TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-collar-multifield-20261016/P1-COVARIANT-INSERTION.txt
Original file SHA-256: ebb9e0cb15cdc017914d8567131c8d8b75855f20e05551b6f7b350989061e152
Inclusive original lines: 147-213
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000147 | 4. First physical-field test: preserve the earlier fermionization result
000148 | 
000149 | The earlier source-z8-parity-descent-20260921/PROOF.txt section5 already
000150 | constructs the D8 -> Z^8 fermionic extension conditional on the selected
000151 | E8 realization, nonanomalous Z2, spin structure and twisted sectors.
000152 | It gives sixteen real chiral fermion fields with internal action
000153 |   (10,1) direct_sum (1,6)
000154 | under the fixed Spin(10) x Spin(6) cut. Reuse this result, not a fresh model.
000155 | The primary CFT reference is arXiv:2303.16917v2, section5.1. Its free chiral
000156 | fermions are not automatically elementary 3+1D TFPT matter fields.
000157 | 
000158 | The smallest decisive obstruction to using THESE local fields as the required
000159 | internal Spin(10) spinor is their central character, not their dimension.
000160 | In orthonormal D5 coordinates let z be the nontrivial kernel of
000161 | Spin(10)->SO(10), represented on weights by exp(2pi i p_1).
000162 | It is +1 for all vector/singlet weights of the above sixteen fields and -1
000163 | on every D5 half-spinor weight p_i=+/-1/2. The fixed D5 subgroup action is
000164 | part of this test. It is not an identification with Lorentz spin.
000165 | 
000166 | Since z acts trivially on each generating local fermion field, it acts
000167 | trivially on all their finite products, derivatives, OPE coefficients and
000168 | algebraic/norm/weak closures in that same NS representation. Thus local composites in this
000169 | unchanged NS field algebra cannot acquire the missing Spin(10) spinor
000170 | character. No search for a special coefficient V_a can repair this mismatch.
000171 | This extends the existing representation check to its generated local algebra;
000172 | it is not a new selection rule.
000173 | 
000174 | It does NOT exclude spinorial Ramond/twisted STATES, intertwiners between
000175 | different sectors, changed group embeddings, or another physical field theory.
000176 | Those must not be silently treated as ordinary fields of the same NS algebra.
000177 | The existing source-sector-reconstruction-20260920/PROOF.txt:176-205 explicitly
000178 | retains odd intertwiners and their cocycles as extra source data; four traces
000179 | alone do not determine them. Its positive sector reconstruction and the
000180 | other known dressed-fermion construction are preserved with their premises.
000181 | 
000182 | Therefore this already known fermionization branch is stopped at its first
000183 | failed matter identification. No new60-component coupling is optimized on
000184 | those fields, and no old fermionization classification is rerun here.
000185 | 
000186 | 5. Result and precise scope
000187 | 
000188 | The ordinary derivative V_a is insufficient as a physical identification:
000189 | source/frame motion can produce a nonzero off-diagonal entry with exactly
000190 | zero intrinsic effect. Equations(1)-(2) identify the actual source variation
000191 | and normal embedding motion that survive this test. The original P1 formulas
000192 | still do not choose Phi, its transformation law, that intrinsic source
000193 | variation, or the physical charged spinor intertwiners.
000194 | 
000195 | The most explicit existing ordinary fermionization does not supply the
000196 | required internal spinor matter under the fixed group action. Its local
000197 | composites cannot cure that central-character mismatch. Other retained sector
000198 | and dressed constructions already require their microscopic/source map.
000199 | 
000200 | Consequently no physical Phi-dependent B, physical fermion vertex or3+2
000201 | selection is derived. This is not a proof of universal underivability from
000202 | every possible original-source selection theorem. It states the exact tested
000203 | boundary and prevents pure frame motion or a known wrong local matter map
000204 | from being presented as the requested solution. All physical gates remain open.
000205 | 
000206 | The next source-level target is the actual charged-sector intertwiner and
000207 | intrinsic Phi family, including their common state/time and domain action.
000208 | Reconstructing more spectra or adding a desired Yukawa does not define them.
000209 | 
000210 | Independent read-only review accepted the collar identities, induced-frame
000211 | signs, covariance of(1)-(2), equivariance requirement and central-character
000212 | argument with precisely these conditions. It did not validate a physical
000213 | source map or promote a physical gate.