TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/e_series_role_review/ROLE-AUDIT.txt
Original file SHA-256: e0d2041a68f53d499844f88d732469afc3ad493a0c7f997ac83a9584c035c270
Inclusive original lines: 74-111
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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000074 | the object and its source response. Total c remains8 in each complete window.
000075 | 
000076 | 5. Two important old E6 results were present before this review
000077 | 
000078 | compiler-e6-seam-readout-20260918/PROOF.txt:140-198 uses the ORIGINAL root
000079 | operators to identify E6 and A2 as mutual commuting centralizers and to
000080 | prove the closed charged-current module
000081 |   (27,3), 27=16_1+10_-2+1_4.
000082 | The old48=(16,3) currents require30+3 further directions for E6 closure.
000083 | The charges1,-2,4 are the named internal U1, not hypercharges or spins.
000084 | The fixed physical carrier-Y values are retained on each16 component.
000085 | 
000086 | compiler-vacuum-current-cubic-20260918/PROOF.txt:20-105 computes the actual
000087 | affine grade-one248 Gram and the common vacuum correlation
000088 |   <Omega,J^a_1 J^b_0 J^c_-1 Omega>=kappa(a,[b,c])
000089 |   C_(A,i)(B,j)(C,k)=d_ABC epsilon_ijk
000090 | on(27,3). The E6 cubic is symmetric, with45 signed source-basis monomials;
000091 | its Ward matrix has rank44 on45 candidates. This fixes its relative
000092 | coefficients; source normalization supplies the overall factor. These are
000093 | completed source-level tensor identifications, not mere numerical branching.
000094 | They were present as resolved_results of old Atlas contracts with empty
000095 | supporting_findings; historical PARTIAL was not mathematical openness here.
000096 | 
000097 | The same old proof explicitly corrects I4/4: it is a normalized CURRENT
000098 | RESPONSE GRAM, not a partial trace of the grade-zero vacuum. Equal current
000099 | norms do not select physical populations, particle numbers or masses.
000100 | Likewise d times epsilon is not already a4D fermion Yukawa functional.
000101 | 
000102 | 6. Inclusion and projection have different algebraic functions
000103 | 
000104 | An E6/E7 current subalgebra is a valid closed inclusion. The orthogonal
000105 | root/Cartan cut projector FROM e8 ONTO it is not a Lie homomorphism.
000106 | For example in the (+++) E6 chart remove alpha=e0+e5 and its negative.
000107 | Both root currents project to0, but their bracket is a nonzero signed
000108 | coroot. Its retained Cartan component is
000109 |   e0+(e5+e6+e7)/3, norm squared4/3.
000110 | For neutral E7 choose alpha=e0+e1. Its retained Cartan component is
000111 |   e0+e1-q/4, norm squared3/2.