Independent verification: exhaustive binary residual and phase-interface census (no new kappa)

[ToikY]

Result and mathematical scope

Independent finite verification; no new kappa. A code-disjoint vector-set oracle checks the historical binary-frame compiler and parity-side repair for ambient dimensions 0 through 6. Completed coverage: 3,290 subspaces, 29,899 nondegenerate nested pairs, and 1,634,803 ambient phase inputs, each checked in both directions. It validates exact residual spans, characteristic-vector acceptance and returned orthonormal bases, including alternating endpoints and zero residuals. No defect was found in this finite domain.

Only research/binary-residual-exhaustive/ is added. Existing sources, default commands, selected frontier and upstream/ are unchanged. Selected conditional kappa remains 1661634653669567/10^18.

Validation

Python 3.10+, standard library only, from the repository root:

python3 -I -B research/binary-residual-exhaustive/verify.py
python3 -I -B research/binary-residual-exhaustive/test_verify.py

Expected marker: PASS_BINARY_RESIDUAL_EXHAUSTIVE subspaces=3290 nested_pairs=29899 phase_inputs=1634803 controls=10 kappa=unchanged.

The oracle uses complete vector sets and coordinate pairings, with no predecessor elimination or arithmetic imports. Each space has two presentations. A separate powerset enumeration of all 32,768 subsets of the nonzero F2^4 vectors agrees with the 67-space extension census; Gaussian-binomial dimension counts agree independently.

Ten explicit controls distinguish exact span from rank, orthogonality from unit norms, weight-three phases from unit phases, and forward from reverse edges. Faulty classification, characteristic, residual and orthonormal functions, omitted coverage, source drift and receipt-value/type corruption are detected.

Seven test groups pass normally and under -O, including a complete optimized replay in a minimal closure with spaces in its path. Unchanged predecessor sources are compiled explicitly with optimize=0 to preserve assertions; direct historical execution under -O is not claimed. Normal/optimized receipts are byte-identical. Three relevant predecessor tests and selected-record integrity pass. Eleven predecessor/context inputs have SHA256 and exact base Git-blob pins. Published tree equals the tested local tree.

Executed on macOS arm64 / CPython 3.12.14. No Linux, hosted CI, whole-repository make verify, selected cold supplier replay or Lean result is claimed. PROOF.md separates written mathematical arguments from finite implementation evidence. SOURCES.json, EXPECTED.json and VALIDATION.json retain exact pins, full census and validation scope.

Pins, overlap and attribution

Exact base: f567884. OS-random seed 83, independent-verification track. The local claim records three candidates and the exhaustive stopping rule. Main refreshed unchanged. No sprint coordination issue exists in the inspected open-issue inventory; final PR refresh reached #906 and targeted all-state binary-frame/residual searches found no duplicate.

Credit Douglas R. Colkitt for the historical compiler/parity repair and OpenAI's original manuscript for orthonormal absorption and signed phases. PR771 checks full-space isometry orders/invoices, PR831 studies F4 phase interfaces, and PR712 checks one cold wrapper; this all-subspace/nested-pair census adds distinct evidence and imports none of their pending code. Selected PR799/PR741/PR589/PR555 ancestry remains credited in NOTICE.md.

Prepared for ToikY with substantial OpenAI Codex assistance, including a separately implemented set oracle and scoped AI mathematical/code reviews. Apache-2.0; predecessor notices retained. No independent human review claimed.

All inherited all-size/compiler, realization, hosting, precision/tape and analytic obligations remain. This does not establish a new supplier, optimum or full multiplication theorem.