TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/canonical-seam-fermionization-20261025/PROOF.txt
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Inclusive original lines: 89-118
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000089 | 3. What the winding already does to neutral local observables
000090 | -------------------------------------------------------------
000091 | Retain the supplied CAR representation with C=1_(B_a<0), the same positive
000092 | time, and W1 c(f) W1*=c(u f). For every proper interval I, multiplication
000093 | by u preserves support, so Ad(W1) F(I)=F(I). If gamma_t is the source U1
000094 | action c(f)->exp(-it)c(f), then
000095 | 
000096 |   tau_t Ad(W1)=gamma_t Ad(W1) tau_t.                     (3)
000097 | 
000098 | It follows that Ad(W1) commutes with time on the source U1-neutral net.
000099 | This is stronger than mere equality of dimensions or energy spectra. It
000100 | does not say that all parity-even fields are charge-neutral, or identify
000101 | source U1 with physical hypercharge or electromagnetism.
000102 | 
000103 | On the finite-energy core,
000104 | 
000105 |   W1*QW1=Q+1,  W1*HW1=H+Q+a,
000106 |   W1*J(f)W1=J(f)+average(f).                              (4)
000107 | 
000108 | Thus the excited state is observable by neutral currents; neutrality does
000109 | not erase the defect or the earlier Cartan four-word discriminator. The
000110 | old rank-one covariance and directed relative determinant remain
000111 | 
000112 |   uCu*-C=Pi_0,
000113 |   det_F[(I-z(C+Pi_0))(I-zC)^(-1)]=1-z.                  (5)
000114 | 
000115 | Equation (5) is not a physical EM coupling theorem. The original supplied
000116 | index weight q=delta_top exp(-2 alpha_EM), susceptibility 5/4 and exact
000117 | residual-sector ratio criterion remain as in the previous direct-defect
000118 | contract. No new heat-to-EM calibration is needed.