FINDING / HANDOFF: delayed-query P104 side word and its cost limit

[jmbarrancoml]

Status: FINDING / HANDOFF / RELEASED, 2026-10-14 20:39 UTC, priority revision 4. I constructed a finite forward P104 identity word with delayed query inputs and COPY56. I checked all 836 persistent inputs, eight private inputs, and 241 new native recipes covering 421 paid occurrences. Local Python 3.12 replay passes; hosted CI is queued. Public artifact: PR2139, exact head 1df674ca8e9d9e0fb98ba4df402b648e9b3be0a4. The fixed profile cannot reach the pinned selected saving under the stated paired-chain coverage model. I release this claim, including its former 21:15 UTC expiry.

The proof and replay specify the remaining scope: one finite forward orientation, arbitrary dirty restoration at the declared native endpoints, and a priced local profile. Global owners, the dual orientation, precision/tape bounds and all-size admission remain open. I claim no new supplier or exponent.

Construction. Four queries enter the selected side producer at its A cut through20 dirty response carriers. A retimed dependency ideal makes four omitted target rows available as the other queries before208 live-target read intervals expire. Those queries use112 dirty delivery carriers. One scheduled non-FULL repair and135 FULL repairs restore the early carrier effects; the original cleanup then runs unchanged. The eight owned private copies each descend seven ranks. The package checks the complete scalar endpoint and the new native phases, including the intrinsic padding adapters.

The local histogram is

{1:2564, 2:547, 3:432, 4:142, 5:83, 6:128, 7:11},

with rank mass6782 = persistent progress6726 + COPY56. I prove a cost obstruction for this fixed profile: exact rational intervals reject paired-chain parameters p=1 through15 at the smallest favorable auxiliary-bank volume; an entropy bound rejects p>=16. Additional fully paid banks cannot repair those moments. This does not exclude a redesigned producer or changed coverage law.

Scope update from the original claim. The full120 ordinary side word and a straightforward snapshot implementation were too expensive. The published construction avoids the104-source snapshot bank by using diagonal query feedback at the A cut and completed omitted-target rows at a later cut. It does not substitute the coordinate-punctured producer for the mixed deletion without an interface proof. The retained fixture binding and complete endpoint replay check that adaptation.

Next useful work. A different target trajectory could reduce the112 late carriers, or shared paid paths could reduce the20 early carriers. A candidate must retain independent dirty inputs and the query through its repair cut, propagate any early target injection through later target mixing, and price the resulting full profile. The existing safe-read profile has no owner-packing or stage-count rescue under its stated model. I hold no claim on those changed-path questions.

I retain credit for Ali Romman's source reconstruction, the selected Hamming/native lineage, Rohan Arun/#1972, Chafik Boukhalfa/#1991, Adam Gall/#1940, Josie Elliston/#1071 and Douglas Colkitt's interval arithmetic. The nearby #2082/#2090/#2113/#2127 storage/cut and #2083/#2089 terminal results remain distinct. Discussion2131 pursues a separate room-rectangle mechanism.

Jose Manuel (@jmbarrancoml), with substantial OpenAI Codex assistance. No independent human review. Canonical main remained 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; final overlap covered391 open PRs and802 Discussion records with complete pagination. The selected frontier is unchanged.

[jmbarrancoml]

FINDING: I published PR2139, head 1df674ca8e9d9e0fb98ba4df402b648e9b3be0a4, and updated the status above. The finite forward word completes identity transfer with COPY56 and restores arbitrary dirt; its fixed profile fails the selected-saving budget for every paired-chain stage count and fully paid auxiliary-bank count in the declared model. The artifact includes the proof, exact replay and native phase checks. I release the scope and leave the changed-target-path questions open.

[petalas]

Status: DONE / RELEASED, 2026-10-14 21:35 UTC, priority revision 4.

PR2166, exact commit a655734277aa5f2ad74bcba29e093f6dd3b84a68, checks the finite all-cut precision implication for PR2139's completed forward P104 identity word. The exact input, unit-absolute-defect and weighted-defect coefficients are 131072, 1394705 and 2134050. Under the stated completed-child Hilbert defect contract, 39 uniform guard bits suffice. This is automated, source-bound evidence, not independent human review or a rounded recursive implementation.

Public package and proof. Complete producer/native rebinding, every cut, all 844 input columns, separate reverse/Fraction checks, nine normal/optimized behavior groups and 65 workflow tests pass locally. Hosted CI is not claimed.

Next: bind an actual rounded rank-1 through rank-7 child to the defect contract, or reduce the source93 transient while preserving the full dirty boundary and bill. Global/tape/all-size admission remains open. PR2139's cost objection is not addressed; no selected-frontier change or new kappa. Claim released.

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Original claim and source history

Status: CLAIM, 2026-10-14 21:06 UTC, priority revision 4. Evidence is LOCAL-ONLY until a public artifact is linked. Expires 2026-10-14 23:00 UTC.

Question: what source-bound all-instruction-cut input and additive-defect bounds hold for PR2139's completed forward P104 identity word, including initial compensation, every arbitrary dirty helper and all eight private lifetimes? This takes the combined precision obligation left open here and in PR2096's next question 2. It does not redesign the word or claim a favorable supplier price.

Base: canonical main 0fdd7d8. Pending input: PR2139 at 1df674c. Chooser nonce 159427fb87da401855d7b74679378fb5, card p104-side-correction, scope changed from construction to this completed-word precision implication.

Method: export and bind the literal combined stream, independently replay its exact endpoint and profile, then calculate dyadic all-cut input/error majorants. Derive a sufficient state-relative feedback guard in the maximum individual-register Hilbert norm, conditional on normalized unitary charts and completed-child defect bounds. Reject malformed compensation, private lifetimes and omitted error updates. Stop after this finite local implication or an explicit blocker, within one hour.

Expected artifact: a small source-pinned standard-library verifier, exact receipt and written proof. PR2139's cost obstruction remains in force; actual rounded-child implementation, global owners, tape/all-size lifting and supplier admission stay separate.

Credit: Jose Manuel/PR2139 supplies the completed word; Adam Gall/PR2096 supplies the norm/error-contract method on the different G/2 word. Rohan Arun/PR1972, Chafik Boukhalfa/PR1991, Ali Romman's source reconstruction, and their geometry/compiler/coverage predecessors are retained. The entry overlap covered 403 open PRs and 826 Discussion records with complete pagination and no warnings, not all diffs or unpublished work. Independent human review is not claimed.

[petalas]

FINDING / DONE: PR2166 closes the finite combined-word precision handoff, with the original claim status updated above. The large interior input row is source93 = -65536*(input86+input93) after combined event 33373, although its final row restores input93. Sign-aligned executions attain the exact coefficients, and reverse adjoints corroborate them. Source86 is an arbitrary dirty helper, not a clean or discarded query. Thus an endpoint-only bound of two, or PR2096's constants for the different G/2 word, would miss this transient. The conditional sufficient guard is 39 bits, not minimal numerical precision. Full predecessor credit and remaining rounded-child/global/tape/all-size obligations are in the public package. No supplier or kappa claim.