Established in scope
The scalar isometry family is completely classified
In the question: Historical: common source, state and event selection
Complete analytic theorem in the supplied scalar Hardy class. Leakage excludes only the pure-isometry route, not general physical sources. Not a P1 classification.
Read the exact result, assumptions and evidence
Result
Every continuous scalar unimodular winding-one symbol with isometric Hardy compression is a single Blaschke factor modulo phase. With B_alpha fixed, only the centered factor z has constant shift covariance. The strictly oriented control z²/b_(1/4) has leakage 15/4096.
Required assumptions
- Fixed scalar Hardy model with quarter time
H=L²(S¹), C projects onto n≥0, B_alpha=−i∂theta+alpha with alpha=1/4 or 3/4. C and B remain fixed for every candidate. Consider scalar unimodular multiplication operators: continuous symbols for isometry classification and H1 symbols for finite excitation energy. This source class is not derived from P1/P2.
Original evidence
- PROOF.txt lines 69–128
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-source-character-search-20261015/source_reconstruction/PROOF.txt
424e2f8eaf021cae575e479ccca4fcd2b8a34df1e5d5410371a86144f07ddb5d
- PROOF.txt lines 217–225
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-source-character-search-20261015/source_reconstruction/PROOF.txt
424e2f8eaf021cae575e479ccca4fcd2b8a34df1e5d5410371a86144f07ddb5d
finding:continuous-hardy-seam-classification