Noncommuting workspace drift through a sign-character output

[Arham-Tahir64]

DONE — PR #1571, head 9dba8f255b5c491f08caf720664f13e19a99067f, from main bce54fb3f895cbe5cd4c0eb477c3afeed100190f.

The six-child S3 regular-workspace/sign-character construction is exact on arbitrary dirty inputs. Its complete source-only echo uses 240 instead of 372 ADD/NEG instructions, including both source calls, every child/inverse and workspace restoration. The declared complete group-operation boundary has sharp price six output negations. At child two the output is canonical while workspace carries a nontrivial three-cycle: an output checkpoint retains boundary price 6, while a workspace checkpoint needs 30.

Written proof, literal words, source pins, complete arithmetic/access/word-movement invoices, checkpoint plans and limits are in the package.

The standard-library registered Python 3.12.14 replay and nine optimized test groups pass. Python 3.14.6 agrees. Verification includes all 46,656 normalized endpoint-correct boundary schedules including entrance, all 729 ternary readers, five observer policies at three tariffs, 624 forward/inverse basis columns, twelve rational probes, twelve semantic controls, immutable-source/receipt corruption and relocation.

python3.12 -B scripts/research_package.py --package research/noncommuting-quotient-restoration

Scope: characteristic zero; fixed indivisible children; complete group corrections and output NEG. Opening the toy children permits cheaper direct evaluation. No actual supplier is identified, no new kappa or full multiplication proof is claimed, and physical frames/hosting, rounded precision/tape, all-size compiler and analytic transfer remain unrun. The selected frontier is unchanged.

Credit Ross Richardson PR1287, Sagar Thakrar PR1227/1199, PR1145's six-ADD cycle, mightyOil PR1203, Adam Gall PR1205, Aaron Wang/Navinor PR1155, PR889 and the retained lineage. Concurrent Hanson Sun / bbMisk PR1488, head 13d780ea51248ddd51901cd546b9f59adc76eb43, gives faithful two-dimensional S3 transport and explicitly distinguishes this sign quotient. General noncommuting transport is shared concurrent work; the nontrivial kernel checkpoint and fixed-reader boundary price are the scope here. PR1488 is credited, not replayed.

Final overlap: 718 open PRs and 218 Discussion body/comment/reply records, complete pagination of both. The task card records chooser nonce d43d0282092e46edce787623f2f939e8 and the persistent-boundary refinement. No priority or exclusivity is claimed. This advisory claim is released.

Prepared for @Arham-Tahir64 with substantial OpenAI Codex assistance in algebra, implementation, verification and writing. Apache-2.0; no independent human review or hosted CI success is claimed.