TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-collar-multifield-20261016/BOUNDARY-OPERATION-PROOF.txt
Original file SHA-256: a55bc1d8bcda606e274092873dedf00709d40bd093d3ec0e08ce7ff25ecf5a47
Inclusive original lines: 151-170
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000151 | 
000152 | In the scalar circle local unitary multiplier class, [B,M_u]=-i M_u', so
000153 | preserving this fixed graph requires constant u. With nontrivial B spectral
000154 | multiplicity, its commutant CAN be nonabelian: the theorem does not prove all
000155 | source symmetries commute or select physical access to those degeneracies.
000156 | The exact checker tests simple and doubly-degenerate examples separately.
000157 | 
000158 | In particular diag(U,U) for U=e^(i theta) fails to preserve G at fixed B.
000159 | Applied covariantly it changes B to U B U* and G to S G S*. Transporting the
000160 | vectors and kernel together preserves all comparisons. This is an isomorphic
000161 | source presentation, not evidence of an applied physical mixing pulse.
000162 | Holding the old kernel/state fixed while applying a pulse is a different
000163 | intervention and needs its own source justification.
000164 | 
000165 | 6. Why time times a phase is not the missing local quantum operation
000166 | 
000167 | On the supplied circle T_real(t)=exp(-itB) gives
000168 |  T_real(t) U T_real(t)*=exp(-it)U,
000169 |  (U^m T_real(t))(U^n T_real(s))=exp(-int)U^(m+n)T_real(t+s).
000170 | This is a valid noncommuting time/coordinate operator product on that given