Independent audit: rank-two defect and dirty cleanup of three staged entries

[tekuuu]

Independent mathematical audit of PR #4076 at 9744f9df268590295a9872b1952c695a678192b9; exact canonical base bb4bccbf42844d2801487450727c2f63e10d1d0f.

The three staged entries have a common, explicit register-coefficient rank-two defect before cleanup on both providers:

δ417 = (h608+h609)/2       δ565 = h600/2
δ610 = −h608−h609         δ602 = −h600

All other rows are unchanged. Inputs denote original arbitrary helper fields. All eight subsets compose without cross terms. Every subset realizes the required target update and returns all 91 arbitrary dirty private fields after its regenerated projected cleanup. The prefixes themselves differ. For D-dimensional fields the full defect rank is 2D; this does not imply a physical two-role saving.

This provides small reusable staging witnesses and new-source independent evidence beyond the existing binary ledger and retained interpreter replay. algebra.py executes no predecessor Python and works over the exact rational free-group algebra, with no native-operator commutation assumed. PROOF.md states the identity, soundness argument and cleanup boundary. A separate raw-word evaluator tests noncommuting 2×2 operators against the actual literal cleanup.

Validation:

python3.12 -B scripts/research_package.py --package research/staged-entry-release-audit

Expected: PASS_STAGED_ENTRY_RANK_TWO_DEFECT (2 providers, 16 subsets, 723 full-state blocks, 28 rejections), PASS_NONCOMMUTING_STAGING_ORACLE and PASS_STAGING_ALGEBRA_CONTROLS, followed by registered-package success. All three registered commands pass; official 16-file committed-byte/source-history and export/check pass. All three commands pass normally and under -O in a read-only Git-free export with empty effective PATH; all 17 files retain bytes, modes and inodes. Local Python 3.12.14; hosted CI is separate.

Four exact source words are retained and checked by SHA256/Git blob. PINS.json records original PR paths/head; publication history authenticates the local freeze at d39e1a8d3685e711e6a13658df3cfeda175bfc7f. The pending predecessor is not an ancestor, and source-history preflight does not claim otherwise. No source or selected-frontier file changes.

Scope: finite exact word/composition audit, not formal-kernel verification. Hybrid subsets have no frame/owner admission. Native Gaussian phases, numerical precision, physical source/owner/tape costs, complete supplier/outer admission and the later #4085 receiver-sharing construction are separate. No new κ is claimed. TASK.json records the next useful compiler question and blockers. Final overlap refresh found #4085 but no duplicate defect factorization.

Credit Rohan Arun/#4076; Ross Richardson/#3605, dataisfire/#3734, ChaloupeMusic/Erwan Secousses/#3949, Dugongue/#3945; Sagar Thakrar/#3687, roger-sato/#3693, Arham Tahir and the retained source/compiler/cleanup lineage. Complete source notice retained. New factorization, implementation and checks by Tekalign (tekuuu) with substantial OpenAI Codex assistance; Apache-2.0. No independent human acceptance is claimed.