Original ledger status
SEAM.EQUIV.CONTINUUM.03
SEAM.EQUIV.CONTINUUM.03
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).
Recorded status: 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)
Dependencies, status detail and source
Canonical status: [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: SEAM.EQUIV.01; v301; v302; v336; v351; v297; v58; v40
Scripts: v356_continuum_mmst_applicability.py
Location: tfpt_research_contracts
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