Source-bound OR-Tools screen for T740 idle-axis reassignment

[Gonzalo-Mier]

This source-bound package audits four idle children in the T740 schedule using exact eight-stream operator replay and OR-Tools. It reports a scoped negative result: no new κ, supplier admission or selected-frontier change.

Exact transfer census

The registered replay authenticates PR3148's T740 fill and checks all 112 port recipes for owner replica zero. All 21,504 eligible single-axis moves and all 5,376 paired moves change the exact Gaussian-integer operator at the relevant Fourier character.

The retained PR #3184 star artifact (head 6faefe1) sends axes [16,32,64] from child 10 to 12 and [128,256,4096] from child 10 to 13 for replica 0 / port 0. At each of the six moved-axis characters, its complete overlay equals the corresponding isolated one-axis overlay and differs from baseline. The package also isolates every nonempty same-centre star in this audited owner-zero class.

OR-Tools results

The optional rank-only CP-SAT model finds [51,51,51,39] from [48,48,48,48] with 12 moves per port, but each minimum-move representative fails exact replay. A second optional run (Python 3.10.12, OR-Tools 9.11.4210; about 47 minutes) enumerates all 256 Z4^4 phase deltas at each of 73 coordinate characters. In every character table for every port, only delta (0,0,0,0) preserves the exact matrix; the SHA256 of each complete per-port receipt is ed9ef60a17efb46b44a064986acf28935c7ab07a46ddc8007dc802bbc8200a83.

CP-SAT asks whether any rank-changing assignment can satisfy these equalities while assigning the 192 residual-axis tokens arbitrarily among children (8,10,12,13), with hosted axes fixed, final child bases orthonormal and ranks at most 51. It omits the per-axis translation and commuting gates, making it a broader assignment relaxation. All 112 models are INFEASIBLE. This is a finite-coordinate cross-check on the source-bound owner-zero fill, not an all-character symbolic theorem.

Related live results and limits

The final overlap refresh (2026-10-17 18:20 UTC) found PR #3204, which claims a broader written four-site rank-rigidity proof under the fixed schedule, and PR #3220, which analyzes added paid phase-child repairs in a bounded domain. This finite receipt neither replaces #3204's proof nor settles repair mechanisms outside its assignment model.

At that snapshot, the latest open conditional κ claim was PR #3200 at 0.001734807021726127552033; the selected κ remains 0.001672660197076918. This package does not validate or refute PR #3200's complete allocation or invoice.

Registered replay:

python3.12 scripts/research_package.py --package research/idle-star-paired-axis-census

Optional exact-coordinate run:

python3.10 research/idle-star-paired-axis-census/operator_ortools_screen.py

The optional long run stays outside registered CI so normal package replay does not require OR-Tools. Exact source pins, receipts, limitations and predecessor credits are in the package.