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Original ledger classification: Continuum chain assembly [C]/[E]/[O] (edge-existence reduced via anomaly inflow; residual = lattice realization tied to seam one-sidedness; B already closed by v40)

Recorded statement: DIRECTION A (2026-06-23): the continuum chain of SEAM.EQUIV.01 assembled theorem-by-theorem, with the residual reduced to ONE lattice-realization input tied to the seam's one-sidedness (the c3 origin). After the reverse-audit/bandwidth…

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SEAM.EQUIV.CONTINUUM.03

Original ledger classification: Continuum chain assembly [C]/[E]/[O] (edge-existence reduced via anomaly inflow; residual = lattice realization tied to seam one-sidedness; B already closed by v40)

Original claim text

DIRECTION A (2026-06-23): the continuum chain of SEAM.EQUIV.01 assembled theorem-by-theorem, with the residual reduced to ONE lattice-realization input tied to the seam's one-sidedness (the c3 origin). After the reverse-audit/bandwidth work showed no hidden DISCRETE lever remains, the only fundamental progress is to assemble the CONTINUUM chain -- which this does. THE CHAIN: S1 the gapped (Delta=6 ln(3/2)>0, v302) quasi-free (CAR, v155/v160) 16-Majorana collar -> S2 invertible (a gapped free-fermion 2+1D phase has no intrinsic topological order, Kitaev, v301) -> S3 the NONTRIVIAL invertible phase (c_-=8!=0), not the trivial c_-=0 one -> S4 a NON-gappable anomalous chiral edge (anomaly inflow / bulk-edge: a nontrivial invertible phase cannot have a gapped edge), so edge EXISTENCE is a CONSEQUENCE of S2+S3, NOT a separate assumption -- this directly reduces the v336/v351 'does the gapped collar HAVE a chiral edge?' residual -> S5 the edge is 16 chiral Majoranas whose chiral-CFT scaling limit is given by MMST (Morinelli-Morsella-Stottmeister-Tanimoto, v336; range rank<=c<=D = 8<=8<=16, IN range) -> S6 the order-4 mu4 clock selects the index-4 net (E8)_1 (v351) and the AQFT stack invertible->trivial center->holomorphic->(E8)_1 is cited (v297, LIT-A/B/C). [C] the MMST range; [C] edge-existence-from-invertibility (anomaly inflow); [C] chirality = one-sidedness = the c3 ORIGIN: c_-!=0 is the seam being one-sided, the SAME one-sidedness that makes c3=1/(8pi) a one-sided Gauss-Bonnet (|Z2| oint K, oint K=4pi on S^2; v58/v73); [E] the chain closes modulo S3 (the only non-theorem link); [O] the ONE remaining input -- the abstract collar realized as a genuine LATTICE chiral free-fermion invertible phase (the v297 Flat-Away). NET: SEAM.EQUIV.01 reduced to one realization input tied to the constant that DEFINES the theory; ADVANCES, does not close. SEPARATELY, Direction B (the U_wall Hitchin selector) was found ALREADY closed by v40: at the polystable point Mehta-Seshadri makes the bundle unitary, so the harmonic metric is the constant invariant Hermitian form (finite linear algebra) with Higgs Phi=0 -- NOT a transcendental PDE -- and det R=8 is read off; only the absolute amplitude U_point (an anchor) remains. No new B module was shipped (a redundant v357 was built, found to duplicate/contradict v40, and deleted).

Original classification detail

[C] the MMST range + edge-existence-from-invertibility + chirality=one-sidedness=c3-origin; [E] chain-closes-modulo-S3; [O] the one lattice-realization input. A genuine assembly reducing SEAM.EQUIV.01 to one realization input tied to the seam one-sidedness; does NOT close it. Direction B found already closed by v40 (harmonic metric = finite linear algebra, not a PDE); no redundant B module shipped.

Dependencies as recorded

SEAM.EQUIV.01; v301; v302; v336; v351; v297; v58; v40

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  • v356_continuum_mmst_applicability.pyRegistered verification module · core
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    Direction A: the continuum chain of SEAM.EQUIV.01 assembled theorem-by-theorem, residual reduced to ONE lattice-realization input tied to the seam's one-sidedness. Chain: gapped (v302) quasi-free 16-Majorana collar (v155/v160) -> invertible (Kitaev, v301) -> the NONTRIVIAL invertible phase (c_-=8) -> a non-gappable anomalous chiral edge (anomaly inflow: edge EXISTENCE follows, reducing the v336/v351 'does the edge exist?' residual) -> chiral-CFT scaling limit (MMST v336, 8<=8<=16) -> order-4 mu4 clock + AQFT stack pin (E8)_1 (v351/v297). The only non-theorem link is the seam one-sidedness = the c3 origin (c_-!=0 = one-sided = the |Z2| oint K = 8 of c3=1/(8pi), v58). [C]/[E]/[O]; ADVANCES SEAM.EQUIV.01 to one realization input, does not close. (Direction B was found already closed by v40.)

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