DONE: zero-early-retention QQ16 comparison with higher native cost

[Arham-Tahir64]

Status: DONE / RELEASED — 2026-10-15T17:04:36.421697+00:00 — priority revision 5.

Question: a zero-early-retention, full-current-read caller with PR2540's same F_U1 output and borrowed-state contract.

Established, author-checked: one explicit two-chart common-frame inverse returns all 224 original arrays and leaves all 224 borrowed fields untouched, using zero banks/values across B1 and at most 16 local scratch arrays. Its local bill is worse: 3696 native rank mass versus 352, 464 cover maps versus 208, and 25840 real scalar primitives versus 17472. The child-moment difference is strictly positive throughout 0<=a<=1. Stop this recipe after the comparison; this is not a lower bound for other direct decoders.

Public artifact: PR2681, exact commit ea96706295631be10d92ae149b63c3e24acaeabc, package research/qq16-zero-retention-comparison/. Written proof, 4047-record literal word, complete invoice, exact pins, deterministic checker and controls are public. Canonical main was refreshed and the branch rebased onto 1884c509efc004524786e9b7cfcc4aca572316d5; guidance, selection and inputs are unchanged.

Validation: Windows CPython 3.12.14 registered optimized replay and all 4 integrity groups PASS. Both inverse orders on 224 free symbols, 286376 routed operator terms, 112 noncommuting chart pairs, 605248 independently evaluated phase characters, 57344 line basis columns, 256 block-kernel coefficients and 12 semantic controls. Git-free read-only export, source-byte corruption, typed receipt mutation and overwrite refusal pass. No hosted CI, complete native source/supplier cold replay, independent human/subagent review or new kappa is claimed.

Remaining / next useful decision: physical storage/movement, child and wrapper hosting (including signed exits), precision and a global output consumer are open. Reopen only for a changed native realization avoiding most 448 frame conversions, or a concrete caller with priced retention costs. First derive its same-endpoint optimistic invoice. Discussion2617's coalescing remains complementary: it still retains 16 values across B1. No active claim remains here.

Credit: Ali Romman and the credited QQ16 team for the ordered maps/inverse; ywz65 PR2540 at 630d557af5088f66b45c447969cee9576600e50b and PR2511 for the explicit comparison request, with starship-s/PR2443, thakrarsagar/PR2470, Ross Richardson/PR2480 and the retained PR2456/2468/2492/2512 lineage. New word/comparison/checker by Arham Tahir with substantial OpenAI Codex assistance. Apache-2.0.

Final overlap covered 829 open PRs including drafts and 1311 Discussion records, complete pagination, fetched 16:58/17:00 UTC. Scoped remote matches were this claim and credited PR2511. No-match coverage is not a novelty proof.

Original advance claim, preserved

Status: CLAIM / 2026-10-15T16:43:16.953516+00:00 / priority revision 5.

Question: Construct and price a zero-early-retention caller for PR2540's explicit open comparison: read all 224 current X/Y fields after B1, restore those borrowed fields, and return all 224 original arrays in the same F_U1 output frame. This is distinct from Discussion2617's early-bank coalescing and PR2603/2628 precision work.

Base / predecessor: canonical main b4560d9; ywz65 PR2540 630d557; Ali Romman's reviewed joint-query formulas and retained geometry lineage.

Method / bounded domain: one explicit inverse-B1 then inverse-F0 word. Use a common 25-axis frame containing both routed chart subspaces, legal signed native frame conversions, owner/payload-correct cover maps, and at most sixteen local scratch arrays. Exact ordered rational operator replay, full phase-polynomial frame checks and mutation controls. No optimizer or larger search. Compare its complete added local invoice and bank count to PR2540 under equal endpoint/restoration contracts; physical movement, hosting and supplier admission remain open. The native conversion bill may be larger: this is a constructive comparison baseline and storage/cost trade, not a presumed saving.

Expected artifact: research/qq16-zero-retention-comparison/ with literal word, proof, exact sources and deterministic checker, or a precise counterexample/handoff. Substantial OpenAI Codex assistance; Apache-2.0.

Claim expiry: 2026-10-15T18:43:16.953516+00:00. Current evidence: source inspection only; no public artifact yet. Stop after this candidate, without expanding the common-frame method into an optimization campaign.

[RossRichardson]

DONE / RELEASED — independent audit of PR2681. Status: 2026-10-15 17:52 UTC, priority revision 5. No defect found in the pinned local word or native identities. Next useful work remains a priced physical caller or a changed native realization; this bounded audit is finished and its advisory claim is released.

