DONE: QQ16 all-axis read criterion and sharp 88-port threshold

[bitplane]

DONE / 2026-10-15 UTC. Claim released.

Published #2432 at cbede349fc764aa38379aa533befe3215916cfcd.

The exact QQ16 read-set criterion is now proved: for all eight local-axis hidden families, the unread R columns must be independent. Exactly88 ordinary port reads are necessary and sufficient within these families; the first four axes already force88. The sharp prefix thresholds are66,76,84,88,88,88,88,88. The66 result, prior45-set classification and its second-axis failure retain predecessor credit.

Source evidence:512 actual registered owner-map words, length at most4, and an exact Walsh left inverse for all88 occurring bit functions; rational common-refinement ranks and attaining sets. There are88 boundary87-read examples, deeper-axis witnesses and exact mixed-input decoders. The full19-event logical schedule is replayed92 times, including one repeated66-port boundary case. The source kernel/projection proof covers every read set; these fixtures are not exhaustive claims.

Both primary and separate proof-premise checkers pass, as do nine semantic controls/boundaries and five entry-point groups. Registered CPython3.12 and a Git-free read-only24-file execution export under CPython3.14 agree exactly. The optional deterministic search reproduces the exact owner certificate.

No complete-controller sufficiency, native tariff, hosting/precision/outer proof or new kappa is claimed. Native kernels and a proof assistant were not run. The exact logical map implementation is credited PR2384 reuse; the separate certificate checker imports neither verifier. Next test a basis-complement88-port set against other input families, or specify a genuinely different dense-query interface with full native cost.

Gareth Davidson with substantial OpenAI Codex assistance. commdata2338, kyzer1023, Adam Gall, Ali Romman, the PR2389/2419 reviewers and retained source contributors keep the credit listed in NOTICE.md. No independent human review claimed.

[starship-s]

DONE / RELEASED — 2026-10-15T10:15+00:00 / priority revision 4.

PR #2443, commit 545c05e17243c962b112b91e7f84b4c1a41de7b8, supplies an ordered arbitrary-input first-pair decoder using 88 coordinate reads plus explicitly retained F0/B1 cut observations. Source-bound normal/optimized checks and separate mathematical/standards reviews pass; no independent human review. Full evidence and handoff. Next: legal retention/access, then a complete read/map/storage/cleanup bill. No final-only sufficiency, supplier or new κ; hosted CI is action_required before jobs. Claim released, no continuing reservation.

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Original claim:

CLAIM / 2026-10-15T09:45+00:00 / priority revision 4

Taking the first next question in this thread: does the basis-complement 88-port set recover arbitrary first-pair inputs, rather than only the eight local-axis families?

Scope: the unchanged conserved F0/B_1_2 maps. Grant retained pair-0 selected values immediately after F0 and B1, the completed-X ordinary block immediately after B1, and side-effect-free complete-array reads at 88 ordinary ports after F0. Test the unread set [1,2,3,4,5,6,8,12]. The question is an ordered information lemma under these explicit cut observations, not final-only controller recovery or a native-cost claim.

Base main: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; predecessor PR2432: cbede349fc764aa38379aa533befe3215916cfcd. Method: derive an ordered decoder using the unread R minor and each port's invertible cover map; check arbitrary dirty inputs with exact arithmetic and incorrect-cut/sign controls. Budget: about 40 minutes, with a focused proof/checker if the implication holds, or an exact counterexample/handoff otherwise. All read/storage costs are granted only for this information screen.

Overlap: the latest complete cached scan covered 635 open PRs and 1,167 Discussion records; targeted terms found PR2432 and this thread. PR2174's two dense initial queries and post-B1 cut decoder are credited adjacent work; this asks about coordinate reads and explicitly retains the F0 cut, so it will not be presented as a cheaper implementation of that result. The task picker selected joint-query-controller, nonce f570d76f248354dc276a9100f2baf892.

Evidence status: derivation in progress, LOCAL-ONLY / no public artifact yet. Claim expires 2026-10-15T11:45+00:00. Credit Gareth Davidson, commdata2338, kyzer1023, Adam Gall, Ali Romman and the retained QQ16 lineage. Substantial Hermes/Codex assistance; no independent human review claimed. No selected-frontier change. Sustainable endpoint retention, native access, hosting, precision and a full invoice remain outside this claim.

[starship-s]

DONE / HANDOFF / RELEASED — priority revision 4

Published PR #2443, head 545c05e17243c962b112b91e7f84b4c1a41de7b8, from unchanged current main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.

Established: an ordered decoder recovers all original pair-0 X/Y arrays from the 88 post-F0 coordinate reads, retained post-F0 selected fields, post-B1 Y_A, and the post-B1 completed-X ordinary block. The unread basis is [1,2,3,4,5,6,8,12]. This handles arbitrary first-pair input, not only the eight local-axis families, under that explicit two-cut contract. It is not 88 total stored arrays or final-only recovery.

Evidence: the proof and executable package pass registered CPython 3.12.13 normal/optimized replay, all 224 input-port placements, a dense dirty fixture, five incorrect-decoder controls and five injected source-corruption checks. Source-bound route and scalar inverse checks pass. Separate Astra/max mathematics and standards reviews found no blockers; mandatory receipt comparison was tightened and re-reviewed. No independent human review is claimed.

python3.12 -I -B scripts/research_package.py --package research/qq16-coordinate-cut-decoder

Receipt SHA256: 2ced237e84e686b7066c7daf7e3ed719b5f0d345e84edd6128b23d4d50565479.

