Research construction: restored X4 target pairs save 33,800 primitives per orientation (no new kappa)

[ToikY]

Finite complex-supplier circuit construction; no new κ. The selected PR799 X4 word’s zero-frame arbitrary-helper compensation shrinks from 6,320 to 3,276 additions, including all target preparation and restoration. Both complete emitted programs save 33,800 real-component primitives under the unchanged binary-Horner lowering.

Full scalar program	Original	Candidate
Forward real primitives	193,162	159,362
Inverse-transpose real primitives	193,210	159,410
Scalar macros, either orientation	19,197	16,153

The 56-pair schedule implements T⁻¹(Ty + TCh) = y + Ch with arbitrary target/helper dirt. All source accesses, coefficient work, basis changes and clears are paid. No helper is written by the replacement. Every non-scalar event and paid child is unchanged. The reverse positive prefix rises slightly; budgets stay at 55/72 bits.

Reproduce with Python 3.10+ and the standard library:

python3 -I -B research/complex-x4-compensation-pairs/verify.py
python3 -I -B research/complex-x4-compensation-pairs/test_package.py

Expected main marker: PASS_X4_COMPENSATION_PAIRS pairs=56 compensation=6320->3276 saved_real=33800 columns=728+9 orientations=2 no_new_kappa.

Verification covers every literal primitive on 728 logical plus nine arbitrary private input columns, both orientations; an independently implemented sparse integer/dyadic engine checks the full baseline/candidate logical words and compensation boundary. Public dirty helpers restore; inherited private centres/coefficient work erase via charged CLEARs. Nine focused tests pass normally and under -O, including corruption controls, recompression and standalone relocation. A missing-preparation control passes helper-only checking but fails arbitrary-target checking. Selected-record integrity and its five existing tests pass.

The complete 24,864 ordered target-pair/sign census has 2,978 profitable scores; one seed-39 greedy disjoint pass selects 56 pairs. Recipe, census hash, complete prices, prefix bounds and program hashes are reproducible. No matching/circuit optimality claim.

Exact base: f567884. Inputs are unchanged accepted integrated799-replay.tar.gz members, matching PR799’s exact canonical/program pins. Only research/complex-x4-compensation-pairs/ is added. Current main was refreshed unchanged; final PR inventory reaches #897. The API-published tree equals the tested local tree.

Credit Sricharan Vagvala’s #749 for the rational restored target-pair mechanism on earlier JP8, following the #713/#716 binary work; its implementation is not imported. Credit Jeremy Kothe #799, Chafik Boukhalfa #741, icekylinx’s gauge44, and retained compiler/cold/owner contributors. Concurrent Philipp (@mightyOil) #883 changes the preceding 168-macro precondition, which is byte-identical here; its code/saving is not consumed and no combined saving is claimed. #864 frame-only exclusion has different scope.

The accepted conditional κ remains 0.001661634653669567. Production integration needs a typed alternative-compensation step and refreshed bindings, global hosting/invoice and assembly admission. No full supplier cold replay, repository-wide suite, hosted CI or Lean multiplication theorem is claimed. All-size/compiler, realization, hosting, precision/tape, analytic transfer and bit H1–H5 remain inherited.

Prepared for ToikY with substantial OpenAI Codex assistance, including a bounded delegated integer-checker implementation/review. Apache-2.0 and predecessor notices retained. No independent human review claimed.