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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000148 | 5. Exact ordered unitary current histories, without a fitted product
000149 | 
000150 | For the above real profiles V,W the original current commutators give
000151 | 
000152 |  [J(V),J(W)] = sum_n n (Vhat_n.What_-n) I =i sigma(V,W) I,
000153 |  sigma(V,W)=-i sum_n n (Vhat_n.What_-n), which is real.
000154 | 
000155 | Let U(V)=exp(iJ(V)); this defines a stated mathematical operation class,
000156 | not a physical coupling or a permission derived from primitive P1.
000157 | The product is fixed by the existing CCR:
000158 | 
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
000189 | by CLOSED endpoints in precisely this Cartan-Weyl class. It does not
000190 | exclude open processes with exterior memory, nonunitary products of
000191 | fields, root currents, interleaved stress/current histories, composite
000192 | fields, or every local E8/P1 operation. Do not unite it with earlier
000193 | separate source exclusions to claim an all-source no-go.
000194 | 
000195 | 6. What changes in the actual derivation frontier
000196 | 
000197 | Positive: in the accepted original current realization, one literal
000198 | local product joins native current4, quartic5, singular erasure20 and
000199 | regular primary20 with fixed coefficients and actual native action.
000200 | No fitted algebra/coupling, chosen root or family omission is involved.
000201 | 
000202 | Excluded identification: pure native annihilation mode = local physical
000203 | boundary intervention. The original locality definition does not permit
000204 | this identification; retaining the full field restores the omitted
000205 | regular carry and higher modes. Their exact current response and ordered
000206 | Cartan-Weyl product are now determined, not another freely fitted model.
000207 | 
000208 | Still OPEN: an actual primitive source variation inducing a specified
000209 | local current/composite field; its map to the supplied current net,
000210 | its A/A*-invariant H_adm restriction, physical history/time/state, and
000211 | the marked noncentral logical action. The first unresolved map is the
000212 | P1-to-current insertion map and its physical restriction. The original
000213 | spectral action does not by its differentiation formula alone specify
000214 | delta D_rel or this map. No broad corpus absence proof is asserted.
000215 | 
000216 | Next use the ORIGINAL source constructor for a non-Cartan or composite
000217 | intervention, if selected there, to compute its full insertion and
000218 | admissible-sector action before a logical compression. Do not relabel
000219 | a_a as local, optimize Cartan profiles/pulse order, vary pure stress
000220 | schedules, discard the carry, assume the code is H_adm, or add detector,
000221 | Yukawa, projection or matching coupling rules. Root-current-only zero
000222 | modes and the already tested two-insertion branch retain their exact
000223 | earlier exclusions; remaining histories are not automatically allowed
000224 | or ruled out. Physical3+2 remains an open derivation.