[dillona]

The reciprocal helper mode survives the exact #7118 edit and raises the conditional claim to κ = 0.003639143435066, up 0.000000100503559. One paid rank-five MOVE becomes ranks four and one; two neutral advances bring the required fields to chart 246. Another independent helper9 target becomes helper8+helper1. The previous split's changed role789 path is checked explicitly, and the signed 17-stage caller is retained.

The complete deltas are ΔP={1:+17,4:+17,5:−17}, ΔT={1:+17,8:+17,9:−17}. The new invoice has 110,706 paid positions, 22,240 productive fields, surplus 1,424 and zero empty credit. Ordinary work is 777,686,320 <10⁹. Fresh precision raises c from 2338 to 2342; native grid1125/F24 and caller grid675 are separately derived and charged.

• Exact source: Conditional κ = .003639042931507 (+1.00498024e-7 over #7117): residual helper split #7118 3f6ff8c34b22af12b40c5a8bcee585cd1aafdb9c, with its complete 25-file export and unchanged nested sources. Every source native byte is reconstructed.
• Source cut44124/chart246/pivot299. Main role17 pays the subdivision; roles789 and745 neutrally advance rank4 and rank1 moves. Added 26 ADDs + 8 SCALEs + 1 net MOVE. All54 owned lifetimes, peak43 and23 rises of mass56 remain unchanged.
• Native SHA256 7a45d092b0bf8075e3d00242c72ac897be234e005cbcdfc47d06e9d2967359f0; 73,663 events, 1,488 public inputs and1,088 independent helpers. The caller remains byte-identical to Rohan Arun's Conditional κ = .00363797977 via a 17-stage signed caller #7113.
• Full arbitrary-input forward/adjoint,16 native corruption controls, five512-column chart checks, finite native/signed routes and the complete17-stage application pass. All3,048 paid/helper maps and104 main boundaries receive exact signed-Pauli/absolute-phase checks, alongside owner, grid, ordinary, precision, fixed-tape and54+4 outer checks.
• Both exact engines reject Conditional κ = .003639042931507 (+1.00498024e-7 over #7117): residual helper split #7118's invoice at the new claim. Independent raw crossing: (0.00363914343506692386360470011163804,0.00363914343506692386360470011163805). This is the emitted invoice's ceiling. BIT headroom is0.000127546564934; no global optimum is claimed.

python3.12 -B scripts/research_package.py --package research/p104-funded-reciprocal-split

Both complete direct CPython 3.14.7 runs and the final registered isolated CPython 3.12.16 replay passed. Every frozen native and composition receipt field matched. REPLAY.txt preserves the actual output; metadata was marked completed afterwards. No scientific code or receipt changed after the successful comparison.

Committed bytes and executable modes pass on both commits. Source-history checks pass at canonical-based scientific commit 004c198d7f09f516c2507785ad5e4e5c25502c5d. Public commit bd244b0e5034cb1b9f72641494c3421f757ec2e4 carries the identical25-file package tree ff7676dd3e214a9abcbeb56ca6c3887412ccf669. Publication is package-only atop the older account fork because the credential cannot push workflow-history changes; canonical provenance remains pinned. The scientific replay requires neither Git nor network.

Exact-head run42883037811 failed onboarding at19:17UTC (760tests,1failure,24skips), and skipped scientific replay. test_current_ci_section_matches_selected_record reports the same guide6030/selected7000 mismatch. The predecessor #7118 workflow failed canonical onboarding because the CI guide names #6030 while the selected record names #7000, skipping scientific replay. The existing correction handoff remains available. No hosted scientific pass is claimed.

PROOF.md gives the concrete arbitrary-input identity and positive concave gain H8+H5−H9−H4. APPLICATION.md supplies the source-specific argument, including 18,496 fresh stage/helper inputs,867 native banks,42,280,864 scalar services and25,471,767,360 elementary monomial records. The five framework assumptions remain. Independent human/formal review, maintainer admission and compiled top-level execution remain open. Selected#7000 is unchanged.

Credit Ali Romman, Jerry Chen/CubeJerry, Matarener, Rohan Arun, DreamingOfClouds, ToikY, Douglas Colkitt/#7000 reviewers, preceding dillona/OpenAI Codex contributions through #7118 and all retained notices. ToikY's pending chart120 rank8 lead is distinct and unclaimed. Substantial OpenAI Codex assistance; no subagents. Canonical investigation.