[mihir-s-05]

PR #5369 left an open request for a separate audit of its native tensor identity criterion. This reviews Sections 2, 3 and 5—phase-character realization, affine-bucket separation and residue quantifiers—and adds a sharp one-axis result: widths 3,4,5,6 suffice, and both four tests and maximum width six are necessary.

The proof and scope find no gap in those general implications under the written hypotheses. The one-axis evaluation rank is 2 min(f+1,4); an explicit nonzero residual vanishes at all positive widths below six and has entry 16 at width six. This sharpens the source's sufficient one-axis window without disputing its general theorem. A separate implementation imports no predecessor executable or arithmetic module.

Package and reproduction · canonical claim/result · original handoff

Validation at head 5fe6693dd023cedddb0972f1006d7fa50ba94595:

• Complete exact enumeration of 391,275 multisets / 2,192 phase characters through three axes; 29,760 literal phase-generator probes and 200,378 affine-map restrictions.
• All 32 one-axis group elements; exact Gaussian rational ranks from 2,044 literal matrix-entry rows at widths 1..9. Four-width windows starting at 1, 2 and 3 have joint ranks 26, 30 and 32.
• Native Windows / CPython 3.12.0 normal and optimized reports agree. Registered replay passes. Twelve deliberate regressions are rejected at their named mathematical or source-hash checks.
• All 12 package/input files match committed bytes. Official export integrity and complete normal/optimized replays, including mutation controls, pass in a read-only Git-free tree with empty PATH; all file hashes stay unchanged. Planning selects only this package. Whitespace and the current selected metadata baseline pass.

Exact result · mutation receipt

python -I -W error -B research/native-cutoff-independent-audit/verify.py
python -B scripts/research_package.py --package research/native-cutoff-independent-audit

Limits: this is an agent-assisted mathematical audit with independently written finite checks, not independent human or formal-kernel acceptance. Section 6's complexity reduction, the predecessor's general compiler/native implementation, event8814 adapter and physical supplier obligations remain unreviewed here. No selected cold replay or full-history provenance preflight was run. Higher-dimensional minimum cutoffs and full nonmonomial Cliffords are separate. No new kappa or selected-frontier change.

Started from and refreshed against canonical main 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority revision 7. Final overlap at 06:22 UTC covered 378 open PRs, 4,797 Discussion records and all 7,402 tracked base notes, with complete reported pagination/inventory. Hiroki KUMAZAKI's concurrent two-axis claim is complementary; this package does not claim its representation-kernel result.

Ali Romman retains the general theorem and witness construction. Credit Jose Manuel, ywz65, Chris R, Douglas Colkitt, JoyboyBrian, Cinna Davis, zxv, Krzysztof Wójt and the retained source lineage. Binary symmetric factorization, Fourier inversion and central projectors are classical. Prepared for Mihir Srivastava with substantial OpenAI Codex assistance, one agent; Apache-2.0. Frozen sources and the existing archival review disposition are unchanged.