TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/COVER-SECTOR-REVIEW.txt
Original file SHA-256: 71a2104f84132f4d574e3a48cb4fdd4aa58b3c3d80899c2c2c7d55b9dfb46741
Inclusive original lines: 1-36
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000001 | INDEPENDENT COVER SECTOR AND NORMAL SYMBOL REVIEW
000002 | 29 October 2026. Original source read directly. No new source or test run.
000003 | 
000004 | The existing BOUNDARY-SOURCE.txt:145-175 identifies the longitudinal part
000005 | of the actual annulus involution with V=T_pi. Its plus i and minus i
000006 | character spaces are the even and odd Fourier modes of ONE NS circle.
000007 | The actual unitary maps, including Sobolev domains, are
000008 |   W0 g(theta)=exp(i theta/2)g(2theta),
000009 |   W1 g(theta)=exp(3i theta/2)g(2theta),
000010 |   B_cov W_j=2 W_j A_alpha_j, alpha_j=1/4,3/4.
000011 | The original geometric involution also exchanges the radial boundaries.
000012 | Its two longitudinal character spaces are not thereby two pointwise
000013 | normal spinor components, nor the two separately labeled radial faces.
000014 | 
000015 | In this same OLD-complex two-sector coefficient space,
000016 |   sigma_1(B_cov)(x,xi)=2xi I.
000017 | Any local old-complex-linear zero-order bundle map N(x) therefore has
000018 |   sigma_1({B_cov,N})=4xi N(x).
000019 | Thus anticommutation forces N=0; it cannot supply a normal Clifford map
000020 | with N^2=-I. Derivatives of N contribute only lower-order terms.
000021 | The actual V commutes with B_cov. Its square -I alone does not supply the
000022 | missing anticommutation. The actual winding satisfies [B_cov,u_cov]=u_cov.
000023 | 
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