Finite construction: CK helper-run sign normalization saves 224 primitives per orientation (no new kappa)

[RossRichardson]

Finite complex-supplier circuit construction; no new kappa. Deferring negations inside same-frame helper runs, then paying every boundary restoration, saves 224 real primitives per orientation of the historical PR626 CK word after accepted PR696 lowering.

Complete scalar projection	PR696	Replacement
Forward	169,618	169,394
Backward / inverse transpose	169,634	169,410

The complete census checks 2,219 runs per orientation. Fourteen nonzero-frame helper runs each save 16 real primitives; 2,205 have zero cost change. All source operations, coefficient preparation, copies, clears and boundary negations are charged. Paid children and non-scalar events are unchanged. This does not change the selected #799 result, whose conditional kappa remains 0.001661634653669567.

Reproduce offline, standard-library Python 3.9+:

python3 -I -O -B research/ck-sign-normalization-seed22/check.py

Expected: PASS_CK_SIGN_PACKAGE runs=2219+2219 columns=725 saved=224/224 kappa=unchanged.

The Fraction interpreter checks the complete scalar projections on 725 arbitrary input columns, every boundary, expected final shears, helper restoration and private clearing. A separately written integer-dyadic interpreter and event splitter check every run as a full arbitrary-input operator and every candidate prefix row modulo sign. Both stream hashes and counts agree. Scalar-projection row-l1 maxima remain 5120/4847 and fractional depths 3/8. These are finite scalar checks; physical frame/Clifford events are not executed by these interpreters.

Validation passes under isolated optimized CPython 3.14.6 and 3.9.6: 56 actual-run mutants, five toy adverse controls, boundary segmentation, copy-fanout cost growth, minimal relocation, gzip repackaging, source/receipt corruption and selected-record integrity. Package tests: python3 -I -O -B research/ck-sign-normalization-seed22/test_package.py. The generic proof explicitly accounts for cases where sign propagation increases cost; no universal savings or optimum is claimed.

Only research/ck-sign-normalization-seed22/ is added, including proof, exact certificates, source pins, local claim, validation and AI disclosure. Base: f567884. OS assignment seed 22, complex-supplier track. Refreshed main 91a2094f2e022930069e8cfdc810a3ea1b81cd09 retains all four consumed input pins and the selected certificate. No pinned sprint issue existed.

The pre-submission refresh inspected 707 open PRs through #917. #807/#816/#917 change CK frame-zero compensation, #860 shares signed coefficient work, #750 relocates a cleanup scale, and #883/#916 concern selected-X4 preconditions/admission. This contribution instead normalizes signs in historical CK nonzero-frame helper runs. No pending code is imported and savings are not assumed additive.

Credit Sagar Thakrar #696, icekylinx, Jeremy Kothe #622, Chafik Boukhalfa #626, DreamingOfClouds, eumemic, Rohan Arun and the retained predecessor lineage. Prepared by Ross Richardson with substantial OpenAI Codex assistance, including separate arithmetic implementation and AI review. Apache-2.0; no independent human review is claimed.

Native physical admission, typed production integration, fresh global owner/invoice/assembly bindings, and inherited all-size/compiler/hosting/precision/tape/analytic obligations remain open. Full repository/cold supplier suites, Lean and hosted CI were not run. Finite circuit evidence is not a full multiplication theorem proof.