfs", lambda *a, **kw: (result, run))
+    monkeypatch.setattr(uq_bayes, "run_processing_ensemble", lambda *a, **kw: run)
+    monkeypatch.setattr(uq_bayes, "gibbs_dvv", lambda *a, **kw: result)
     row = C.run_realization(1)
     assert row["ok"]
     assert row["n_member_epochs"] == 2
     assert row["member_coverage68"] == row["member_coverage95"] == 0.5
     assert row["missing_fraction"] == pytest.approx(2 / 3)
     assert row["member_rmse"] == pytest.approx(np.sqrt(4.5))
+    # Constant chains: split R-hat is undefined (zero within variance).
+    assert np.isnan(row["rhat_tau2"])
+    assert len(row["heldout_fit_members"]) == 1
     members[:] = np.nan
     assert not C.run_realization(1)["ok"]
 
@@ -107,6 +117,10 @@ def test_run_realization_smoke_and_failure_path():
         r["n_epochs"] > 10 and np.isfinite(r["rmse"]) and np.isfinite(r["member_rmse"])
     )
     assert 0.0 <= r["prior_weight_tau2"] <= 1.0
+    assert 0.0 <= r["heldout_member_coverage95"] <= 1.0
+    assert len(r["heldout_fit_members"]) == 6
+    for k in ("rhat_tau2", "rhat_s2", "rhat_lambda"):
+        assert np.isfinite(r[k]) and r[k] > 0.5
     bad = C.run_realization(
         1, "clean", years=0.01, cadence=6, n_iter=10, burn=2, thin=1
     )
diff --git a/tests/test_deviations.py b/tests/test_deviations.py
index 289bcfa..45ffcd0 100644
--- a/tests/test_deviations.py
+++ b/tests/test_deviations.py
@@ -44,18 +44,64 @@ def test_moving_reference_is_worse_than_fixed(small_dataset):
 
 
 def test_oat_returns_baseline_and_deviations():
-    rows, ctx = D.oat_effects(years=1.2, snr=8.0)
+    rows, ctx = D.oat_effects(years=1.2, snr=8.0, seeds=(55,))
     assert any(r.axis == "baseline" for r in rows)
     # Every deviation axis appears.
     axes = {r.axis for r in rows}
     assert "Reference scheme" in axes and "Estimator" in axes
     base = next(r for r in rows if r.axis == "baseline")
     assert np.isfinite(base.rms)
+    # Common-support RMS and availability are reported for every row.
+    assert all(np.isfinite(r.rms_common) for r in rows)
+    assert all(0.0 < r.availability <= 1.0 for r in rows)
+    moving = next(r for r in rows if r.option == "moving")
+    assert moving.availability < 1.0  # warm-up epochs are missing
+    assert ctx["common"].sum() < len(ctx["days"])
+
+
+def test_inversion_reference_rejects_other_estimators(small_dataset):
+    s, days, truth, ccfs = small_dataset
+    cfg = dict(D.BASELINE, reference="inversion", estimator="MWCS")
+    with pytest.raises(ValueError, match="stretching-based"):
+        D.run_pipeline(ccfs, s.t, s.fs, cfg)
+
+
+def test_gate_applies_to_every_estimator_and_reference(small_dataset):
+    """The gate reads the stretching coherence at the same band/window/stack/
+    reference, so a gated MWCS or moving-reference run drops exactly the
+    epochs the stretching probe drops."""
