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Route Boolean-sector query families with O(n log n) ordinary work - #5658
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The published T7 sector family can use one query per block, but its generic compiler uses quadratic ordinary work. This package gives an explicit butterfly route for every
n=2^sand every number of disjoint blocks, with all ADDs and shifts charged.For the same input-preserving contract at 32 sectors, the circuit uses 994 ADDs and 160 pure shifts instead of 2,080 ADDs, with the same one query, 34 CLEARs, and 33 extra fields including outputs. The in-place variant uses one extra field and two CLEARs; the native projector gauge needs none. The query count is optimal in the faithful-sector model. The workspace and CLEAR counts are sharp only in the stated dyadic ADD/shift/query/CLEAR alphabet. Arbitrary nonunit scalar overwrites are outside that storage proof.
Validation: registered Python 3.12 normal and optimized replays pass: 28 full-column group-ring maps, five retained-input maps, 48 exact native-address cases, a reverse-adjoint oracle, five changed-word rejection controls, and a nonunit-scale scope control. All 15 committed files match working bytes; export integrity and a Git-free scientific replay pass. The general construction and polynomial prefix/suffix bound are proved separately from the finite tests. Full source-history preflight is unavailable in the shallow checkout.
This builds on PR5626, Dugongue's PR5578 T6/T7, PR5586 C8, PR5615, and their retained authors. Ali Romman with substantial OpenAI Codex assistance. No independent human review is claimed.
Canonical base
df0137efd35e11b4445734bf612bdd4c7ebc330c, priority revision 7. Fresh main and remote overlap checks found no competing sector-routing scope; sparse local coverage was supplemented by the all-main note search. The claim is in Discussion5623. This does not supply a profitable complete caller, physical tape price or native arithmetic-interior precision certificate. No new kappa; selected .00310045 is unchanged. The current baseline planning job has two unrelated missing-link assertions; hosted replay may remain blocked until those are repaired.