[Matarener]

Requested by Mark · project thread

Change and mathematical scope

Status: independent verification plus a scoped proof; no new κ, no selected change. Assumption ID native_all_columns, selected word of #5599 (κ = 62009/20000000).

All 2,887 distinct paid chart changes Γ_b Γ_a^{-1}, the 540 helper normalizer pairs (2,923 distinct maps) and the 208 main adapters of the selected word equal their compiler-lowered recipes (Gaussian monomial · rank-r Fourier child · Gaussian monomial) entry by entry on dense 512×512 exact matrices, including the absolute phase. The column support 2^r gives r = |dim b − dim a|, the paid rank charged by the invoice (rank mass 6,014 over 3,447 occurrences); helper pairs are strictly productive with the author's profile. The certified recipes hash to the author's registered recipe_payload_sha256. Every one of the 3,711 distinct Gaussian monomial factors is realized as a fixed f-independent record list (#5445 grammar, at most 96 records, bound 171). The lift to every column multiplicity is the factorwise tensor power (#5442 lemma); on the first MOVE (event 9589, U = ((1+i)I + (1−i)X_11 Z_3)/2) the verifier shows the factorwise lift equals U^{⊗2} while the termwise lift of the closed form differs at widths 2 and 3.

Remaining obligations: the record tariff (compact-control Proposition, domain f ≤ p), the front/back control-field reservations of the #5599 caller layout, spectators and whole-job adapters; owned_erasure, compiler, precision_tape, analytic_recovery.

Task and overlap

Base commit 19fdb086ea96af9a9f87936a2b888e10af4ed810; inputs pinned by SHA-256 and git blob in SOURCES.json (the #5599 WORD.json.gz and RESULT.json, the vendored clifford_exact.py as candidate compiler, lift.py of #5445). Card uniform-transfer-audit, scope refined (TASK.json).

Nearest overlaps: #5442 (same certificate for the older #5413 caller), #5837 (scalar instructions of this word lift; asked about the 3,447 MOVEs), #5894 (traced the selected checker's signed-Pauli and |0> coverage, replayed one pair, and asked that a fresh census be justified as independent verification of existing coverage). Added value: that verification for every map and adapter of the current caller, by a method sharing nothing with the selected checker (no tableau, no sparse state column, no compiler semantics; dense matrices, one exact product per pair, support counts for the rank), the payload-hash binding, and the record lists of this word's factors. Checked PRs through #5973 on 2026-10-27: no other all-width census of the #5599 native layer.

Validation

python3 -m pip install numpy==2.3.5
python3 -B scripts/research_package.py --package research/p104-allwidth-native-certificate

Python 3.12, NumPy 2.3.5 (declared in VERIFY.json). verify.py ends with PASS_P104_ALLWIDTH_NATIVE_CERTIFICATE pairs=2887 distinct_maps=2923 helpers=540 adapters=208 monomials=3711 frames=1089 (304 s with four worker processes) and compares the rebuild with RESULT.json; test_verify.py rejects ten controls (PASS_P104_ALLWIDTH_NATIVE_CONTROLS faults=10: pinned-input drift, phase and offset mutations, reversed factor order, conjugated child, extra Fourier axis, uncomplemented Gram diagonal, termwise tensor lift, a Gaussian offered as a monomial, tampered RESULT.json). The harness reports PASS_REGISTERED_RESEARCH_PACKAGE. The NumPy arrays hold Gaussian integers below 2^40, asserted after every step, so all arithmetic is exact. Finite checks: dense equality at width one and the width-2/3 tensor controls; the all-f statement is the written corollary in PROOF.md. Not run: make frontier5599-verify, Lean, any physical tape simulation.

Credit

Ali Romman (#5599 word, invoice and registration; #5565 base via Pierre-Loic Doulcet / hexapode), Chris R / Clear1nsight (independent interpreter lineage), unpaidmoon (#5837), DLamdata (#5894, closed form of event 9589), zxv (#5428 target), Dugongue and icekylinx (Clifford engine lineage), Cinna Davis (compact-control notes), and the retained lineage credited in research/p104-helper-subspace-splits/README.md. Lifting lemma and record grammar: #5442, #5445 (Matarener). Prepared by Mark (Matarener) with substantial Claude Code assistance. Apache-2.0. No independent human or proof-kernel review.

Open next questions

1. Place these record lists and the rank-r children in the actual Raise conditional kappa to 0.00310045 with independent helper splits #5599 caller layout with the compact-control front/back reservations for every active slot pair, at the retained tariff, starting with event 9589 (the physical half for the current caller). Blocked by the source-bound layout of the Raise conditional kappa to 0.00310045 with independent helper splits #5599 physical caller.
2. Execute the compact-control rotation scheme bit by bit at small f, K, G (guard core audited by seed71/seed73/carry-repair/seed29; the complete scheme with chunk swaps is not executed). No blocker.

Workflow feedback (optional)

The 600 s per-command cap of research_package.py is not stated in the package documentation; a dense verifier that is exact but slow had to be parallelized to fit it.

🤖 Generated with Claude Code

https://claude.ai/code/session_011VhYmApWjLeEPa4dg2w4Hp