TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/WINDING-MULTIPLICITY-PROOF.txt
Original file SHA-256: e00dde693771c8b4150fb420ed3703f153a8b11e29263e770d60b341ad626971
Inclusive original lines: 1-40
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 | R083 follow-through: all 18 original retained quark channels
000002 | 
000003 | The preceding one-channel result must not be mistaken for the complete
000004 | R081 retained source. In that actual original v252 construction the quark
000005 | space is 36-dimensional and gamma+ has rank 18. For fixed real H background,
000006 | the given radial force is odd; its off-diagonal P/Q block has singular
000007 | values s_j, j=1,...,18. With p=n+alpha and m_j=r*s_j, its retained
000008 | covariance eigenvalues are
000009 |   c_j(n)=[1+p/sqrt(p^2+m_j^2)*tanh(ell sqrt(p^2+m_j^2))]/2.
000010 | For finite j each differs from the positive Hardy step by O(n^-2), so the
000011 | entire 18-channel covariance C-P_+ tensor I18 is trace class. In particular,
000012 | this is a FIXED-background diagnostic retained-sector statement.
000013 | 
000014 | If, and only as an ADDITIONAL tested hypothesis, the original common seam
000015 | operator acts as the same scalar circle shift Ue_n=e_(n+1) on all 18
000016 | retained channels, then
000017 |  Tr[U(P_+ tensor I18)U*-(P_+ tensor I18)]=-18,
000018 | and the already established pair-index theorem gives for |z|<1
000019 |  det_F[(I-zUCU*)(I-zC)^-1]=(1-z)^(-18).
000020 | The -1 result is ONE component, not the full retained 18-component answer.
000021 | At z=.03, N=10000 the independently executed native 36-block check gives
000022 | 1.73024970119 against .97^(-18)=1.73024970237. The one-channel factor is
000023 | 1.03092783505. No new physical Yukawa fit, no added parent bosonic field,
000024 | no new physical shift selection, and no universal alpha inference.
000025 | 
000026 | Consequence for the proposed shared-origin principle: the original primitive
000027 | one-unit seam readout must be related to these 18 matter channels through the
000028 | ACTUAL source's selector, opposite orientation, relative reference or other
000029 | derived full-source mechanism. These are alternatives to investigate, not
000030 | choices asserted by this test. This counts a conditional ordinary Fredholm
000031 | determinant, not a physical Majorana Pfaffian. It does not establish an
000032 | E8-to-quark embedding, physical state, clock identification, 3+1 geometry or
000033 | universal gravity. A full original source may cancel or weight factors in a
000034 | way not encoded by the diagnostic retained quark block.
000035 | 
000036 | Reproducible native check: check_winding_multiplicity.py, results in
000037 | WINDING-MULTIPLICITY.json. Five explicit checks passed. Existing relevant
000038 | proofs: PAIR-INDEX-DETERMINANT-REVIEW.txt and
000039 | EINSTEIN-NOETHER-HYPOTHESES-PROOF.txt. No new Lean, ledger promotion or
000040 | experimental verification.