Conditional result
Full faithful KMS covariance or transfer reconstructs magnitudes
In the question: Physical time and complete transfer
Applies on a faithful finite KMS sector or the same gapped transfer sector; physical TFPT transfer remains unidentified.
Read the exact result, assumptions and evidence
Result
For known nonzero beta and faithful finite KMS covariance 0<C_beta<I, H=beta^-1 log((I-C_beta)C_beta^-1) is injectively determined. Alternatively, a full operator T=exp(-tau |H|), known tau, and [T,sgn H]=0 reconstruct the gapped H=sgn(H)(-log T)/tau. A population or eigenvalue list is insufficient; physical identification of TFPT transfer with this T must be shown separately.
Required assumptions
- Known KMS scale or full transfer
Positive dynamics reconstruction assumes either known nonzero beta and faithful finite covariance 0<C_beta<I, or the same full transfer operator T=exp(-tau |H|), known tau, and commutation with the sign; a spectrum alone or physical identification of the TFPT channel is insufficient.
Original evidence
- README.md lines 55–106
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-state-dynamics-injectivity-20260918/README.md
9b3d02af286051e4476b2bf079ae01abd97fe5634a10728521b09e8739c02e91
- v258_dirac_covariance_induction.py lines 10–21
Source checked at this snapshot
Original location and fingerprint
verification/v258_dirac_covariance_induction.py
16c60e831dceba773f3629466895f1009654827286e5b760ae01bd755fd5c0b1
- v258_dirac_covariance_induction.py lines 149–155
Source checked at this snapshot
Original location and fingerprint
verification/v258_dirac_covariance_induction.py
16c60e831dceba773f3629466895f1009654827286e5b760ae01bd755fd5c0b1
finding:full-faithful-kms-or-transfer-recovers-magnitudes