TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPINE-FOLD-C6-CONSUMER-REVIEW.txt
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000001 | ROOT REVIEW OF ACTUAL SPINE TO ORIGINAL C6 CONSUMER
000002 | 30 October2026. Reuses existing original P/Q and Gmetric results.
000003 | 
000004 | The actual four edge transports satisfy R T0^-1 T3 R^-1=M0. Thus the
000005 | original positive mark1 P/Q pair is realized by P=T3 and Q=T0^-1, with
000006 | actual source/target metrics H0,Hinf. Flat parallel transport depends on
000007 | these original relative path classes. The existing finite endpoints can
000008 | be joined through the mark-free interior/exterior; this introduces no
000009 | additional loop around another marked puncture.
000010 | 
000011 | Let Tau=[[0,Q],[P,0]] and C=diag(R^-1,P R^-1). From the already verified
000012 | source isometries one directly obtains
000013 |  C* diag(H0,Hinf) C=I, C^-1 Tau C=[[0,M0],[I,0]]=F.
000014 | This is an actual coefficient-fiber isometry, not a claim that these
000015 | fibers are the physical two boundary faces of the F5 field source.
000016 | 
000017 | Root independently checked EXACTLY, by simplifying matrix differences:
000018 |  M0*M0=I, M0^3=I, F*F=I, F^6=I,
000019 |  J*J=I, J*F^-1J=diag(M0,-M0),
000020 |  J*(yI-delta F^-1)J=yI-delta diag(M0,-M0),
000021 |  J*[(yI-delta F^-1)*(yI-delta F^-1)]J=D_y*D_y,
000022 | where star denotes the Hermitian adjoint and
000023 |  J=1/sqrt2[[I,I],[M0,-M0]].
000024 | All eight independent symbolic checks pass. The same statement with
000025 | added epsilon^2I follows immediately; uniqueness of positive functional
000026 | calculus carries inverse square roots and already given compressions.
000027 | Here Pstr must be the ORIGINAL projector, conjugated by the sameE=CJ,
000028 | not replaced by the marked rank1 family endpointP0.
000029 | 
000030 | No new normalization, clockwise orientation, Yukawa coefficient, state
000031 | or time is selected. The inverseF is essential to the originalU6 map.
000032 | Any ALREADY GIVEN whole6operator transports by the sameE. The comparison
000033 | embedding diag(kappaM0P0,0) is one explicitly declared positive-branch
000034 | embedding; the known3componentHardy answer alone has not selected this
000035 | whole6operator or set every opposite-branch physical response tozero.
000036 | It must not be called the full original source insertion. Opposite,
000037 | adjoint, Clifford and KO legs retain their actual already given types.
000038 | 
000039 | Together with the registered four actualpaths, this closes the explicit
000040 | spine-to-originalP/Q-to-C6Gram consumer dictionary. Execute the actual
000041 | original coefficient/insertion/sourcedomain rule on this shared structure;
000042 | its full physical selection and time origin are not inferred from the
000043 | coefficient-fiber conjugation.
000044 | 
000045 | Independent exact output: ROOT-SPINE-FOLD-C6-CONSUMER-CHECK.json.