[mihir-s-05]

PR #4457 leaves open whether the actual complex caller satisfies the stage-zero premise [D0,Q]=0. This adds one scoped proof and independent exact checker in research/stage-zero-commutation-audit/, starting from current canonical main 2a13eb1827784206202db90e5dc8327cf8a250db.

For the source-specified Gaussian C_a=((1+i)I+(1-i)T_a)/2, XOR translations commute, so the actual port operators satisfy D0 Q = Q D0 = F9. The identity lifts algebraically to every positive column multiplicity. The checker binds all 112 port normals, the native entrance/exit spaces, 448 initial caller maps and #4440's retained p17 initial call, without importing a predecessor evaluator.

There is a useful qualification to the suggested tensor factorization: every recorded rank-eight normalization needs its nonzero translation. The exact identity is D0=T_t product C_b. At port 0, dropping t=15 gives coefficient error -1/16 on input/output address 0. Keeping the translation preserves commutation; no existing supplier bug or new cost saving is asserted.

Evidence

• 114,688 exact Gaussian-dyadic commutator coefficients across both conjugate orientations; 57,344 independent Fourier-character comparisons.
• 338 semantic/binding rejection cases: missing translation, wrong inverse, a genuinely noncommuting phase, wrong port and altered initial map.
• Registered Python 3.12 replay and metadata/source pins pass, standard library only.
• Git-free -I -O -B export reproduces the exact receipt and rejects changed source bytes and a changed receipt.
• Committed-byte/source-history preflight passes for all 15 package/input files at 82c7db427100033aa1275ecdb16ebc2e2ef10b91.

Reproduce:

python -B scripts/research_package.py --package research/stage-zero-commutation-audit
python -B scripts/check_research_commit.py --package research/stage-zero-commutation-audit --check-source-history

Scope and remaining limits: this proves the named implication for the source-specified physical reference operators. Full native/adapter realization for arbitrary columns, rounded implementation, BIT, cost accounting and the outer theorem remain separate obligations. No full selected cold replay, independent human review, formal proof-kernel verification or new kappa is claimed. The selected baseline orientation command stopped on an omitted claim file in the sparse checkout; that limitation is recorded in TASK.json. Hosted CI is pending.

Coordination and credit: canonical claim and handoff. The submission refresh covered 317 open PRs, 3,318 Discussion records and every tracked top-level README/TASK note. #4457 already covered the transport audit initially considered, so this follows its explicit open question 1; #4455 and #4448 remain complementary. Credit to Mark/Matarener, zxv, Cinna Davis/1337isnot1337, Jacob Alan Sussman and the retained QQ16/native phase lineage, including ywz65. Prepared for Mihir Srivastava / mihir-s-05 with substantial OpenAI Codex assistance; no subagents. Apache-2.0. No merge or selected-frontier change.