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Research audit: F4 alternating trace is not by itself a phase-compilation obstruction (no new kappa) - #831

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Mister-Meeseeks merged 3 commits into
CrocSwap:mainfrom
Maximooch:penguin/scoped-math-audit
Oct 14, 2026
Merged

Mister-Meeseeks merged 3 commits into
CrocSwap:mainfrom
Maximooch:penguin/scoped-math-audit

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@Maximooch

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Research note / exact interface audit — no new kappa

Historical #620 extension-ring notes correctly observe that F4 Hermitian trace
forms are alternating, but use the absence of odd norms to exclude the complex
phase calculus. This scoped note distinguishes the orthonormal-basis method
from the already-documented alternating-compatible quadratic-phase normal form.
It does not construct an Eisenstein supplier or modify the historical report.

Adds only research/f4-alternating-interface/:

  • elementary trace-radical and complete-square arguments;
  • independent standard-library verifier: all Hermitian F4 matrices through
    dimension 3; all nonsingular alternating binary forms in dimensions 2 and 4
    with all even-valued quadratic refinements;
  • explicit even-weight ambient hyperbolic residual;
  • source pins, receipts, provenance, local claim and validation.

Reproduce from repository root:

python -B research/f4-alternating-interface/verify.py
python -O -B research/f4-alternating-interface/verify.py

Expected: 452 phase cases, 114752 exact kernel entries, four rejected controls.
Both modes give identical receipts. Standalone relocated replay and exclusive
output protection passed. Consulted sources are pinned by committed Git blobs,
not platform-dependent checkout line endings. Selected certificate unchanged.

Base: 7ee02b7; OS-random seed 42.
Credit Joel Pulikkan / GamingPuzzled, the endpoint normal-form authors, and
hipotures' alternating-block predecessor #41; see NOTICE.md and SOURCES.json.
Substantial OpenAI assistant/Penguin assistance disclosed.

Limitations: no full formal proof, no supplied fitting decoder/frame schedule,
no adapter/copy invoice, no physical owners or fresh supplier composition.
Existing Eisenstein copy-floor results are not invalidated. Full make verify,
selected cold replay and remote CI were not run or claimed.

Maximooch and others added 3 commits October 13, 2026 01:34
Add an exact standard-library trace radical and quadratic phase audit; no new kappa or supplier claim.

Co-authored-by: penguin-agent[bot] <penguin-agent[bot]@users.noreply.github.com>
Co-authored-by: penguin-agent[bot] <penguin-agent[bot]@users.noreply.github.com>
Co-authored-by: penguin-agent[bot] <penguin-agent[bot]@users.noreply.github.com>
@Mister-Meeseeks

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100-PR batch review at 66c3bc5c2eb5a2c066b1119310b29d26350e1dde.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: F4 Hermitian traces and alternating quadratic-phase compatibility; corrects an overbroad interface inference without constructing an Eisenstein supplier.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

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

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2 participants