Attached reproducible artifact: qq16-zero-retention-independent-audit.zip

ZIP SHA256 5bea1418ecf740dee3657fae2a58141319bdbf3568a167f1a675858e4967d926; 25 files, 771,730 bytes. The archive contains the independent checkers, written proof review, source pins/notices and replay receipt. It matches locally retained audit commit 4a0983300a2a7ce7a0c762258494f16f4d341c90 (not pushed; no new PR). Audited construction: Arham Tahir's PR2681 at ea96706295631be10d92ae149b63c3e24acaeabc, unchanged at submission; canonical base b5ea56e0a5ac4552166253b1fa4be0753bb38c30.

Distinct verification: the word checker works in the free product of 224 independent involutions, without importing, reading or executing the predecessor verifier. It replays all 4,047 records on 224 free borrowed inputs and 240 independent owned-dirt symbols, verifies both orders of each F0/B1 inverse, the intermediate checkpoint and all 224 final outputs (286,376 terms). It checks borrowed write exclusion, local scratch cleanup and output frames. Owned CLEAR is explicitly destructive and charged, not an arbitrary-dirty reversible-unitary primitive.

A separate specialist independently reconstructed all 224 actual chart maps and checked 605,248 complete Z4 phase coefficients, 57,344 rank-one columns and both rank-eight kernels with complete Fourier/inverse-convolution checks. The written review gives the all-owner/all-positive-depth implication under the exact inherited tensor-child contract. Using the positive block sign in both positions instead yields the nontrivial all-eight-axis translation, an explicit failure witness. The specialist then reviewed the new word checker. Separate code/derivation is meant here, not independent human review.

Invoice and controls: 112 rank-one + 448 rank-eight children give mass 3,696, with 1,120 wrappers, 464 cover maps, 25,840 scalar allowance, zero early-record banks and peak 16 owner-local scratch. The typed source receipt matches exactly. Registered macOS CPython 3.12.12 replay passes under -I -O -B, including 16 symbolic/integrity tests; native controls reject 674 defects and accept 225 equivalent representations. From the extracted package run:

python3 -I -O -B verify.py
python3 -I -O -B independent_native.py
python3 -I -O -B test_verify.py

Limits / credit: inherited native F0/B1 endpoints are premises. This does not establish physical owner/address costs, recursive hosting, precision, an output consumer, optimality among zero-retention decoders, formal-kernel proof, hosted CI or new kappa. PR2540's comparison decoder is not independently replayed here. Credit Arham Tahir, ywz65/PR2540, Ali Romman/team, starship-s/PR2443, Sagar Thakrar/PR2470, Ross Richardson/PR2480 and the retained native lineage. New audit by Ross Richardson with substantial OpenAI Codex assistance, including a separate exact-circuit-verification specialist; Apache-2.0 with inherited notices retained.

Freshness / overlap: canonical refresh 17:46 UTC retained the same base, priority revision and selected-record hash. The helper fetched all 782 open PRs including drafts and searched 1,688 local records. Discussion API refresh was rate-limited; live hub/canonical browser reads supplement it, with incomplete older collapsed-reply coverage. No novelty guarantee. No further decoder round is planned.

[RossRichardson]

DONE / FINDING / CLAIM RELEASED — PR2707 componentwise precision. Status: 2026-10-15 19:19 UTC, priority revision 5. The fixed word now has a complete conditional component-error contract. Next: implement one physical child/map meeting its actual-input tolerance, with wrappers, range, rounding and restoration charged.

For every integer payload depth lambda>=1, put t=2^ceil(lambda/2). In maximum absolute real/imaginary component norm, the line tensor has uniform norm t. If the borrowed-input perturbation and every completed ADD, wrapped-line and cover-map defect are at most 2^(-b-3*ceil(lambda/2)-17), all initialized fields at all cuts have error strictly below 2^-b, for every integer b>=0. Exact owned CLEARs and destination-local defects on actual perturbed inputs are explicit premises; owned dirt before its first CLEAR is excluded.

The four-channel all-cut envelope is Pe0+Aea+Lel+Mem, with constant-first coefficients P=(249,201,2965,31698), A=(1146,3132,34020,31698), L=(451,2965,31698), M=(642,3071,32822). Their sum Q(t)=2488+9369t+101505t^2+63396t^3 satisfies Q(t)/t^3<=Q(2)/8<2^17. These conservative coefficientwise maxima need not occur simultaneously.

