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Original ledger classification: Strict-locality obstruction exhibited [E]/[C]: the chiral collar's Wilson-loop/Wannier-centre winding = Chern = 1!=0 (vs 0 for the gapped trivial control), the exact obstruction to exp-localised Wannier (Brouder et al./Thouless); so no strictly finite-range commuting projector exists for c_-=8!=0 (Kapustin-Fidkowski) -- v424 sub-step (i)'s realisation is PROVABLY the quasi-local NPW26 LTO net, sharpening v460 from citation to exhibited obstruction; SEAM.EQUIV.01 stays [O]

Recorded statement: The Kapustin-Fidkowski/Thouless strict-locality OBSTRUCTION made EXPLICIT (2026-06-30) -- sharpening v460's verdict from a cited statement to an exhibited topological obstruction on the same v367 p+ip collar. v460 realised the S3 input as…

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SEAM.S3.LOCALITY.01

Original ledger classification: Strict-locality obstruction exhibited [E]/[C]: the chiral collar's Wilson-loop/Wannier-centre winding = Chern = 1!=0 (vs 0 for the gapped trivial control), the exact obstruction to exp-localised Wannier (Brouder et al./Thouless); so no strictly finite-range commuting projector exists for c_-=8!=0 (Kapustin-Fidkowski) -- v424 sub-step (i)'s realisation is PROVABLY the quasi-local NPW26 LTO net, sharpening v460 from citation to exhibited obstruction; SEAM.EQUIV.01 stays [O]

Original claim text

The Kapustin-Fidkowski/Thouless strict-locality OBSTRUCTION made EXPLICIT (2026-06-30) -- sharpening v460's verdict from a cited statement to an exhibited topological obstruction on the same v367 p+ip collar. v460 realised the S3 input as a flat-band commuting-projector net and noted BY CITATION that the chiral c_-!=0 forbids strict finite-range locality; this module EXHIBITS that obstruction. [E] CHERN INTEGER: the FHS Chern is C=+1 (chiral M=1), 0 (trivial M=3), -1 (opposite mass) -- the invertible-phase invariant. [E] WILSON-LOOP / WANNIER-CENTRE WINDING = CHERN: the hybrid Wannier centre theta(ky) winds by |C|=1 (chiral) and 0 (trivial) over the BZ; exp-localised Wannier exist IFF the winding is 0 (Brouder-Panati et al. PRL 98 046402; Thouless), so the chiral collar has NONE. [E] OBSTRUCTION INTEGERS TIED: winding=|C|=1!=0 and c_-=16/2=8=g_car+N_fam=rank E8!=0; winding!=0 <=> C!=0 <=> c_-!=0 (the same 8 as c3's one-sided count, v456). [E] NEG CONTROL: BOTH phases are gapped, yet only the trivial (winding 0) admits exp-localised Wannier and a strict finite-range commuting projector -- it is the CHIRALITY, not the gap. [C]/[O] Kapustin-Fidkowski: a strictly finite-range commuting projector would force winding 0, C=0; since C=1!=0 NONE exists, so v424 sub-step (i)'s realisation is PROVABLY the quasi-local NPW26 LTO net (strict locality topologically forbidden, not a missing premise). SEAM.EQUIV.01 stays [O] (continuum theorem MMST v336 the backbone).

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SEAM.EQUIV.01; SEAM.S3.LTO.01; SEAM.S3.FROM-P1.01; SEAM.EQUIV.EDGE.CHERN.01; v460; v447; v456; v367

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  • v461_seam_strict_locality.pyRegistered verification module · frontier
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    SEAM.S3.LOCALITY.01: the Kapustin-Fidkowski/Thouless strict-locality OBSTRUCTION made explicit -- sharpening v460's verdict from a cited statement to an exhibited topological obstruction. [E] CHERN INTEGER: the FHS Chern of v367's p+ip collar = +1 (chiral M=1), 0 (trivial M=3), -1 (opposite mass). [E] WILSON-LOOP / WANNIER-CENTRE WINDING = CHERN: the hybrid Wannier centre theta(ky) winds by |C|=1 (chiral) and 0 (trivial) over the BZ -- exp-localised Wannier exist IFF winding=0 (Brouder et al.), so the chiral collar has NO exp-localised Wannier basis. [E] OBSTRUCTION INTEGERS TIED: winding=|C|=1!=0 and c_-=16/2=8=g_car+N_fam=rank E8!=0. [E] NEG CONTROL: BOTH phases gapped, yet only the trivial (winding 0) admits exp-localised Wannier and a strict finite-range commuting projector -- it is the CHIRALITY, not the gap. [C]/[O] a strictly finite-range commuting projector would force winding 0, C=0; since C=1!=0 none exists, so v424 sub-step (i)'s realisation is PROVABLY the quasi-local NPW26 LTO net; SEAM.EQUIV.01 stays [O]. Python-only (numpy).

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