Research: borrowed-source Gray mask fanout

[1337isnot1337]

Contribution

A borrowed source row can travel through three parity masks and fan each one out to arbitrary target rows, then return to its arbitrary input value. In the exact 12-row instance, the closed Gray tour costs 13 row ADDs, compared with 21 independent target ADDs.

The target boundary is

X_i' = X_i + A + B
Y_i' = Y_i + A + B + C
Z_i' = Z_i + A + C       (i = 1,2,3)

with A, B, C, and all nine target rows arbitrary at entry. The anchor schedule uses four charged source transitions and nine target writes. The transition path is minimal within one-anchor schedules that visit the four required mask states and write each target once. No unrestricted CNOT optimality is claimed.

Cost and scope

At row width L, the local bill is 13L versus 21L bit XORs, with 13 versus 21 source-row reads and destination-row writes. The complete restoration is included. No clean row, copy, extra recursive child, frame change, or precision operation is used. The abstract row-register model has no tape-head or hosting cost.

This is a local XOR-network construction. It has not been located in a source-pinned multiplier word, admitted as a supplier, or integrated into the selected paid profile. No kappa change is claimed.

Reproduction

• python3 -I -B research/borrowed-source-gray-mask-fanout-seed9b2fe133/verify.py
• python3 -I -O -B research/borrowed-source-gray-mask-fanout-seed9b2fe133/verify.py
• python3 scripts/research_package.py --package research/borrowed-source-gray-mask-fanout-seed9b2fe133 --check-only

Both local verifier modes pass all 4096 one-bit arbitrary-dirty inputs, inverse execution, four failure controls, and exact 21-versus-13 accounting. Package metadata and base pins pass. Local runtime is CPython 3.14.7; Python 3.12 is unavailable here, so the registered 3.12 replay remains for CI.

Assignment and overlap

Cycle 45 accepted seed 9b2fe13334259f250375373f4f2b3806, track bit-mechanisms, task bit-helper-contract with scope changed. Exact research base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; priority revision 4; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

The full claim and current handoff are in Discussion #2270. Nearby work and scope distinctions are recorded in README.md and SOURCES.json, including PRs #2241, #1968, #2259, #1937, and #2045, plus earlier fixed-mask dirty-helper fanout. The final overlap refresh at 2026-10-15 03:05 UTC paginated 495 open PRs and 980 Discussions without warnings and found no exact mask-tour match.

Prepared by Cinna Davis with substantial OpenAI Codex assistance. No independent human review or proof-kernel verification is claimed.