TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/FOUR-STARTING-POINTS-STATE-RELATIVE-EQUIVALENCE.txt
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000158 | 4. FULL CHARGED AND ORDERED COMPLETION, NOT A NEUTRAL TRUNCATION
000159 | 
000160 | Work in the same radial branch/ordered punctured chart and i0 boundary
000161 | prescription as the original lattice/current representation. For Cartan
000162 | vector h(z), normal polynomials P_A(h(z)), and charged vertices E_beta(w),
000163 | the entire vacuum functional of the supplied twisted module is generated
000164 | by the following Gaussian expression. Differentiate in auxiliary vectors
000165 | t_A with P_A(partial_tA), and then set all t to0:
000166 | 
000167 |  delta_(sum beta,0) epsilon_order(beta)
000168 |  * product_k w_k^(d.beta_k)
000169 |  * product_(k<l)(w_k-w_l)^(beta_k.beta_l)
000170 |  * exp[sum_A t_A.(d/z_A+sum_k beta_k/(z_A-w_k))
000171 |        +sum_(A<B)t_A.t_B/(z_A-z_B)^2].
000172 | 
000173 | The bilinear dot and actual positive/negative Cartan polarizations are
000174 | retained. Adjoint fields use the original conjugate/radial adjoint and
000175 | reference subtraction, not an independent Euclidean probability law.
000176 | There are no same-insertion self-contractions, precisely because P_A is
000177 | normal ordered. Descendants follow by position derivatives; normal field
000178 | products use the actual regular OPE coefficient before taking coincidence,
000179 | not an unregulated product or an added contact extension. This formula
000180 | therefore includes arbitrary ordered quartic/erasure/current/root words,
000181 | their correlated charged intermediate sectors, and the original h5 primary
000182 | carry r=t-7/85 L_-2 g+3/170 L_-1^2 g through its EXISTING field constructor.
000183 | Twist its whole constructor; do not replace its stress by an unshifted one.
000184 | 
000185 | For nonzero total charge, the vacuum expectation vanishes by charge
000186 | orthogonality, but the OUTPUT VECTOR does NOT vanish or get discarded.
000187 | The pure vertex word has charge p=sum beta and creation factor
000188 |  exp[sum_n>0 h(-n).(sum_k beta_k w_k^n)/n]|p>,
000189 | times the same ordered cocycle, pair factors and twist monomials. General
000190 | polynomial insertions also have an explicit generating vector: remove the
000191 | neutrality delta from the scalar generator, retain its entire scalar
000192 | Gaussian/cocycle/pair/twist factor, and append
000193 |  exp[sum_n>0 h(-n).(sum_k beta_k w_k^n/n
000194 |                     +sum_A t_A z_A^(n-1))]|p>.
000195 | Applying all P_A(partial_tA) at t=0 gives the FULL endpoint vector. Charged
000196 | endpoint matrix elements can equivalently be read by attaching the actual
000197 | endpoint bra/vertices.
000198 | Hence charge neutrality of a returned scalar is not an intermediate
000199 | projection, erasure of memory or restriction to neutral histories.
000200 | 
000201 | Clock/time must be the original excitation generator
000202 |  H_exc=8[L0+d.h0], with its specified ground subtraction,
000203 | and fold twist sigma_d=exp(2pi i d.h0) (order16 on roots), with the stated
000204 | charged quarterfold/cover carry. Native J and internal t_v remain separate.
000205 | Do not replace H_exc by L0. A root primary has quotient excitation
000206 | 1+d.beta, source excitation8(1+d.beta); full words retain oscillator/charge
000207 | terms and time phases. No physical units, mode filter or coupling is fitted.
000208 | Finite words are formal exact identities; smooth infinite histories require
000209 | the existing domain/energy-tail controls, not automatic UV coincidence.
000210 | 
000211 | This gives the complete generating family instead of an impossible finite
000212 | list of infinitely many correlations. The actual two-point matrices and
000213 | all240 root time/twist diagnostics are additionally evaluated explicitly.
000214 | Any unspecified physical coupling is still unspecified: under a legitimate
000215 | transport its FULL original tensor must be carried, not chosen to repair q.
000216 |