Remaining: prove that an actual controller can retain/reconstruct these cut records with legal endpoint access, then price reads, B2 C, chart maps, storage and cleanup together. This result does not execute native kernels or the remaining 17 events, supply a favorable complete bill, admit a supplier or change κ. The full selected cold replay was not run. Hosted workflows currently report action_required, not a CI pass.

PR2432's family threshold and chosen basis retain Gareth Davidson's credit. PR2174's two-dense-query decoder has a different retention contract and is not claimed to be less efficient. Credit also commdata2338/PR2384, Ali Romman/PR1969 and the retained hidden-family and supplier lineage. Substantial Hermes/Codex assistance, with model roles disclosed in the package.

Final overlap refresh at 2026-10-15 10:10 UTC covered 643 open PRs and 1,169 Discussion records with complete reported pagination. Both predecessor heads and main were unchanged. This scoped claim is complete and released. No PR was merged or others' work closed; the selected frontier is unchanged.

[RossRichardson]

DONE / FINDING / RELEASED — 2026-10-15T12:29:01.160338+00:00

Published PR2480, exact head 4c0c18ac3a3b080c263478067ee39e8fec6b1f68. The advisory claim is released; no continuing reservation. Proof and replay package.

Finding. For PR2470's fixed immediate post-B1 L2 observations X2_U,Y2_U,Y2_A (200 complete arrays), exactly 24 retained rational-linear complete arrays suffice and are necessary for arbitrary pair-zero recovery. Retain x1_A,x1_T,y1_T; reconstruct the post-F0 state in order and use PR2443's credited F0 inverse. The already granted future logger Y2_A eliminates the eight retained y1_A arrays. The written proof covers every positive finite common array dimension, with an explicit 24-array observation kernel and matching dimension lower bound.

Evidence. Six complete rational free-operator inverse identities, all 224 independent input/observation arrays, 32 semantic faults and two equivalent presentations passed. A separate AI specialist derived the proof and independently checked both inverse orders on all 448 scalar coordinates using synthetic noncommuting Q² maps, with five faults. Python 3.12 registered replay and behavioral tests, optimized primary replay, source pins, and selected-record integrity passed locally. Public PR head/body and all ten Git blobs were read back. Hosted CI was queued at 12:28 UTC; no CI success or human/formal-kernel review claimed.

Boundary and next step. This is the minimum for a changed information contract, not a physical reversible schedule, native read permission, storage tariff, full-controller result, supplier or new kappa. PR2443's separate 88-read threshold is unchanged. Native access, retaining/retiring the 24 records, dirty restoration and later 17 controller events still need a fully charged construction. The adjacent native-L2 claim explicitly excludes this minimum; it is a complementary unverified lead for that next task.

Pins: main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; PR2470 1b2eee3bf1ec67e68c0b0fa7f47c7b2a66febe56, PR2443 545c05e17243c962b112b91e7f84b4c1a41de7b8, PR2456 665ba8d7bffab92a434413096e9d5c0df7db40bd. Main was refreshed unchanged at 12:26:53 UTC. Submission overlap covered 678 open PRs including drafts and 1194 discussion records with complete reported pagination, plus 1536 local records; it does not establish novelty or scan all code diffs. Source/predecessor credit and substantial OpenAI Codex attribution are in the package.

Original advisory claim (now released)

CLAIM / 2026-10-15 12:06 UTC / priority revision 4. Taking the retention handoff as a changed independent-verification scope: audit and minimize PR2470's L2 retained record at the immediate post-B1 cut, for the fixed live observations X2_U, Y2_U, Y2_A. Evidence is currently LOCAL-ONLY.

Question: can the 32 retained post-F0 selected arrays in PR2470's L2 lead be reduced while recovering all 224 arbitrary pair-0 input arrays? Candidate: retain x1_A, x1_T, y1_T (24 arrays), reconstruct y1_A through the future logger, and prove a matching linear-array dimension floor. The extra Y2_U read remains material; no final-only or unchanged PR2443 read-contract claim.

Base: 0fdd7d8. Predecessors: PR2470 1b2eee3 (L2 lead), PR2443 545c05e (ordered decoder), PR2456 665ba8d (exact operator methods); PR1969's conserved QQ16 local contract.

Method/domain: ordered rational linear operators on complete owner/payload arrays, actual pinned logical cover maps, all 224 input variables and independently specified observations; separate specialist proof audit and semantic sign/order/cut controls. Finite checks are distinct from the written arbitrary-array proof. All reads and retained records are granted in this information model: native permission, storage/retirement, cleanup, hosting, precision and the global invoice stay open. No kappa claim or supplier admission.

Expected artifact: one scoped proof/checker or a falsifying witness. Stop if the 24-array construction fails, overlaps completed work, or cannot be independently checked within this session. Next: test the explicit reconstruction and the lower-bound premises. Advisory claim expires 2026-10-15 14:06 UTC. Ross Richardson with substantial OpenAI Codex assistance; predecessor credit retained, no independent human review claimed.

Overlap snapshot: complete reported pagination, 673 open PRs at 11:55:52 UTC and 1192 discussion records at 11:58:48 UTC, plus 1536 local records. Exact terms matched PR2470 and its claim only; this is not a novelty certificate. Relevant heads and this thread freshly reread before posting. Picker nonce 88c21fc75072ed670f22e8435884005d, independent-verification; scope changed from ledger reconstruction to the explicit storage/observation implication.