Finite construction: two-sided CK compensation saves 8,798 beyond target forests (no new kappa)

[RossRichardson]

Finite complex-supplier circuit construction; no new kappa. Combining a restored target forest with disjoint helper shears on the historical PR626 CK compensation saves 75,318 real primitives per complete orientation, including 8,798 beyond target forests alone. The transformed matrix is repriced; predecessor savings are not added.

Complete program	Original	Two-sided
Forward	224,938	149,620
Inverse transpose	224,986	149,668

The 106 target edges and 112 helper pairs include every preparation/restoration gate, source access, coefficient operation and clear. Compensation drops from 8,704 to 2,541 additions. All non-scalar events and paid children remain unchanged. Prefix bounds are 41/65 bits within the inherited 192-bit local allowance; exact denominator budgets remain 3/8 bits.

Reproduce

python3 -I -B research/complex-ck-two-sided/verify.py

Expected: PASS_CK_TWO_SIDED, saved_real=75318, additional_vs_target=8798, columns=716+9, controls=10+25, no_new_kappa.

Validation includes full literal primitive replay on 725 arbitrary input columns in both orientations, using Fraction and separately implemented integer-dyadic arithmetic; independent Prim/census verification; unchanged native emitter/frame/wrapper audit with 25 inherited controls; 10 new corruption controls; 13 package tests; isolated normal/optimized execution; minimal relocation; recompression; source/recipe/typed-receipt corruption and output preservation. Selected-record integrity and its five tests pass. No cold supplier rebuild, full repository suite, global admission, Lean or hosted-CI pass is claimed.

Exact base: f567884. OS seed 38, complex-supplier track. Complete search covers 12,544 target edges and 128,524 ordered helper-pair/sign cases, followed by one deterministic disjoint greedy pass; no joint optimality claim. Source hashes, historical SPEC binding, exact recipe, complete receipt, proof and local sprint claim are included. Only research/complex-ck-two-sided/ is added. The final overlap check found 705 open PRs through #915 and no competing two-sided CK contribution; no pinned sprint issue was available.

Credit David Awad #807 (b1a5c533a22c2665600102d872f6a84e0664a70d) for helper pairs and @dd-hemant #816 (133735a2cc2319c12ba5d786214b2217e083e7da) for target forests, following Sricharan Vagvala #749 and Oscar Fennell #759. No pending code is imported. Credit the unchanged icekylinx / DreamingOfClouds / Jeremy Kothe #622 / Chafik Boukhalfa #626 construction and retained predecessor lineage.

The selected conditional result remains PR799, kappa = 0.001661634653669567. No transport to X4 is claimed. Production integration needs an admitted typed compensation rewrite, refreshed bindings and complete global invoices/assembly; all-size/compiler, realization, hosting, precision/tape and analytic obligations remain inherited. Finite evidence is not a full multiplication theorem proof.

Prepared by Ross Richardson with substantial OpenAI Codex assistance, including separate AI arithmetic implementation and mathematical review. Apache-2.0; no independent human review claimed.