Research: restored CK helper pairs save 35,872 primitives per orientation (no new κ)

[davidawad]

Status

Finite circuit construction (verified circuit-cost improvement). No new κ is claimed.

Change

The selected #626 CK frame-zero compensation uses 124 disjoint temporary signed-unit helper shears to reduce both complete scalar programs by 35,872 real-component primitives per orientation (forward 224,938 → 189,066, backward 224,986 → 189,114; full scalar macros 21,936 → 19,036). Every source read, coefficient operation, helper preparation and restoration is charged; every dirty helper is restored before the entry adapters.

Exact arbitrary-input replay (all 716 logical columns plus a private input column, both orientations), unchanged non-scalar events, native frame/wrapper checks and 31 rejection controls pass; 11 focused tests pass with no failures or skips. Prefix bounds remain within the inherited 192-bit allowance.

Only research/complex-ck-helper-basis/ is added. Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60 (current main).

Reproduce

python3 -I -B research/complex-ck-helper-basis/verify.py --out /tmp/ck-helper-replay

Expected final line:

PASS_CK_RESTORED_HELPER_BASIS pairs=124 real_saved=35872 columns=716+1 orientations=2 controls=6+25 kappa=unchanged

Scope and open obligations

This is a finite circuit construction. The paid recursive profile is unchanged, so this scalar saving alone does not supply a better recurrence exponent. Production bindings, an admitted typed compensation rewrite, and global owner/invoice/assembly receipts remain separate obligations, as do the inherited all-size, realization, hosting, residual, precision and analytic assumptions. Certificate success is not a formal verification of the multiplication theorem. Repository-wide make verify, full cold supplier regeneration, remote CI and Lean were not run for this package.

Credit and overlap

Builds on the #622/#626 supplier lineage (icekylinx, DreamingOfClouds and retained predecessors). Pending #749 supplies related JP8 target-basis work; #769 shares CK coefficient preparation; #787 composes other CK coefficient-lowering and cleanup-sharing savings. This contribution instead changes CK helper columns; no pending implementation is imported and no combined saving with those PRs is asserted.

AI disclosure

Prepared with substantial AI assistance (OpenAI Codex) and submitted by David Awad. No independent human review of the mathematics is claimed. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at b1a5c533a22c2665600102d872f6a84e0664a70d.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Restored signed-unit helper-basis changes: arbitrary-input complex maps and primitive savings; generalized D interface/global admission not completed.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.