Independent audit: confirm κ of #699 (0.001660666354374641) and #685 (0.001660339298410333)

[Rohansguliani]

Independent finite audit of the two newest κ-record PRs by Rohan Guliani (@Rohansguliani). Both submitted κ values are confirmed exactly. No mathematical, owner-map or arithmetic error was found. This PR does not change the selected bound.

PR	Reviewed head	Base / first parent	κ	binding b
#699 (jeremykothe2)	03e8d7ca494a083e5053cd6b1228f66b98414479	66849e1475c930fd7732b1a0067ffee7e1e95f60	0.001660666354374641	complex 0.001663428754540205730067
#685 (chafreaky)	5fc2a0c4e10558f09f03a8e42559dcf8e381e57e	17ce0c79b7b51c2634b439ea5a2b754f09909693	0.001660339298410333	complex 0.001663100609709845015347

Both records use the #589 bit supplier, c = 0.001733427039589844234749.

Base commit: 66849e1475c930fd7732b1a0067ffee7e1e95f60

Reproduce (one command, about 71 min on Linux, Python 3.13.7):

PYTHON=/path/to/python-with-numpy bash research/pr-record699-685-audit/replay.sh /tmp/new-output-dir

The command ended with exit code 0. It does the following:

• Freshly constructs and replays both packages. This includes Conditional κ = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word #699's strict global admission and two-engine outer-47 price, and all 20 stages of Conditional κ = 0.001660339298410333: four entrance promotions and 72 cold ends #685's verify.sh.
• Runs independent_check.py, which imports no repository code. It recounts frames and ranks from the raw gates, replays the exact rational scalar maps and Horner invoices, and checks the literal 72×504 owner maps. It also brackets b and c strictly within 10⁻²⁴ with its own rational log/exp enclosures and recomputes the κ grid point. It confirms that SW4 leaves Conditional κ = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word #699's end-of-B map unchanged on all 728 columns, and that Conditional κ = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word #699 and Conditional κ = 0.001660339298410333: four entrance promotions and 72 cold ends #685 occupy the same 36,288 physical slots.
• Rejects these negative controls: b ± 2·10⁻²⁴, κ + 10⁻¹⁸, and one moved owner offset.

The standalone #589 bit-circuit pipeline (research/e8-bit-p111-tuned/tune/verify.sh, with Boost) was also replayed separately. It reproduces the nine record in both PRs' byte-identical PR589-EXPECTED.json.

#699 has since gained f042731. It changes only the package README and MANIFEST, fixing the PLAN/OWNERS wording noted in #699 (comment). The audit stays pinned to 03e8d7c.

Credit: This audit builds on Jeremy Kothe's #699 and his #659/#676 line, and on Chafik Boukhalfa's #685. It also builds on icekylinx's #645, #664's promotions, PR635's local compiler/auditors and eumemic's merged #589. Their notices and credits are retained.

Scope: This is a finite replay. The inherited all-size, hosting, precision and analytic-transfer assumptions remain open. It is not a formal verification of the multiplication theorem, and it makes no packing-optimality claim.

License / AI disclosure: Apache-2.0. This audit was prepared with substantial AI assistance through Mux (OpenAI GPT-6 Astra and Claude Opus 5.5).

[Mister-Meeseeks]

100-PR batch review at ea3ceae40d5fa19dc0361d3f15546df0182459c4.

This remains open after scoped triage. Next review step: Research audit also edits generated ledger/contributor state. Reconcile numerical replay scope with current authoritative dispositions for #699/#685; do not overwrite the newer ledger.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.