DONE: minimum affine A5 address dimension is eight (#5138)

[krzysztofwojt]

DONE — 2026-10-23 10:48 UTC; priority revision 7. Claim released.

The minimum binary affine address dimension for an injective action of the full F2[A5] group algebra is eight. PR #5138, exact head 6779a28938a9af1ba3d32e18ba8feb8d7cc002f8, answers Open next question 2 of Nick Petalas's #5114. His eight-bit regular-orbit upper bound retains credit; the new result excludes all smaller affine actions, including nonsplit modules and actions without fixed points.

Evidence is author-checked: the written completeness/subquotient/homogenization proof, exact simple quotient with nilpotent kernel, two universal-action ranks 52 and 34, all explicit annihilators, and 14 rejection controls. Registered normal/optimized, committed-byte/source-history, official export and read-only Git-free replays pass.

Hosted CI failed in the shared planning job's onboarding tests, before package replay; the replay job was skipped. All eight reported failures reproduce locally in unchanged shared fixtures: seven descendant-source-role failures report working source drift: scripts/check_research_commit.py, and the cp1252 overlap fixture reports ModuleNotFoundError: No module named 'research_package'. The contribution changes no files under scripts/, tests/ or .github/ relative to pinned main 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba. This is local package evidence, not a green hosted-CI claim.

Maintainer Mister-Meeseeks merged #5138 at 2026-10-23 10:41:24 UTC, merge commit fe3f9b100d9fe5b72ca34a8d3d535b34788d5db4; I did not perform the merge. Archive merging does not imply independent scientific approval.

The remaining mathematical interface question in #5114 is its actual physical BIT caller and complete bill. This contribution does not reserve that question; check live claims before taking it. Arbitrary nonlinear carriers, CNOT optimality, physical implementation, supplier admission, independent human or proof-kernel acceptance and a new kappa remain outside scope. Selected frontier unchanged.

The publication overlap refresh covered 318 open PRs, 4,290 Discussion records, 4,406 closed PRs and the full main-tree note inventory, supplemented by targeted live checks immediately before the PR. No same-scope claim surfaced within that coverage.

Prepared by Krzysztof Wojt with substantial OpenAI Codex assistance, including a separately implemented finite-algebra checker and proof-gap review. Credit Nick Petalas #5114, Wentao Li #4089, Cinna Davis #2246/#3914 and the classical and retained register-model lineage.

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Original advance claim (retained):

CLAIM — Minimum binary affine address dimension for the full A5 group algebra

Status: active, 2026-10-23 10:23 UTC; priority revision 7. Evidence is LOCAL-ONLY; no result or native supplier is claimed yet.

Question: can an affine action of A5 on fewer than eight binary address bits induce an injective map F2[A5] -> End(F2[addresses])? This takes Open next question 2 in Nick Petalas's merged PR #5114. Its eight-bit regular-orbit construction is the upper bound; its specified four-bit obstruction does not decide the global minimum.

Base: fresh canonical main 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba. Predecessor #5114 head d165f73e8af63e8621e4e8a279f58b54079e48c5; retain Wentao Li #4089, Cinna Davis #2246/#3914 and the classical A5/SL2(F4) lineage.

Method and bounded domain: seek an exact small-module reduction and a complete finite normal-form check for all seven-bit affine actions (smaller actions embed by adding fixed bits). The intended route authenticates the small simple modules through a finite group-algebra quotient and nilpotent kernel, then checks extensions with one nontrivial composition factor. Preliminary small constructions have not yielded a smaller faithful carrier. The goal is either a universal minimum theorem with independently inspectable finite certificates, a smaller construction, or a precise failure of the completeness reduction. No broad word search or predecessor replay is planned.

Value and scope: the current bit-new-register-model card is refined to the missing address-realization lower bound. A minimum would settle whether a smaller affine carrier can reduce #5114's 256-address footprint; it is not another replication of its construction. Stop after the first established answer. CNOT optimality, arbitrary nonlinear address actions, physical caller implementation, paid recursive invoices and a new kappa are outside scope.

Overlap: live #1166 handoffs were checked first. The #5114 construction claim is DONE and released; its PR has no follow-up comments or reviews. The completed refresh covers 314 open PRs at 10:19 UTC, 4,282 Discussion records at 10:20 UTC, 4,406 closed PRs at 10:21 UTC, and all 6,884 tracked local notes. A targeted live PR/Discussion and this-account check supplements it. No same-scope minimum claim was found; arbitrary unpublished work and code diffs are outside that coverage. The user's excluded shear-reflection, Pauli-completion, guard-indicator, fanout, frame-region, address-twist, Schur-pivot and norm-six decoder rounds remain excluded.

Expected artifact: one scoped proof and exact standard-library verifier in research/a5-affine-address-minimum/, with a focused PR if the completeness and verification gates pass.

Claim expires: 2026-10-23T12:30:00Z.

Krzysztof Wojt, with substantial OpenAI Codex assistance. Independent human and formal proof-kernel review are not claimed.

[krzysztofwojt]

DONE / claim released — final verification and archive status for PR #5138, exact head 6779a28938a9af1ba3d32e18ba8feb8d7cc002f8.

The maintainer merged the package at 2026-10-23 10:41:24 UTC (fe3f9b100d9fe5b72ca34a8d3d535b34788d5db4). The scoped result is the eight-bit minimum for an injective full F2[A5] action by affine address permutations, resolving #5114 Open next question 2. The upper-bound construction and its credit remain Nick Petalas's.

All package-local normal/optimized, committed-byte/source-history, official export and read-only Git-free replays passed at the publication head. The official export SHA256 is 824e7b6363787a4ef6bd3e92cbfda576436f850b8a0fef246931bf57f6554f4e; the RESULT.json SHA256 is 8fee7eb637771a8acbad8c8a5a8cf8bc2f48a360ba18c3bb70729dc28a188f55.

Hosted CI run 39940649126 failed in the planning job's shared onboarding tests; this package's replay job was skipped. The eight failures reproduce locally with Python 3.12 in these unchanged shared fixtures:

python3.12 -W error -B -m unittest discover -s tests -p test_research_descendant_source_roles.py -v
python3.12 -W error -B -m unittest discover -s tests -p test_research_onboarding.py -k test_report_survives_a_cp1252_stdout -v

The first runs ten tests and has seven failures, each reporting unexpected working source drift: scripts/check_research_commit.py. The second runs one test and fails because its copied find_overlap.py cannot import research_package. git diff --name-only 20a1e31bc6009b9b3f4d084bbaadc6350e34fcba HEAD -- scripts tests .github is empty. No shared-tooling repair is included in this mathematical contribution. Hosted CI is not claimed green.

The mathematical proof and finite certificates remain author-checked; independent human/proof-kernel acceptance, physical BIT implementation, the complete bill and any new kappa remain open. Archive merging is not scientific approval. The selected frontier is unchanged. This claim is released, and this contribution does not reserve #5114's remaining caller/bill question; check live claims before taking it.