+    s, days, truth, ccfs = small_dataset
+    for ref in ("fixed", "moving"):
+        probe = dict(D.BASELINE, reference=ref, gate=False)
+        _, _, cc = D.run_pipeline(ccfs, s.t, s.fs, probe, return_cc=True)
+        keep = np.isfinite(cc) & (cc > D.GATE_CC)
+        cfg = dict(D.BASELINE, estimator="MWCS", reference=ref, gate=True)
+        dvv, valid = D.run_pipeline(ccfs, s.t, s.fs, cfg)
+        assert not valid[~keep].any()
+        ungated, valid0 = D.run_pipeline(ccfs, s.t, s.fs, dict(cfg, gate=False))
+        np.testing.assert_array_equal(valid, valid0 & keep)
+
+
+SMALL_AXES = {
+    "estimator": ["stretching (TS)", "MWCS"],
+    "window": [(10, 30), (4, 14)],
+    "stack": [1, 10],
+    "reference": ["fixed", "moving"],
+}
 
 
 def test_multiverse_sobol_sums_sensible():
-    mv = D.multiverse(years=1.2, cadence=6)
-    assert mv["curves"].shape[0] == mv["n_pipelines"]
+    # A reduced factorial: the full 108 on the daily grid takes minutes.
+    mv = D.multiverse(years=1.2, cadence=6, axes=SMALL_AXES)
+    assert mv["curves"].shape[0] == mv["n_pipelines"] == 16
+    # MWCS on the 4-14 s window holds two 6-s sub-windows, fewer than the
+    # three its delay fit needs, so those four pipelines return no epoch.
+    assert mv["n_empty"] == 4 and mv["n_valid"] == 12 and mv["n_sparse"] == 0
+    assert mv["n_valid"] + mv["n_sparse"] + mv["n_empty"] == mv["n_pipelines"]
+    assert all(e["config"]["estimator"] == "MWCS" for e in mv["empty"])
+    assert all("three sub-windows" in e["reason"] for e in mv["empty"])
+    # Output is decimated after stacking on the daily grid.
+    assert mv["days"][1] - mv["days"][0] == 6
     # First-order indices are fractions in [0, 1].
     for v in mv["sobol_rms"].values():
         assert -1e-9 <= v <= 1.0 + 1e-9
@@ -171,3 +217,27 @@ def test_prefiltered_rejects_estimators_without_linear_bandpass(
         cfg = dict(D.BASELINE, estimator="WTS")
         with pytest.raises(ValueError, match="prefiltered"):
             D.run_pipeline(ccfs, s.t, s.fs, cfg, prefiltered=True)
+
+
+def test_multiverse_step_uses_the_event_day_not_the_nearest_epoch(monkeypatch):
+    """With cadence 3 the nearest decimated epoch to the event day (730) is
+    729, a pre-event day; the step must be measured about the event day."""
+    days = np.arange(0, int(2.5 * 365), 3, dtype=float)
+    assert days[np.argmin(np.abs(days - D.ERUPT_DAY))] == 729  # the trap
+    seen = []
+    real = D._drop_amplitude
+
+    def spy(dvv, days_, valid, eq_day=D.ERUPT_DAY, span=120):
+        seen.append(eq_day)
+        return real(dvv, days_, valid, eq_day=eq_day, span=span)
+
+    monkeypatch.setattr(D, "_drop_amplitude", spy)
+    one = {
+        "estimator": ["stretching (TS)"],
+        "band": [(0.4, 1.0)],
+        "window": [(10, 30)],
+        "stack": [10],
+        "reference": ["fixed"],
+    }
+    mv = D.multiverse(years=2.5, cadence=3, axes=one)
+    assert mv["n_pipelines"] == 1 and seen == [D.ERUPT_DAY]
diff --git a/tests/test_uq_bayes.py b/tests/test_uq_bayes.py
index 0e281c0..08366a8 100644
--- a/tests/test_uq_bayes.py
+++ b/tests/test_uq_bayes.py
@@ -258,3 +258,85 @@ def test_shared_artifact_is_not_detected():
     res = B.gibbs_dvv(M, S, t, n_iter=600, burn=200, thin=2, seed=11)
     err_rms = np.sqrt(np.mean(res.mu_mean**2))
     assert err_rms > 10 * np.median(np.sqrt(np.diag(res.Cd)))
+
+
+def test_split_rhat_near_one_for_iid_and_large_for_shifted_chains():
+    from codameter.uq_bayes import split_rhat
+
+    rng = np.random.default_rng(0)
+    iid = rng.standard_normal((2, 400))
+    assert abs(split_rhat(iid) - 1.0) < 0.05
+    shifted = np.vstack([iid[0], iid[1] + 5.0])
+    assert split_rhat(shifted) > 1.5
+    assert np.isnan(split_rhat(np.ones((2, 40))))
+    assert np.isnan(split_rhat(np.arange(6.0)[None, :]))
+
+
+def test_gibbs_keeps_hyperparameter_chains(bayes_run):
+    res, _ = bayes_run
+    assert res.samples_hyper is not None
+    n = res.samples_mu.shape[0]
+    for key in ("tau2", "s2", "lambda"):
+        assert res.samples_hyper[key].shape == (n,)
+        assert np.all(res.samples_hyper[key] > 0)
+
+
+def test_duplicating_the_ensemble_is_not_new_information(bayes_run):
+    """Audit UQ-03: what duplicating every member does to the two objects.
