TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/CARRIER-SOURCE.txt
Original file SHA-256: c65245f53c363472b5bcffb5a6c81693a70eaa53fcf55fc5ed3374637890586f
Inclusive original lines: 95-118
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000095 | 3. THE FULL FIELD/TIME/REFLECTION MAP IS ALREADY PROVED
000096 | 
000097 | In the original graded thermal HS source let
000098 |  H=sum_j |lambda_j| n_j^exc, rho=exp(-2ell H)/Z_(2ell),
000099 |  a_R=L_a, a_L=-Gamma R_a,
000100 | where Gamma is conjugation by the genuine excitation parity. The exact map
000101 | is
000102 |  iota(c(T_faces(v0,v1,bar w0,bar w1)))
000103 |        =a_R^*(v0)-a_L^*(v1)+a_R(w0)-a_L(w1).
000104 | This is the natural CREATION chart, with its actual conjugate/adjoint legs.
000105 | Its whole covariance is exactly G(h) above. The GNS map identifies every
000106 | CAR word, not just the two-point matrix. The original circle group maps to
000107 |  U_t Y=exp(i tH)Y exp(-i tH)
000108 | with the SAME t. Both creators carry exp(i t h); adjoints carry the actual
000109 | antilinear test-vector convention. Its HS generator is L_H-R_H, distinct
000110 | from the positive H on the one-face excitation Fock space.
000111 | 
000112 | The product reflection is J_R=Q_Gamma^*J_HS,
000113 |  Q_Gamma=P_even-iP_odd.
000114 | For every bounded even A the reflected form is the positive HS Gram of
000115 | rho^(1/4) A rho^(1/4). This is a genuine whole even-algebra statement.
000116 | Neither H, its HS Liouvillian, the geometric h nor radial transport is
000117 | silently equated with the original physical OS Hamiltonian of a different
000118 | S_adm. The source itself explicitly retains that physical identification.