Scoped exclusion
The fixed marked M4 channel has no homogeneous GKSL logarithm for any positive integer power
In the question: Physical time and complete transfer
Only the specified M4 endpoint channel, positive integer powers, same system and homogeneous GKSL time. Intermediate covariance is not assumed. Positive GNS Hilbert transfer and classical B recovery semigroup remain valid; larger systems and time-dependent dynamics are not excluded. Contract remains PARTIAL and physical source derivation open; source review is not a fresh kernel/numerical run.
Read the exact result, assumptions and evidence
Result
For Phi(X)=7X/12+sum_{j=1}^5 Gamma_j X Gamma_j/12 on M4 with the specified Clifford matrices and 1+5+10 spectral blocks, no Phi^n for positive integer n is the exponential of a time-homogeneous GKSL generator on the same M4. The proof covers all logarithm branches using block traces and Clifford twirling; the forced canonical coefficient beta=n log(3/4)/16 is negative. This is a different channel from the shared S3 register hierarchy.
Required assumptions
- Fixed marked M4 Clifford channel
Five specified Hermitian Gamma_j on M4 satisfy {Gamma_i,Gamma_j}=2delta_ij I. The endpoint is Phi=7id/12+sum_j Ad(Gamma_j)/12 with spectrum 1,1/3,2/3 on orthogonal blocks 1,5,10. Comparison class is any homogeneous GKSL generator on the same M4 with exp(L)=Phi^n for positive integer n.
Original evidence
- PROOF.md lines 15–53
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/source-continuous-marked-time-search-20260922/PROOF.md
62fd2844ecc3e84134d1400335cf4dd469312305d6cfb3eae427aba01beb0ac8
- PROOF.md lines 65–132
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/source-continuous-marked-time-search-20260922/PROOF.md
62fd2844ecc3e84134d1400335cf4dd469312305d6cfb3eae427aba01beb0ac8
- PROOF.md lines 164–188
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/source-continuous-marked-time-search-20260922/PROOF.md
62fd2844ecc3e84134d1400335cf4dd469312305d6cfb3eae427aba01beb0ac8
finding:marked-m4-channel-all-powers-homogeneous-gksl-excluded