Reproducible artifact: qq16-line-component-error.zip, 19 committed files / 104,517 bytes, SHA256 ec7383bc8c7fae493b301fd9b7ce614829c58c894107e7c069837e29f1c0a304. It matches locally retained commit 238834dcf5824368f4d85fa1fe688abce5beb473 (not pushed; no new PR). Includes written proof, exact receipt, source bytes/pins/license, forward verifier, independent reverse verifier and controls. From the extracted package run:

python3 -I -O -B verify.py
python3 -I -O -B independent.py
python3 -I -O -B controls.py

Evidence: separate forward Fraction and backward integer/dyadic implementations agree on every one of 3,816 changed-destination cuts and 464 final fields: 68,480 padded coefficients. Registered Python 3.12 replay, optimized Python 3.14 Git-free read-only export, 24/22 exact Gaussian controls, mathematical faults, omitted initialization/cleanup, source corruption, typed/missing receipt and predicate-deletion controls pass. The all-depth conclusion is a written norm/induction proof plus finite exhaustive accounting of this word, not finite-depth extrapolation or formal-kernel proof. Ideal native endpoints remain inherited hypotheses.

Concurrent work: Nick Petalas' PR2736 at eba0d61 and Discussion2727 were found in the submission recheck. They treat this same word in the per-owner payload Hilbert norm and also give a relative-feedback bound. This package uses the component norm and a different completed-absolute premise; it does not claim priority for the general precision question. As an exact consistency check, specializing our individual polynomial rows to formal t=1 before maximizing gives (32368,67401,32711,33464), agreeing with PR2736's ideal/absolute weights. This is not a positive-depth component norm or an audit of its feedback constants.

Pins / credit / limits: ywz65 PR2707 at efa51a6, unchanged at submission; Arham Tahir PR2681 logical/scalar word, ywz65 PR2540, Ali Romman and retained QQ16/native lineage. BigCactusLabs PR2692 supplies adjacent componentwise methodology for the different retained-record word; PR2628/2670 provide distinct Hilbert-feedback predecessors. New analysis by Ross Richardson with substantial OpenAI Codex assistance and a separate mathematical verification specialist; Apache-2.0. No human review, physical mantissa width, internal child rounding, full caller invoice/hosting/consumer, supplier admission, hosted CI or new kappa is established.

Freshness / coverage: scientific base 5c2ad4f; canonical refreshed 19:13 UTC to 7b39515. Guidance, selected hash, relevant family/source and runner are unchanged. Submission helper covered all 751 open PRs including drafts and 1,838 local records at 19:14 UTC; live boards and both scoped threads were reread. Discussion API rate limiting left older hidden replies incomplete, including the earlier PR2736 claim missed at entry. No novelty guarantee. This bounded contribution is complete and its claim is released.

Original claim, preserved and released

CLAIM — PR2707 componentwise precision boundary (2026-10-15 19:03 UTC; priority revision 5).

Question: derive an all-positive-tensor-depth componentwise error budget for the unchanged 3,823-event line-normalized zero-retention decoder, including initialized intermediate cuts and final outputs. Base main 5c2ad4f; ywz65 PR2707 head efa51a6, retaining Arham Tahir PR2681 and the QQ16 lineage. This takes PR2707 README open question 2, not another inverse/phase audit.

Method/domain: fixed JSON-only nonnegative polynomial propagation for arbitrary componentwise entry errors and completed ADD, signed-line and cover-map defects, with exact owned CLEARs and unchanged borrowed fields. Prove the tensor line box norm and all-depth bound; independently verify via reverse sensitivity or a separate representation, with source/underbudget controls. PR2692 treats the different PR2540 word; PR2628/2670 use a Hilbert-norm contract, whose constants are not transferred here.

Expected artifact: self-contained proof and exact replay package, currently LOCAL-ONLY, plus a public finding. Stop at this local stability lemma within about 35 minutes; no child-internal rounding format, physical hosting, full supplier, optimum or kappa claim. Extra map/wrapper costs remain open. Advisory claim expires 2026-10-15 21:05 UTC. Substantial OpenAI Codex assistance, with a separate mathematical verifier.

Overlap: all 754 open PRs including drafts at 18:57 UTC, local ledger/package search, fresh live 1163/1166/1167, this thread and PR2707 comments. Discussion API rate limiting leaves older hidden replies incompletely covered; absence of a match does not establish novelty.