TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-collar-multifield-20261016/PROOF.txt
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000178 | 7. General interacting sewing from the original Schwinger family
000179 | 
000180 | The original 04_qft_source.tex:1499-1514 defines connected S_n^T by functional
000181 | derivatives of W_rel=log Z_rel. Its reconstruction theorem at2746-2782 is
000182 | conditional on the full OS/CAR hypotheses. Under those hypotheses, define
000183 |   K_OS(F,G)=<Theta F,G>_rel,   T_t[F]=[tau_t F].
000184 | Time translation and the OS null-space quotient give T_(s+t)=T_s T_t on ALL
000185 | positive-time polynomial histories. For a complete orthonormal OS basis {e_a},
000186 |   K_OS(F,tau_(s+t) G)
000187 |     = sum_a <[F],T_s e_a><e_a,T_t[G]>.
000188 | This is the general multi-field sewing rule. It includes interaction vertices
000189 | and any required memory in the full reconstructed state space. It cannot in
000190 | general be replaced by determinants of a two-point kernel, a truncated basis,
000191 | or by a boundary-configurations-only Markov assumption.
000192 | 
000193 | This theorem gives a reconstruction from an ACTUAL complete source family; it
000194 | does not calculate that family from a lone numerical c3, an index, or a spectral
000195 | list. In particular, the original source has not supplied the physical
000196 | identification of its full Schwinger functional with the finite graph-state
000197 | quantization used in sections3-6. No unconditional physical completion follows.