Scoped exclusion
Sign projector does not determine energy magnitudes
In the question: Physical time and complete transfer
Exact finite-dimensional counterexample for zero-temperature sign projection; refutes neither modular uniqueness for a fixed standard pair nor a complete TFPT source derivation.
Read the exact result, assumptions and evidence
Result
For C=(I+sgn H)/2, H_a=diag(1,a,-1,-a), a>0, gives the same fixed projector C and rho_0 but different positive energies. Thus [rho,C]=0⇒[rho,H]=0 is false without an extra premise. The counterexample concerns only inference from state/sign covariance to complete dynamics.
Required assumptions
- Only sign covariance is given
The conditional counterexample assumes C=(I+sgn H)/2 and [rho,C]=0, without knowing positive magnitude |H| or a complete transfer.
Original evidence
- README.md lines 11–48
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-state-dynamics-injectivity-20260918/README.md
9b3d02af286051e4476b2bf079ae01abd97fe5634a10728521b09e8739c02e91
finding:sign-projector-does-not-determine-time-magnitude