TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/LOCAL-CURRENT-ERASURE-AND-ORDERING.txt
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Inclusive original lines: 159-188
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000159 |  U(V)U(W)=exp(-i sigma(V,W)/2) U(V+W).
000160 | 
000161 | Thus any finite ordered history of these Cartan Weyl unitaries is a
000162 | scalar phase times one displacement. Ordering has a coherent effect,
000163 | but only through this central phase. It is not a nonabelian logical
000164 | five-code interaction. For disjoint supports the local symplectic form
000165 | vanishes. No physical time or clock calibration is read from the order.
000166 | 
000167 | On the neutral Fock module zero modes act0. In normalized oscillator
000168 | coordinates, let alpha be the total nonzero-mode displacement, which is
000169 | square-summable by smoothness. The Bargmann form is
000170 | 
000171 |  D(alpha)P(z)=exp(-||alpha||^2/2) exp(alpha.z) P(z-bar(alpha)).
000172 | 
000173 | If alpha!=0 and P is a nonzero finite polynomial, the right side cannot
000174 | be a finite polynomial: restrict to a line in a nonzero displacement
000175 | coordinate, with the other coordinates fixed so P is notzero, and use
000176 | the exponential factor. The same argument applies with infinitely many
000177 | available modes because the input polynomial uses finitely many and
000178 | some displacement coordinate is nonzero.
000179 | Therefore no nonzero finite Fock polynomial is sent to a finite Fock
000180 | polynomial by a nonzero displacement. In particular an exactly
000181 | code-preserving endpoint of ANY such finite Cartan-Weyl history must
000182 | have alpha_total=0 and acts only as a common phase on the neutral code.
000183 | Individual profiles may be nonzero and cancel; constant-profile zero
000184 | modes are also trivial here. Nontrivial means the TOTAL oscillator
000185 | displacement, not a single chosen pulse.
000186 | 
000187 | This all-history statement is analytic, not inferred from truncating an
000188 | exponential or enumerating finite profiles. It excludes R5/P2 selection