TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/canonical-seam-fermionization-20261025/PROOF.txt
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Inclusive original lines: 176-209
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000176 | localized endpoint in the actual physical net is not thereby proved.
000177 | 
000178 | 6. A spurious new sign gap is removed
000179 | -------------------------------------
000180 | In a fixed charge-algebra representative, with X=E_s,
000181 | 
000182 |   W_kappa X W_kappa* X*=(-i kappa)I.                       (10)
000183 | 
000184 | X is a bounded global charge shift, not a localized spinor vertex. The
000185 | diagonal gauge
000186 | 
000187 |   U_tau|n+c0 s>=(-1)^(c0 Q(n))|n+c0 s>                    (11)
000188 | 
000189 | is pointwise I on both given subtheories 0+v and 0+s and sends W_kappa to
000190 | W_-kappa. It transports X only on its additional v<->c component. A fully
000191 | transported mixed word is conjugated and unchanged. Thus the two kappas
000192 | are the same completion up to this intertwiner basis. They are not a new
000193 | physical free parameter. Only an independently fixed extra mixed junction
000194 | would make the relative sign of (10) a new marked comparison.
000195 | 
000196 | There are nevertheless two DIFFERENT operators, in order (0,v,s,c):
000197 | 
000198 |   geometric Cartan sign: (+,+,-,-), commuting with W_ext;
000199 |   standard defect lift:  (+,-,-,+), anticommuting with W_ext.
000200 | 
000201 | Both restrict to the same E8 character on 0+s. They must not be substituted
000202 | for each other in a named source holonomy word. Both can coexist in the
000203 | four-sector system. A physical identification of an original operator with
000204 | one of them requires its actual action, not a choice based on their common
000205 | restriction. The source Cartan four-word stays +I throughout.
000206 | 
000207 | 7. What this closes and what the original full solution still needs
000208 | ------------------------------------------------------------------
000209 | Closed in scope: the local A4 spin consequence, the precise quarter