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: 138-206
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000138 | 5. Which reversible operations preserve the SAME source graph?
000139 | 
000140 | This is a separate complete classification in a specified class, not an axiom
000141 | that every physical intervention must be a symmetry. Let U0,U1 be bounded
000142 | unitaries on the two labeled fibers and S=diag(U0,U1). Then
000143 | 
000144 |  S L_graph=L_graph <=> [S,G]=0 <=> U0=U1=U and U commutes spectrally with B.
000145 | 
000146 | Proof: the (0,0) block gives U0 A=A U0. Since A=(I+exp(-2ell B))^-1 is an
000147 | injective Borel function of B with Borel inverse, U0 commutes with B's spectral
000148 | projections and with C. The (0,1) block gives C(U0-U1)=0; C is injective,
000149 | so U0=U1. The converse follows immediately. All arguments use bounded blocks
000150 | of G, controlling the possibly unbounded transfer domain automatically.
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
000171 | Hilbert space. Nevertheless T_real(t) M_f T_real(t)*=M_(f(theta-t)); all such
000172 | scalar multipliers at all times STILL COMMUTE. Adjoining an evolution
000173 | implementer does not show that it is a locally insertable quantum field.
000174 | The geometric angular B is also not automatically the physical Hamiltonian.
000175 | Thus this shortcut cannot replace the intervention/source correspondence.
000176 | 
000177 | 7. Physical obligation and next source calculation
000178 | 
000179 | [OMITTED: non-scientific conversation or execution metadata]
000180 | [OMITTED: non-scientific conversation or execution metadata]
000181 | [OMITTED: non-scientific conversation or execution metadata]
000182 | [OMITTED: non-scientific conversation or execution metadata]
000183 | 
000184 | To close that requirement, the original source must supply the response to
000185 | an actual localized intervention and its chronological composition, including
000186 | the associated preparation/readout or physical history kernel. Then check
000187 | whether it realizes L_f, another map, or no such intervention at all. Neither
000188 | the raw mask (null-unstable) nor a chosen compressed/Lueders operation may be
000189 | declared to be this map by definition. In a doubled-history description this
000190 | means evaluating the actual two-branch kernel for inserted boundary profiles,
000191 | not merely its zero-intervention projector G.
000192 | 
000193 | The primitive relative spectral action alone differentiates a GIVEN operator
000194 | path and does not specify an independent instrument/source coupling. Existing
000195 | CAR two-face quantization gives more responses only after the field/covariance
000196 | and oriented-pairing premises; preserve it as a conditional result. Known
000197 | relative-Cauchy-evolution methods likewise start with a specified theory and
000198 | allowed source perturbations; see Fewster--Schenkel, arXiv:1402.2436. They do
000199 | not derive TFPT's absent intervention law from an unlabeled spectral trace.
000200 | 
000201 | Evidence: boundary_operation_response.py and its exact JSON; no finite cyclic
000202 | shift approximation, source/Phi fit, physical preparation claim or ledger
000203 | promotion. Independent mathematical review accepts the analytic identities,
000204 | domains and scope and independently reproduces the exact JSON. The graph and
000205 | physical dictionaries remain separate. The global
000206 | physical-source task remains OPEN; 3+2 selection is not advanced to a claim.