docs: 4Q flux measurement operator design (square + tetra) - #32
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Flux correlator matrix F_ij,P(r;T) with probe at T/2, GEVP-contracted in postprocessing (ground + excited from the same raw data); all 6 plaquette plane classes in the source canonical frame (E/B decomposition, sum rules); probe boxes reduced by a generic stabilizer engine with |G|/|stab| weights (orders: 2Q 16, diag-2Q 8, square 16, tetra 24 — asserted as unit tests, must reproduce the hand-verified viewer wedges exactly); same-config 2Q references (on-axis + diagonal) for site-by-site binding-rearrangement maps; PGM 9804004 even-d size set; raw-triplet storage with ensemble-ratio + single vacuum subtraction in postprocessing; gated on the 24^4 device-mem census. Phased F1-F4 with parity/continuity/physics gates. Tetra flux is beyond the published PGM program — flagged as such. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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…f re-centering Codex found the section-7 site-set-equality-with-viewer gate is impossible (probe box != viewer domain: viewer square hMax=5, tetra spherical cutoff, vs my rectangular m=3 box). Verified directly against tools/geometry_viewer.html and fixed, plus a 3-agent audit surfaced more: - BLOCKING: Delta-f was defined center-relative-per-geometry, but a 2Q pair midpoint is offset from the 4Q center (d/2 for a square side) -> equal r subtracts different physical points. Now defined in ABSOLUTE coords with an unfold + re-center-to-pair-center step and a coincidence gate (s7 f). - BLOCKING: s3 repeated the impossible site-set-equality (and self-contradicted Sweights==box-volume). Replaced with predicate/orbit checks on the box. - s7 gate 1 rewritten (adversary-hardened): selector equivalence vs viewer predicates sqSymLevel/tetSymLevel/q2SymLevel on a common G-invariant domain (diagonal-2Q has no viewer predicate -> brute-force ref); orbit-COVER partition test (not a Sweights checksum) to actually exercise |stab| weights; wall-site + parity coverage requirement. - s8 costs: were flat volume/|G| (undercount ~55-65%) and d=8 was arithmetically wrong (137). Replaced with EXACT orbit-representative counts computed by brute force: square 60/84/112/144, tetra 55/91, on-axis 2Q 50/60/70/80, diag 2Q 100/144/196/256; ~15.5k passes/tdir. - Dropped the 'doubled coordinates' convention: false viewer-provenance (viewer is floor-centered, not doubled) and moot for even-d flux. - diagonal 2Q extended to d=8 so the d=8 square B-pairing has a reference. - nits: T_d->D4h square label; T0/T is eigenvector-side not flux sink T; frame map applied at measurement. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Design spec for the 4Q flux operators, requested by Petrus 2026-07-08 ("design the quark flux measurement operators! for square and tetra") — the P4 physics of the accepted 4Q spec (#28), done as a Fable advisor pass per the model routing.
Core design:
§10 has five open questions for Petrus (size set, margin, T_flux, excited-state scope, tetra validation anchor).
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