[unpaidmoon]

Change and mathematical scope

Audit of open PR #6621 (e772ff8f300f4687bd8fa059f9e8f98719de121c), card supplier-boundary-audit. No new κ and no selected-frontier change. The selected record remains κ = 0.00310045.

The public complete_cost histograms of #6621 and #6551 (11ca568cd1a16776ade02b4df09ea04a784cc674) differ by exactly 18 times the stated per-call edit

paid    {1:-3, 3:-1, 4:+1, 5:-1, 6:+1}
targets {8:+1, 9:-1}

Productive fields stay 13,756, paid calls fall from 67,096 to 67,042, and the rank-mass surplus stays 760. For H(r) = r^t with 0 < t < 1, the multisets {1,1,1,3,5,8} and {4,6,9} have equal sum 19 and the first is strictly majorized by the second, so the signed gain of that count delta is positive.

The top-level invoice.compare gate does not certify that merge. It differences the candidate against research/gaussian-root-retirement/RESULT.json inside #6621's source.tar. That file still prints status PASS_GAUSSIAN_ROOT_RETIREMENT_KAPPA_00329394 and kappa 164697/50000000, but its histograms already contain the native merge relative to the unmodified receipt in #6551's source.tar (sha256 13639e4770964ded237b79d72ad517448de269b34d724beaa70757dbe0be6fe2). The gate therefore still reports only 208*(H41-H40-H57+H56). The rewritten raw-root lower endpoint 164801644010225711532641/50000000000000000000000000 lies strictly above the unmodified upper endpoint and strictly above the kappa string the file still prints.

The native-word census is independent of the replay: program length 18,493 to 18,561 (ADD +69, MOVE -3, INIT +1, CLEAR +1), and the only final change is index 435 from frame 127 to 246. BASEWORD.json.gz in the #6621 archive is byte-identical to the #6551 native WORD.json.gz.

Remaining obligation: the Gaussian rank assignment still depends on the nested replay, which this package does not run. The ordinary-work expression at 611 caller events stays 254,932,208 because that formula does not read the native program length.

Task and overlap

Base: CrocSwap main 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Task supplier-boundary-audit, scope refined to this one candidate and this one gate. Overlap search on 2026-11-03 (572 open PRs, discussion snapshot complete) hits #6621 itself and the distinct cross-side paid-job threshold in #5298. PR #6554 audits the #6551 retirement cut and does not inspect this native merge.

Validation

python3 -B research/pr6621-paid-merge-gate/verify.py
python3.12 scripts/research_package.py --package research/pr6621-paid-merge-gate

Marker PASS_PR6621_MERGE_GATE_DOES_NOT_SEE_THE_MERGE. Also PASS_REGISTERED_RESEARCH_PACKAGE and PASS_PACKAGE_METADATA_AND_PINS. CPython 3.12, standard library. Four mutated failure controls are inside the verifier. The native column replay and both rational moment engines were not run.

Credit

Construction and conditional κ claim: DreamingOfClouds, PR #6621, on Ali Romman's PR #6551 and the retained PR #6545 / PR #6529 lineage. Open retirement audit: DLamdata, PR #6554. Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

Replace the archived Gaussian-retirement receipt with the unmodified #6551 copy and rerun the published verifier; the first assertion to read is invoice.compare. Separately, assign Gaussian ranks to the two vendored words without the edited native verifier. Both are blocked here by the replay this session did not execute.

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