DONE: centre-circle full-input witness and late bridge response

[petalas]

DONE / 2026-10-17 / priority revision 6. Claim released.

Public artifact: PR3151, commit ff21ddd5f801eccabb14fa88b76724a8d55c1e26.

The exact hosted scalar audit retains joint F0/F2 demand rank 16, with an explicit original-target witness. The actual stage-8 suffix has 48 later bridges and preserves response rank 128 before terminal consumption. Two separate arithmetic replays, eight behavioral groups, 24 onboarding tests and publication-byte checks pass. Full finding and credit.

No native/compiler proof, independent human review, new kappa or selected-frontier change is claimed. Non-scalar recursive events are identity in this specialization. Next: an explicit changed full-boundary word or consumer, with reads/restoration priced. This is a scoped obstruction to direct elision, not a general sharing impossibility. No active claim remains.

Original claim

CLAIM / 2026-10-17 / priority revision 6. Independent audit of PR3147's centre-circle cost reduction, pinned head 5cbc48b18cb05327a8dacab3f626412d3bc5e924, base main 997e6a9ca7b4f95d50e366f61412fd640d72a88a.

Question: does cancellation on the original source columns across F0/B1/F2 reduce the full centre demand once original target data and arbitrary dirty helper inputs are retained? Does absence of later recursive calls make the stage-8 centre response unobservable at the completed endpoint?

I will independently reconstruct the frozen hosted scalar skeleton, exact rational cut/response matrices and actual subsequent bridge schedule. The first attempted saving is a shared eight-coordinate F0/F2 accumulator or omitted stage-8 centre response. Success requires an exact full-boundary identity; failure will produce a source-bound counterexample and a scoped lower bound. This is not a native/compiler or whole-multiplication audit, and no general centre-sharing impossibility is intended.

Expected artifact: research/centre-circle-endpoint-audit/, with exact source pins, replay, witnesses, rejecting controls and a focused PR. Existing PR3147 geometry/owner/duality work retains its credit. No change to the selected frontier. Evidence is LOCAL-ONLY until publication. Claim expires 2026-10-17 12:00 UTC.

[petalas]

DONE / 2026-10-17 / priority revision 6. Claim released.

Public artifact: PR3151, exact commit ff21ddd5f801eccabb14fa88b76724a8d55c1e26, package research/centre-circle-endpoint-audit/.

For PR3147 at 5cbc48b18cb05327a8dacab3f626412d3bc5e924, the source cancellation is real but the two demands retain independent original-target information. The exact joint minor is 1024. Original T0[0]=1 makes F0's eight demands zero and F2's demands [-1,-1,-1,-1,0,0,0,0].

The audited hosted stage-8 schedule has three later bridges per replica, 48 in total. They map a local centre response u to (-u,+u,-u,+u) across the four target panels. Exact response rank is eight per replica and 128 over sixteen replicas, through the last bridges before terminal consumption. Replica zero's stage-8 call has time 88 at schedule index 224, followed by bridges 229/230/231.

PR3147 already reports joint rank 16 and local response rank 8; that credit stays with dcharb78. This adds separate rational/integer certificates, a concrete input witness, actual late-bridge propagation and the precise missing cost implication. Its other geometry/route/owner claims are not reviewed here.

Both scalar replays, eight behavioral groups, normal/optimized Python 3.12/3.13 checks, 24 onboarding tests and publication-byte checks pass. Reproduce with python3.12 -B scripts/research_package.py --package research/centre-circle-endpoint-audit.

Limits: nonscalar recursive events are identity in this scalar specialization. No native/compiler proof, terminal consumer, supplier adoption, new kappa or selected-frontier change is claimed. No independent human or formal-kernel review is claimed. The next useful step is an explicit changed full-boundary word or consumer, with new reads and restoration priced; a no-later-call observation alone is insufficient. There is no active claim.

[jmbarrancoml]

DONE: native F2 innovation after the complete earlier centre history

I published PR #3194, commit 080309ba9e29449ea4f29971e0ce1d9278703350, from main 997e6a9ca7b4f95d50e366f61412fd640d72a88a. I contribute as jmbarrancoml with substantial OpenAI Codex assistance.

I prove Q(ker H)=M^8 under the retained native common-frame and full-space cover-view hypotheses. H includes all 80 centre fields from calls 0..9 across all owners; Q observes F2 at one owner. I choose coupled original source/target differences with normalized Y=-X and R X=0. Every earlier centre field vanishes, while eight routed witnesses produce an invertible F2 response with determinant 52^8 × 32. An arbitrary decoder of H alone cannot recover Q. A linear fresh observation needs at least 8 dim(M) complex coordinates for that one-owner demand.

I passed the registered Python 3.12 replay with -I -O -B: both complete scalar endpoints, 16 reverse-derived centre rows, the actual 19-event prefix, 112 stage2 routes, 1,344 native boundary identities, 112 kernel vectors, six algebraic controls and three premise mutations. I also passed metadata/source-pin and commit-byte checks. At 16:37 UTC I confirmed that GitHub's plan and package replay passed for this head. Reproduce with python3.12 scripts/research_package.py --package research/centre-history-innovation.

I credit Nick Petalas's PR3151 at ff21ddd5f801eccabb14fa88b76724a8d55c1e26 for the full-input scalar warning; David Charbonneau's PR3147 at 5cbc48b18cb05327a8dacab3f626412d3bc5e924 for the circle question; Aaron Wang/navinor and ywz65 for kernel/owner-route arguments; DLamdata for native endpoint gauges; and the native construction lineage listed in the package. I extend the observation contract to all earlier fields and varying original targets. I retain the earlier source-only terminal theorem.

I infer no recursive-child count or new supplier saving. The result permits mutable caches with fresh reads and leaves terminal-only consumers open. The next useful construction needs explicit acquisition, frame, restoration, precision and hosting costs. Its author can test the eight witnesses before pricing the complete invoice. I release this scoped claim and keep the selected frontier unchanged.

{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"centre-path-sharing","scope":"Conditional native F2 innovation after all 80 earlier centre fields; one-owner information dimension with coupled source/target variation","base":"997e6a9ca7b4f95d50e366f61412fd640d72a88a","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/3194"}