Audit centre-source coefficients with an independent adjoint and sign control

[BigCactusLabs]

Change and mathematical scope

Endpoint identity and full centre-source rank can both pass with wrong bridge signs. This independent audit reproduces the selected common-frame scalar source-history rank already reported in #2622, then checks every source coefficient using a separately written local adjoint and dense controller calculation.

The useful control reverses all 144 bridge signs: the endpoint stays the identity on 14,336 owners and source rank stays 1,152, but 930 source rows change. With only initial owner 224 equal to one, the cut at time 10 / stage 2 / replica 0 / centre 0 changes from +1 to -1. The exact witness and both full row digests are recorded. This is a regression control, not a defect claim against #2622.

Only research/selected-centre-bridge-projection/ is added. There is no new supplier, physical saving, paid-profile change or kappa. Native frame, idle and address actions remain explicitly projected to identity. The distinct endpoint-error injectivity result in #2622 is outside this audit.

Task and overlap

Task centre-path-sharing, scope key a55534776f5479f1686c, seed 283c37d7bfe9aa29a7d597e3ec17d33b, priority revision 5. Scope changed to a deliberate independent coefficient audit after the broader overlap check found that the rank calculation was already covered.

Scientific base: c3c94c2ea2ebcd5d69d1e51b5fe8a36bf79819f5. Refreshed canonical main: 936fac15b1b1b59dc5285c713a77f9f3c07b2906; guidance, selected record and all scientific inputs are unchanged, and the patch applies cleanly there. The selected archive contains the actual 480-helper word.

Nearest work:

• Negative result: calls-only centre-source rank census across all 144 selected calls (PR2048 Q2; no new kappa) #2199 at 30ec048eedcaca970f94bbec0fdd3c52eacf9fdc: calls-only scalar source census and bridge/idle handoff.
• Certify complete projected centre-error endpoint response #2622 at 4ffb893a08e8868057a30a065642d0b5f647f742: complete bridge-aware source rank and identity endpoint, plus a separate output-error response theorem. The source rank is credited, not claimed as new here.
• Certify a source-only terminal quotient for two selected centre ablations #2564 at 64f940a8ee305a1b69f7db329f1ffa232e53c2ad: two-call ablation residual with bridges omitted.

Neither checker imports predecessor implementations. TASK.json records overlap coverage, exact heads, scope and remaining obligations; SOURCES.json pins inputs.

Pre-publication overlap was refreshed at 2026-10-15 20:47 UTC: complete pagination covered 710 open PRs and 1,399 discussion records, with no coverage warnings. The nearest source-history claim remains #2622 at the same head. New merged package paths were also checked against refreshed main.

Validation

On macOS arm64, the registered CPython 3.12.13 replay passed both commands:

python3.12 -B scripts/research_package.py --package research/selected-centre-bridge-projection

Both direct checkers also passed under optimized CPython 3.11.15:

python3.11 -I -O -B research/selected-centre-bridge-projection/verify.py
python3.11 -I -O -B research/selected-centre-bridge-projection/check_adjoint.py

The primary calculation uses exact rational elimination. The independent adjoint uses reverse-row, largest-column elimination modulo 2147483647; all denominators are invertible. Both correct and wrong-sign source matrices have full rank. Controls also cover 18 individually omitted half-bridges, removal of all bridges and dependent duplicate rows. Source bindings, call hashes, ownership maps, local cleanup and the complete projected endpoint are checked.

git diff --check passed. Full make verify, selected cold replay, native 512-address routing, upstream CI, human review and theorem-kernel verification were not run.

Credit

Adam Gall / #1918, Sagar Thakrar / #2199, and ywz65 / #2564 and #2622 retain predecessor credit. Rohan Arun, Jeremy Kothe, Hao Yan, Douglas Colkitt and the retained selected construction lineage supply the pinned scientific inputs. New work is Apache-2.0, prepared for BigCactusLabs with substantial OpenAI Codex assistance. The two algorithms were separately written by the same AI-assisted author.

Open next questions

The package README gives the smallest native follow-up: replay the owner-224 unit input through the actual routed bridge and idle maps to the first changed cut. The blocker is an explicit cover/address boundary; repeating the identity projection would not answer it.