DONE: independent integer-root audit of nine frozen packing ceilings (PR1632)

[bbMisk]

DONE — PR #1632, exact head 225b334a2449189de6f9d1e2f69a236d43cbbb9b.

All nine frozen PR1264 brackets pass the separately written integer-root engine: 18 strict signs at 96/192 exponent/fractional bits and the same 18 at 128/256. Twenty-one original JSON blobs reproduce all fourteen aggregate/idle splits, including W7's exact denominator-333 counts. No numerical discrepancy or new kappa was found. The original common cap kappa < 0.001687314840 is independently corroborated only under its stated model.

Every call count is tied to an original receipt field. Ten live counts are explicit; four (#1124/#1130/#1178/#1195) remain derived from W=896N/9 and are marked as such. Using W7's README display rounding changes the lower-endpoint sign; the predecessor's actual exact calculation is correct.

Registered Python 3.12.13 replay, 13 test groups, 14 semantic controls, 2,640 direct algebraic power comparisons, 72 zero-saving costs, optimized read-only relocation, retained census replay and the selected-record check pass locally. GitHub's 61 checks were queued when last inspected; no hosted pass is claimed. The contribution was rebased onto 0a201997 with all audited inputs unchanged. Source provenance, full exact intervals, proof of enclosure, predecessor authors and the remaining live-inventory question are in the package.

No physical supplier, owner/frame reconstruction, outer/all-size/precision/analytic or full Lean proof is claimed. Credit Douglas Colkitt's PR1240/1264, PR1012, all original construction authors, and the prior integer-root methods in PR706/1577. Claim released.

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Original claim (completed):

CLAIM — independent verification of the frozen PR1264 packing-ceiling census

Question: Do all nine frozen per-call paid profiles retain their stated adjacent 10^-15 relaxation brackets when checked with separately written integer-square-root power bounds, and do all fourteen aggregate/idle splits match their original pinned source blobs?

Base: main ee055dc. Predecessors: Douglas Colkitt's PR1240 and PR1264; PR1012 coverage law; selected Rohan Arun / Jeremy Kothe / Hao Yan construction lineage. Task chooser independent-moment, nonce 488b8bb97d866ded02e80a47a4e9d7e1.

Method/domain: frozen PR1264 SNAPSHOT.json only, all fourteen claims/nine profiles including W7 rational counts; selected PR1094 split as an additional control. Integer fixed-point dyadic exponent brackets and repeated isqrt; no imports of predecessor numerical or extraction functions. Check both strict endpoint signs, source hashes, accounting identities and semantic corruptions. This is independent corroboration; integer-root methods have precedents in PR706/PR1577. PR1605 independently checks the baseline bracket as part of its different rank-one block budget question; PR1606 varies the port count.

Expected artifact: research/independent-queue-ceilings, exact receipt, proof of enclosure, source pins and registered standard-library replay. No new supplier, kappa, physical replay or changing-queue census claimed.

Claim expires: 2026-10-14 06:12 UTC. Prepared by Hanson Sun (bbMisk), with substantial OpenAI Codex assistance.