Bound shared phase-repair rank for independent groups

[Gonzalo-Mier]

Result

This package closes a bounded relaxation left open by PR #3220. For G independent direct-sum copies of its pinned rank-two port-zero defect, the joint defect has rank 2G. Any repair by additional caller-level phase children must therefore carry total rank at least 2G, even when repair children may span groups and routing is free. With each child rank at most 51 and 0 <= a <= 1/400, that repair costs more than G, while the retained residual-repacking allowance is less than 153G/160.

For the two-group integer relaxation, OR-Tools CP-SAT chooses one rank-four repair child and gives a lower-rounded cost of 3.986161, versus a two-group allowance below 306/160 = 1.9125. The standard-library replay independently reconstructs every exact integer-power objective floor and verifies the packing optimum by dynamic programming; OR-Tools is optional for the replay.

Scope

The direct-sum premise is abstract. This does not bind two actual T740 groups, prove their source spaces disjoint, cover repairs absorbed into original children, changed interactions, or provide a complete routing/stock invoice. It establishes no new kappa, supplier admission, or selected-frontier change. The latest conditional kappa observed in the 2026-10-17 overlap refresh remains PR #3200's 0.001734807021726127552033.

The final overlap query covered 274 open PRs and 2,011 discussion records with complete pagination and no warnings; it found no remote matches for the scoped terms. The canonical main refresh was unchanged at 463113d675af7410ac91d53a4fed51ec6494eb9a (priority revision 6). Related open question and attribution are recorded in PR #3220 and the mechanism-proposals hub.

Reproduction

python3 scripts/research_package.py --package research/shared-phase-repair-rank --check-only
python3.12 -B scripts/research_package.py --package research/shared-phase-repair-rank
python3.10 research/shared-phase-repair-rank/ortools_shared_repair.py

The registered replay passed, including the pinned source bytes, exact Gaussian-integer rank, all-parameter cost bound and dynamic-programming verification of the CP-SAT optimum. check_research_commit.py passed for commit 8ec29a31efaaa99b4f7823c2d9db2142a4c810c3.