TFPT scientific source excerpt Original repository path: experiments/theory-contracts/canonical-seam-fermionization-20261025/NEUTRAL-NET-AND-DEFECT.txt Original file SHA-256: 8693dfceba1cd03631bbbcd476029b89734447b6184fda9f766870a2fad750b2 Inclusive original lines: 1-200 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000001 | NEUTRAL NET, SOURCE WINDING, AND THE E8 DEFECT SECTOR 000002 | ===================================================== 000003 | 000004 | 25 October 2026. Independent analytic source review. No Atlas, index, ledger 000005 | or original source was changed. The result concerns the already supplied 000006 | circle CAR source and standard E8 fermionization. It does not identify the 000007 | source circle with primitive P1 or replace the earlier locality exclusions by 000008 | a global odd re-fielding. 000009 | 000010 | Verdict 000011 | ------- 000012 | 000013 | There are two distinct positive statements and one decisive remaining frame 000014 | condition. 000015 | 000016 | First, the old winding implementer W1 defines a support-preserving 000017 | automorphism of the CAR local net. Its adjoint action does not commute with 000018 | the original time on charged fields. The mismatch is exactly a global U(1) 000019 | gauge phase, so it disappears on the U(1)-NEUTRAL observable net. The charged 000020 | state W1 Omega is nevertheless distinguishable by neutral local currents and 000021 | by the rank-one two-point response. Restricting to neutral observables does 000022 | not erase the earlier Cartan four-word witness. 000023 | 000024 | Second, standard fermionization of (E8)_1 supplies exactly the categorical 000025 | home suggested by the D8 cosets: 000026 | 000027 | E8 untwisted sector: 0 + s, 000028 | E8 Z2-twisted sector: v + c, 000029 | free-fermion NS sector: 0 + v, 000030 | free-fermion R sector: s + c. (1) 000031 | 000032 | Both v and c have monodromy -1 with the extending spinor s. This is the 000033 | correct twisted locality. After the spin/Arf fermionization, v is a local 000034 | fermion in the graded spin theory. It is not an additional ordinary local 000035 | field of the bosonic E8 vacuum net. 000036 | 000037 | The v+c twisted sector can therefore carry the necessary sector labels, 000038 | defect monodromy and bounded 2pi answer word in a CONJUGATED, fully 000039 | spin-refined D8 frame. Standard fermionization does not by itself construct 000040 | the full affine source winding W1 with its continuous current response. It 000041 | also does not identify the actual source W1 with the fixed canonical compiler 000042 | frame. The exact frame checker 000043 | shows that the canonical D8 and the M-transported source-CAR D8 have only 48 000044 | common roots. A valid source construction must fermionize the transported 000045 | D8_F=M(D8), thereby transporting its Cartans and quarter time too, or prove a 000046 | new marked intertwiner to the canonical D8. Standard unrefined E8 000047 | fermionization alone does not do this. 000048 | 000049 | 1. Local net preservation is exact 000050 | ----------------------------------- 000051 | 000052 | Let 000053 | 000054 | H=L2(S1), 000055 | B_a psi_n=(n+a)psi_n, 0