Scoped negative result: R420 split target reads cannot lower the paid moment

[thakrarsagar]

Splitting the selected R420 bit word's final three-source target gates into separately framed reads cannot lower the paid recursive moment. This is a scoped negative result / research note, with no new κ.

For each of the 120 targets, all six source orders and all admissible real read frames yield eight legal schedules. Six preserve the baseline profile; two replace the pair of ranks (5,1) with (4,2), increasing the moment by 2^p + 4^p - 1 - 5^p > 0 for every 0 < p < 1. Source cleanup is included. Disjoint source sets extend the result to all 8^120 simultaneous choices and arbitrary interleavings within the final read segment.

This extends the explored domain beyond @yuj1r0's #661, which freezes the 837 gates and their operand lists. It does not reprove that fixed-gate result. Earlier frames, scalar circuits, COPYs, full-frame cleanup and endpoints remain fixed. The full original and all-early profiles both have 2,949 paid calls and rank mass 5,112.

Only research/r420-split-target-reads/ is added. It contains the proof, exact certificate, source pins, two independent standard-library checkers, local sprint claim and validation record.

python3 -B research/r420-split-target-reads/check.py
python3 -B research/r420-split-target-reads/independent_check.py

Expected final lines:

PASS_R420_SPLIT_TARGET_READ_BOUND targets=120 schedules=8^120 controls=4 kappa=unchanged
PASS_INDEPENDENT_SPLIT_READS targets=120 candidates=5760 legal=960 baseline=720 promoted=240 rejected_first_D6=240

Both pass on macOS arm64, CPython 3.14.8, in normal, optimized and isolated modes. The primary integer-arithmetic implementation replays every one of the 660 dirty-input columns for both words. The independent Fraction implementation exhausts all 5,760 local candidates. Four built-in negative controls cover illegal frames, a missing read, shared sources and omitted cleanup cost; separate mutation checks reject changed source bytes and a changed certificate. Selected-result source binding and staged whitespace checks pass. A separate Codex worker reviewed the proof and implementations without finding a concrete defect.

Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. PR543 source: 2065fe4f72a914d907f1046603f5a36f17018535; its word's Git blob matches the base. PR661 scope reference: 9ca7aa3ab0a3260a2f36ac86b9911a31fd88bd89. OS-random assignment seed 3, bit-supplier track. No pinned coordination issue existed, so the claim is local. Final overlap refresh through #717 found no competing split-target-read result.

Credit: eumemic's PR543/493 word and cleanup, Dylan Crow's PR370 E8 decoder, DreamingOfClouds' PR510 pricing lineage, and Tuomo Kiiskinen / yuj1r0's PR661 fixed-gate scope. Prepared for Sagar Thakrar / thakrarsagar with substantial OpenAI Codex assistance, including independent computational checking by a separate Codex worker. Apache-2.0.

Repository-wide make verify, the unchanged full frontier replay and remote CI were not rerun for this standalone addition. This is a finite-family proof with exact computational evidence, not a Lean proof or a discharge of the inherited compiler, physical, hosting, precision, tape or analytic obligations.

[Mister-Meeseeks]

100-PR batch review at 688258f863410419d10e34b0b3014b91cdce632c.

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

Reviewed scope: Complete target split-read frame quotient census; alternative rank split has strictly worse concave moment in the stated domain.

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.