Research: factor center quarters and certify the adapter-cost limit (no kappa)

[ssteeper]

The selected #626 CK and JP8 programs each use 224 signed quarter-coefficient center taps. Factoring the quarter once into each of the eight private centers saves 864 real scalar primitives per orientation, with exact recursive-call inputs, dirty-input restoration and prefix bounds preserved.

Status: finite circuit construction and scoped cost audit / research note; no new kappa. The complete accounting matters: the literal rewrite adds eight scale macros, increasing the generic adapter allowance by 128. The conservative local bound therefore increases by 3,319,594,144 for each provider. This is not a net supplier-cost improvement; the package certifies both the scalar identity and that integration limit.

Scalar program	Original primitives	Factored primitives
CK forward	224,938	224,074
CK inverse-transpose	224,986	224,122
JP8 forward	257,232	256,368
JP8 inverse-transpose	257,280	256,416

The scale occurs after the forward center descent and before the reverse ascent. No commutation with a recursive operator is assumed. A negative control preserves scalar endpoints while changing a recursive-call input, and is rejected. Every source copy, coefficient preparation, scale, clear and recursive child remains charged. Coefficient work is still cleared after each addition. The complete local invoices, original source bindings and unchanged paid profiles are included in the exact receipt.

Only research/complex-center-quarter/ is added: proof, deterministic construction, exact receipt, 14 source pins, integer-matrix crosscheck, focused failure tests, validation record and local sprint claim. The selected frontier and upstream/ are unchanged.

Reproduce

python3 -I -B research/complex-center-quarter/verify.py

Expected final line:

PASS_COMPLEX_CENTER_QUARTER programs=4 centers=32 saving=864_each columns=724 controls=32+50 invoice_delta=+3319594144 kappa=unchanged

Passed on Windows, CPython 3.12.10, standard library only. Verification covers all 724 formal input columns in each original/candidate program; arbitrary private work at every changed block; the unchanged native frame/wrapper auditor and its 50 controls; and 32 new block controls. A separate integer implementation checks 57,600 matrix entries and 32 clear omissions. Five focused tests, isolated optimized execution, a minimal relocated checkout with spaces, gzip repackaging, source/receipt corruption, output preservation, selected-record verification and staged whitespace checks pass.

Provenance, overlap and limits

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. OS seed 35, complex supplier; JP8 first and center 3 for the initial witness/controls. Selected #626 is pinned at 660de893d27bb7abd1d5b01b1640207528a5c851, with #622/#623 and #543 dependencies recorded. No pinned coordination issue exists, so the claim is local.

The pre-submission refresh covered 602 open PRs through #783; upstream main still equals the exact base. New #776's fixed-order A/B frame exclusion leaves scalar rewrites and changed centers outside its scope and does not overlap this experiment.

Concurrent #755 by @taizaki69 is explicitly credited: its coefficient reuse also covers the 224 forward JP8 center taps. This adds the reverse common-target gather, CK coverage, recursive-input equality and the complete extra-macro cost audit. It claims no priority or stronger primitive saving for forward JP8 centers. #745 motivates arbitrary private-center coverage; #750 relocates a live cleanup scale; #696/#723/#734, #722/#739/#751 and #769 use different coefficient lowerings or reuse classes. No pending implementation is imported and no additive saving is asserted.

Credit to icekylinx, Jeremy Kothe/AtomScout, Chafik Boukhalfa, DreamingOfClouds, Dominik Scholz, Dugongue, Rohan Arun, eumemic and the retained predecessor notices. Prepared for @ssteeper with substantial OpenAI Codex assistance, Apache-2.0. Both checking implementations were written in one AI session; no independent human review is claimed.

The experiment stops at this verified local circuit and cost result. A grouped center-microcircuit admission rule, global invoice/hosting replay and production integration are separate work. All inherited compiler, realization, precision/tape, recovery and analytic assumptions remain. Full make verify, cold supplier regeneration, Lean and remote Linux CI were not run or claimed. Finite replay is not a formal multiplication theorem.

[Mister-Meeseeks]

100-PR batch review at c6ae38d9f5a13c53dab623fd6947f08d92173287.

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

Reviewed scope: Center quartering saves 864 primitives but increases conservative adapter invoice; retain negative complete-cost conclusion, no claimed frontier gain.

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.