+
+    Under the working likelihood (independent residuals) duplicated members
+    count as new data, so a data-dominated credible band on mu would shrink by
+    1/sqrt(2). It does not, because the smoothness prior sets the precision
+    of mu at these settings; the single-member covariance C_d, a mean of
+    within variances plus a spread, is close to invariant. The numbers are
+    reported in the manuscript; this test pins the behaviour.
+    """
+    res, run = bayes_run
+    kw = dict(n_iter=600, burn=200, thin=2, seed=0)
+    r1 = B.gibbs_dvv(run.members, run.within_sigma, run.times_days, **kw)
+    M2 = np.vstack([run.members, run.members])
+    S2 = np.vstack([run.within_sigma, run.within_sigma])
+    r2 = B.gibbs_dvv(M2, S2, run.times_days, **kw)
+    half1 = np.median(r1.mu_hi - r1.mu_lo)
+    half2 = np.median(r2.mu_hi - r2.mu_lo)
+    # far from the 1/sqrt(2) = 0.71 that independent new data would give
+    assert 0.85 < half2 / half1 < 1.2
+    cd_ratio = np.median(np.diag(r2.Cd) / np.diag(r1.Cd))
+    assert 0.8 < cd_ratio < 1.2
+    assert np.max(np.abs(r2.mu_mean - r1.mu_mean)) < 1e-3
+
+
+def test_corr_length_recovers_exponential_decay_and_ignores_noise_floor():
+    """AR(1) residuals with a known length: the fit reads the short-lag decay
+    and is not flattened by the noise floor of the long-lag autocorrelation."""
+    rng = np.random.default_rng(3)
+    dt, L_true, K, T = 4.0, 6.0, 12, 300
+    phi = np.exp(-dt / L_true)
+    R = np.empty((K, T))
+    for k in range(K):
+        x = np.zeros(T)
+        x[0] = rng.standard_normal()
+        for i in range(1, T):
+            x[i] = phi * x[i - 1] + np.sqrt(1 - phi**2) * rng.standard_normal()
+        R[k] = x
+    times = np.arange(T) * dt
+    L = B._estimate_corr_length(R, times)
+    assert 0.7 * L_true < L < 1.4 * L_true
+    rho = B.residual_autocorrelation(R)
+    assert rho[0] == pytest.approx(1.0)
+    assert abs(rho[1] - phi) < 0.08
+    # White residuals: no lag exceeds the floor, so L is the cadence.
+    assert B._estimate_corr_length(rng.standard_normal((K, T)), times) == dt
+
+
+def test_residual_autocorrelation_excludes_constant_rows():
+    rng = np.random.default_rng(1)
+    R = rng.standard_normal((4, 50))
+    rho_ref = B.residual_autocorrelation(R, maxlag=3)
+    # A constant row and an all-NaN row carry no autocorrelation and must not
+    # pull the mean towards zero.
+    R2 = np.vstack([R, np.full((1, 50), 0.3), np.full((1, 50), np.nan)])
+    rho = B.residual_autocorrelation(R2, maxlag=3)
+    assert rho[0] == 1.0
+    np.testing.assert_allclose(rho, rho_ref)
+    assert np.isnan(B.residual_autocorrelation(np.ones((2, 50)), maxlag=3)).all()