Established in scope
Whole two-face projector defect detects hidden source loss
In the question: Automated construction of operator maps and sources
Complete finite proof and rational counterexample. The bounded projector identity extends to infinite spaces but unbounded H retains domain requirements. This is a criterion for closed lossless reduction, not a universal physical PF condition.
Read the exact result, assumptions and evidence
Result
At one positive scale K−K²=(QwGW)*(QwGW); K is a projection exactly when VV* reduces H, in which case K=G(V*HV). Single-face equality at every scale is insufficient: symmetric ±a compressed by (1,1)/sqrt2 gives1/2. At a=log2 and ell1 the full compressed cross block is2/5 instead of1/2 with exact defect9/100 I.
Required assumptions
- Whole Fermi two-face projection and common isometric compression
Finite self-adjoint H, positive ell and one isometry V on both faces. G has the full Fermi and cross blocks. This tests closed lossless reduction and does not impose reduction on an open physical subsystem.
Original evidence
- B1-WHOLE-SOURCE-REDUCTION.txt lines 1–183
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/B1-WHOLE-SOURCE-REDUCTION.txt
4e69eb782b67a27e820fdee1f57a6755d4e8674b87c1fcd6242d7e53790e9cb9
- check_b1_whole_source_reduction.py lines 1–132
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_b1_whole_source_reduction.py
d7230cf739c0f0d327c9b8eec369cf42d9b13909cbf06f3c7c0f9d5ef5a7cc65
- B1-WHOLE-SOURCE-REDUCTION.json lines 1–113
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/B1-WHOLE-SOURCE-REDUCTION.json
61b37346a53cf54404153268ff72f69261dc21675fe01e0d73ec309aab917dd6
finding:whole-two-face-compression-projector-defect-detects-hidden-source-loss