TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-partner-original-action-20261015/PROOF.txt
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000116 | 4. THE POSITIVE ORIGINAL-CARRIER PARTNER IS CROSS-SHEET
000117 | 
000118 | The existing CAR.PAIR.02 / CAR.COUNT.01 results already distinguish neutral
000119 | cross-sheet pairings from a second same-sheet vacuum. Reuse them, not as a new
000120 | discovery of the half-spinor pairing. The explicit operator realization is:
000121 | 
000122 |     c_i=epsilon_i+iota_i, B=c1 c2 c3 c4 c5,
000123 |     J_C=B K_complex_conjugation
000124 | 
000125 | in an oriented orthonormal wedge basis. Since the c_i anticommute and square to
000126 | one, B*=B and B^2=(-1)^10=1. B is real in this basis, so J_C^2=1. It exchanges
000127 | epsilon_i and iota_i and reverses exterior parity. It therefore maps S+ to S-.
000128 | For Hermitian h,
000129 | 
000130 |     J_C dGamma(h) J_C^-1=tr(h) I-dGamma(h).
000131 | 
000132 | For g in U5, J_C Lambda(g) J_C^-1=det(g)^(-1)Lambda(g); in particular J_C is
000133 | antiunitarily equivariant under SU5 and S(U3 x U2). Antiunitarity is essential:
000134 | J_C Y J_C^-1=-Y is consistent with J_C exp(itY) J_C^-1=exp(itY).
000135 | This construction uses a Hermitian metric, volume orientation, and real-structure
000136 | convention. The available two sheet orientations remain distinct choices.
000137 | 
000138 | Within Lambda E the zero-hypercharge equation is -2 n3+3 n2=0 with
000139 | 0<=n3<=3, 0<=n2<=2. Its only solutions are (0,0) and (3,2). Thus there is exactly
000140 | one zero-hypercharge carrier label in S+ (Lambda^0) and one in S- (Lambda^5):
000141 | 
000142 |     J_C 1=u1 wedge u2 wedge u3 wedge u4 wedge u5.
000143 | 
000144 | These two labels are gauge singlets. They are NOT two physical vacuum vectors.
000145 | More generally J_C pairs opposite carrier charges, supplying the existing
000146 | neutral scalar channel between the two sheets, not an extra E8 root sector.
000147 | 
000148 | The time identity also explains why conjugacy is not zero physical energy.
000149 | For traceless h, J_C H_h J_C^-1=-H_h, whereas functional calculus gives
000150 | J_C |H_h| J_C^-1=|H_h|. Conjugate nonzero signed eigenvalues can thus have the
000151 | same positive magnitude. This is an illustration on the specified carrier
000152 | operator; H_phys=|H_h| has NOT been derived or adopted as TFPT dynamics.