A registered result in its source context
Original ledger classification: Lattice/topological-order (exact) [E]/[O]
Recorded statement: SEAM SRE CLOSURE (2026-06-17): the closing step of GATE.HOLO.01/02 recast as a PHYSICAL, falsifiable condition -- no topological ground-state degeneracy <=> det K=1 <=> the seam bulk is short-range-entangled (SRE/invertible). Sharpens the…
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Paper context: tfpt research contracts
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GATE.HOLO.03
Original ledger classification: Lattice/topological-order (exact) [E]/[O]
Original claim text
SEAM SRE CLOSURE (2026-06-17): the closing step of GATE.HOLO.01/02 recast as a PHYSICAL, falsifiable condition -- no topological ground-state degeneracy <=> det K=1 <=> the seam bulk is short-range-entangled (SRE/invertible). Sharpens the residual from definitional ('condense the Lagrangian glue', v235) to a yes/no statement about topological order. (1) the abelian K-matrix ground-state degeneracy on a genus-g surface is |det K|^g: carrier D5(+)A3->16, SO(16)_1=D8->4, (E8)_1->1 on the torus; so 'no topological degeneracy on ANY closed surface' <=> |det K|=1. (2) SRE <=> det 1 <=> E8: among rank-8 even positive-definite K (c=signature=8=g_car+N_fam) only E8 has det 1 -- THE unique nontrivial bosonic SRE 2+1d phase (Kitaev E8), edge (E8)_1 holomorphic; D8 and the carrier are long-range-entangled (topologically ordered). (3) PLANE vs TORUS: a unique ground state on the PLANE (RP+gap+cluster+OS, the established admissible-sector facts) is NECESSARY but not sufficient -- the plane has no non-contractible cycles and cannot see |det K|, the torus does; so the residual is exactly 'the seam unique-vacuum property extends to the torus' = SRE. (4) NEG: a topologically-ordered (LRE) bulk has |det K|>1 (D8: 4-fold torus degeneracy + a non-holomorphic boundary 1,v,s,c = SO(16)_1 rival). (5) SHARPENED RESIDUAL: the one open analytic step is now the physical statement 'the free RP gapped seam bulk is short-range-entangled (no topological ground-state degeneracy)' = det K=1 = the Kitaev E8 phase -- sharper than 'condense the Lagrangian glue' (v235) and than 'the seam is P^1 minus mu4' (QGEO.SYM.01). [E] the degeneracy=|det K|^g dictionary + SRE<=>det1<=>E8 selection; [O] the physical SRE premise. NOT a closure.
Original classification detail
[E] genus-g GSD=|det K|^g, no topological degeneracy <=> det K=1 <=> SRE; only E8 (det 1) is the bosonic SRE c=8 phase (Kitaev E8); plane unique-vacuum is necessary not sufficient (torus sees det K); residual = 'the seam is SRE' [O], a physical yes/no statement
Dependencies as recorded
GATE.HOLO.02; GATE.HOLO.01; QGEO.SYM.01
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- Research contracts
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- 2026-06-17 (CP phases as [formula in source] powers — a reduction of red-team Target D)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- Research Contract 1 — [formula in source]tfpt research contracts
- Research Contract 1 — [formula in source]tfpt research contracts
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-06-21 (adversarial-review follow-ups: a structural anti-numerology firewall, an out-of-sample seed cross-validation, an operational data watchdog, and the Target-A holomorphy kill test: v305– v307)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- 2026-07-14 (website + figure refresh — the /verification journey views become live HTML (the stale timeline/residual-chain images replaced by interactive components wired to the in-browser reproducer), the prediction surface's empirical-audit wall of text restructured into dated, expandable rounds, and the generated timeline/residual-chain figures extended to the current suite — presentation only, no content or marker moves)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v237_seam_sre_closure.pyRegistered verification module · frontier
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The closing step as a PHYSICAL condition: no topological ground-state degeneracy <=> det K=1 <=> the seam bulk is short-range-entangled (SRE/invertible). Sharpens GATE.HOLO.02's residual from definitional to physical/falsifiable. The K-matrix ground-state degeneracy on a genus-g surface is |det K|^g (carrier D5(+)A3->16, D8->4, E8->1 on the torus), so 'no degeneracy on any closed surface' <=> det K=1. Among rank-8 even positive-definite K (c=8=g_car+N_fam) only E8 has det 1 -- the unique nontrivial bosonic SRE 2+1d phase (Kitaev E8), edge holomorphic; D8/carrier are LRE. A unique vacuum on the plane (RP+gap+cluster) is necessary but not sufficient (the plane cannot see det K, the torus does), so the residual is exactly 'the seam unique-vacuum extends to the torus' = SRE. NEG: an LRE bulk (D8) has 4-fold torus degeneracy + non-holomorphic boundary. Sharpened residual: 'the free RP gapped seam is short-range-entangled (no topological order)' = det K=1 = the Kitaev E8 phase -- a yes/no statement, sharper than v235/QGEO.SYM.01. Not a closure.
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