[dillona]

This splits a second independent rank-nine helper on exact #7110 into rank-five and rank-four jobs, raising conditional κ from .003636447857731 to .003637417119941: an absolute gain of .000000969262210. It adds one research package. The selected frontier is unchanged.

The new witness uses chart 118, pivot 631 and source cut 37738. The legacy basis routine would choose d3=677/163840 and require an unsupported denominator 677. Choosing d641=−1/4 instead keeps every emitted coefficient and inverse SCALE in the existing 2,3,5 alphabet. The whole prefix/suffix identities, arbitrary inputs and source/target charts are checked. All 872 ADDs and 6 SCALEs are charged; no MOVE is added.

• Complete invoice delta: productive {4:+18,5:+18,9:−18}, paid unchanged; surplus 1,520 and zero empty-root credit.
• Ordinary source-unit bill: 848,738,320 <10^9, including the actual signed caller routes, scalar surcharge and conversions.
• Independent raw bracket: (.00363741711994152260052497254765289, .00363741711994152260052497254765290). The complete Conditional κ = 0.003636447857731 (+(24218633975/908869778093)% over #7109 ≈ +0.026646979093%): cocharted rank-nine helper split #7110 invoice rejects the new claim.
• Fresh rational derivation and independent integer replay retain odd scale 1125, fractional height 24 and signed-caller precision c1342. Lower scale 375 and height 23 reject.
• Exact source: Conditional κ = 0.003636447857731 (+(24218633975/908869778093)% over #7109 ≈ +0.026646979093%): cocharted rank-nine helper split #7110 head fdb1eb55c4c6604e714c6950e656c67ae0e52370; emitted word SHA256 3454c4900245ed1814ceeff79a741a45160eb3a93cf8d15f891fe2a67ba036fc.

Two complete local CPython 3.14.7 runs passed, including the final frozen receipt with all controls: exact cut and forward/adjoint endpoints, all 512 columns and phase of the split maps, complete signed caller/prices/precision/compiler and 54+4 outer gates, full finite physical word and signed routes. Metadata, committed bytes, modes and canonical research-source ancestry passed. Hosted CI is currently blocked before package replay by an upstream documentation mismatch: canonical main's CI guide still names #6030 after selection moved to #7000. A minimal canonical-base correction passes all six current-status/navigation tests locally. It is handed off below; including that changed historical file in the stale-fork transport created a merge conflict, so the PR remains package-only. No hosted Python 3.12 scientific pass is claimed. A complete additional local CPython 3.12.16 replay now passes with every frozen receipt field equal, including physical native and signed-route checks. It used the official Astral python-build-standalone release20261026, archive SHA256 fbf4afef53c2a6b72bb741bc06d5671a9dfaf87bd84e5aa73ac9b3d0d589f14e, extracted into temporary storage; system Python was unchanged. Command: /tmp/kappa-python312/python/bin/python3.12 -I -B /tmp/p104-source7112/package/verify.py. The copied package is the unchanged public scientific tree. Reproduce with:

python3.12 -B scripts/research_package.py --package research/p104-smooth-swap-split

The current selected #7000 application was read at canonical main e54523517d0f03e58352e647c403a5af3e525a57; priority revision 8 is unchanged. A separately reproduced first rank-nine gain overlapped #7110 and was preserved locally instead of submitted. This PR checks a distinct second direction on exact public #7110. The final source-overlap refresh found no existing #7110 successor in the searched PR bodies; this is coverage evidence, not a novelty proof. Canonical investigation and bounded negative screens.

The five retained assumptions and complete changed-source occurrence/storage/root/physical-cost application remain obligations. Passing finite checks and source-unit costs do not establish a complete multiplier, physical tariff conversion, independent human review or formal-kernel proof. The #7000 admission applies to its exact source, not automatically to this successor. Open next questions are in README.md and TASK.json.

Credit Ali Romman for helper/basis splitting; Jerry Chen/CubeJerry for inventories, retiming, shared-wire/caller/BIT and precision; DreamingOfClouds for the native lineage; ToikY for #7003/#7004 and exact #7108/#7109/#7110; #7105/#7107 and all retained original notices. Prepared for dillona with substantial OpenAI Codex assistance; no subagents.

Publication transport: the canonical-base research commit is b809a979e5745682e2ec84e26791dc99b61991f4. The account token cannot synchronize historical workflow changes to the fork, so the public commit contains only this package atop the existing fork parent 66849e1475c930fd7732b1a0067ffee7e1e95f60. Its 19-file package tree 40e91c177e5976d030325728d42ee38a3a86ae8e is byte- and mode-identical to the canonical-base research commit. No workflow files are changed.

Current publication head: e59520bb11b0df5ac33f062f55397d78a491e7af. Its entire tree matches initial package-only head b0d252a2552fad8211de79c70026ca150a56da0c; all 19 package files are unchanged. The tested CI-navigation correction is preserved in canonical-base commit 096553d6fe37afee7bc66470f4bbacf0cffbb3a3 locally, and its exact public file is available for a maintainer to apply to canonical main e54523517d0f03e58352e647c403a5af3e525a57. It only reflects the existing selection and retains #6030 as history. Initial planning failure is retained and is not a scientific replay pass.

Prepared upstream CI fix and maintainer handoff.