TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/mixed-current-origin-20261014/NEUTRAL-DEFECT-PAIRS-AND-VECTOR-WARDS.txt
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000021 | 2. Exact neutral original operation and support
000022 | 
000023 | For arcs A,B with a common seam beginning, the actual v1033 operations give
000024 |   F_A = X^2 tensor P_A,  P_A=(-1)^N_A,
000025 |   F_B F_A* = I_4 tensor P_(A triangle B).
000026 | Thus every finite union E of intervals can be formed by products of these
000027 | transporters. The X factors cancel in EACH interval factor, not only in
000028 | an expectation value. The final operator is
000029 |   T_E = I_4 tensor (-1)^N_E,   [T_E,Z]=0.              (1)
000030 | It belongs to the original matter algebra of E; no register, Gauss rule
000031 | or additional physical Hilbert sector is supplied by (1). Its existence
000032 | does not assert that the register model itself was derived from P1.
000033 | 
000034 | For a BASE interval I=(x,y) avoiding the chosen base cut, define its eight
000035 | source preimages
000036 |   E_I = union_(j=0..7) ((x+2pi j)/8,(y+2pi j)/8).
000037 | The original matter action is exactly
000038 |   Ad T_E (psi(theta)) = sigma_E(theta) psi(theta),
000039 |   sigma_E(theta) = (-1)^1_E(theta).
000040 | The mask is 2pi/8 periodic. For the existing sheet fields
000041 |   eta_j(u)=psi((u+2pi j)/8)/sqrt8
000042 | it therefore gives
000043 |   Ad T_E(eta_j(u))=(-1)^1_I(u) eta_j(u) for ALL j.   (2)
000044 | Realification gives the same sign on all sixteen real components.
000045 | 
000046 | Equation(2) is the actual uniform parity-CUT ACTION of an endpoint PAIR.
000047 | It is not yet an analytic OPE monodromy theorem for a single endpoint
000048 | field: that field, its domain and its charged word limits remain to be
000049 | constructed. The support is eight intervals on the source, one interval
000050 | only under the already given folded localization. No original support-
000051 | preserving P1 identification follows from calling it base-local.
000052 | 
000053 | 3. The cover-holonomy no-go does NOT exclude this pair
000054 | 
000055 | The periodic mask satisfies sigma(theta+2pi)=sigma(theta). A full source
000056 | circuit crosses sixteen endpoints and acquires sign+1. The register
000057 | r and the original cover holonomy h are unchanged. In a fixed finite
000058 | QWZ Hamiltonian conjugation only changes hopping signs at interval ends;
000059 | if E avoids the seam, the old seam link phase is exactly unchanged.
000060 | 
000061 | The previous statement
000062 |   C(-h)^8=-h I != h I=(-C(h))^8                       (3)
000063 | still excludes a fixed-charge identification of the SINGLE register half
000064 | flux with the desired SINGLE global spinor twist. It is INAPPLICABLE to
000065 | (1)-(2): a neutral endpoint pair need not change a global sector at all.
000066 | It is also inapplicable to pair operations merely because they are built
000067 | out of half strings. Relative local cuts and global bundle holonomy must
000068 | be tested separately.
000069 | 
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