TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/COEFFICIENT-PAIRING-AND-CLAUDE34-FIRST-TEST.txt
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Inclusive original lines: 1-61
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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000001 | FULL COEFFICIENT PAIRING AND FIRST TEST OF MODEL RESPONSE34
000002 | Root review, 30 October2026. Original papers/suite/ledger unchanged.
000003 | 
000004 | The actual inverse character is already available, not a missing extra
000005 | line. Pc has its rank-one omega^2 spectral line. More substantially,
000006 | the original normalized two-torsion pairings identify each q sign line
000007 | with its dual. Thus the existing mixed spin products are global sections
000008 | of K tensor Hom(Fq,Fp). Composition with the reverse Hom and trace is a
000009 | canonical bundle evaluation. It cancels the full q/p signs, not merely
000010 | the cubic eigenvalue of one naked line. See the independent full report
000011 | RHO-DUAL-COEFFICIENT-HOM-REVIEW.txt and the exact sign calculation.
000012 | 
000013 | This evaluation does not supply an arbitrary reverse kernel B. If an
000014 | actual source kernel is used, its endpoints, spin factors, order and
000015 | coefficient type must match. It also does not duplicate q and p as two
000016 | independent CAR species or choose a new joint state. A transported
000017 | representation of one given source is distinct from a new direct-sum
000018 | CAR algebra.
000019 | 
000020 | The checked original output formulas are the positive structural kernel
000021 | with its family matrix elements, and separately unweighted tr Pi_triangle.
000022 | They do not explicitly display this mixed Hom contraction. This is a
000023 | bounded source observation, not a proof that no coupled insertion or
000024 | implicit total structural projection can realize it. A one-sided map
000025 | J_coeff is one possible typed realization, not a newly imposed necessary
000026 | architecture. An invariant full tensor is allowed; a naked parallel
000027 | one-dimensional coefficient subsystem is not required.
000028 | 
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000033 | 
000034 |   Ad(Pc)Q=omega^2 Q,
000035 |   ker(Ad(Pc)-omega^2)=span(Q,Q Pc,Q Pc^2).
000036 | 
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000057 | 
000058 | DECISION: reuse the positive full Hom evaluation. Next compose the actual
000059 | original source kernel/insertion in this type, without adding a fitting
000060 | character, a parallel-line condition, a second p source or a new state.
000061 | The complete physical generating rule is not claimed by this result.