A registered result in its source context
Original ledger classification: Free-fermion invertibility [E/C] (topological-order discharge)
Recorded statement: DISCHARGE ROUTE A'S 'INVERTIBLE BULK' VIA THE FREE-FERMION CLASSIFICATION (2026-06-19): the single open hypothesis of Route A (v297 LIT-A, 'the raw quasi-free seam bulk is invertible/SRE'); since v300 collapsed Route B into Route A's…
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Paper context: tfpt research contracts
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SEAM.EQUIV.A.INV.01
Original ledger classification: Free-fermion invertibility [E/C] (topological-order discharge)
Original claim text
DISCHARGE ROUTE A'S 'INVERTIBLE BULK' VIA THE FREE-FERMION CLASSIFICATION (2026-06-19): the single open hypothesis of Route A (v297 LIT-A, 'the raw quasi-free seam bulk is invertible/SRE'); since v300 collapsed Route B into Route A's rationality, this is the LAST unconditional gap of SEAM.EQUIV.01. THE MOVE: a GAPPED free-fermion (Gaussian/quasi-free) 2+1D bulk cannot carry intrinsic topological order -- free fermions give the integer (IQHE/Chern) phases, ALL invertible (no fractional anyons); intrinsic topological order requires interactions. Kitaev's periodic table (class D, no symmetry) Z-classifies them by the chiral Majorana number, the only invariant being the chiral central charge c. [E] CARRIER=16 MAJORANAS, c=8: g_car+N_fam=5+3=8=16/2 (v148 NS/R census). [E] SO(16)_1 contains (E8)_1: dim so(16)=120 currents + 128 spinor = 248 = dim E8, the level-1 currents (v154 simple-current extension). [C] FREE-FERMION INVERTIBILITY: a gapped quasi-free bulk is invertible automatically (Kitaev). [E] INVERTIBILITY INVARIANT |det K|=#anyons=1: the E8 K-matrix (Cartan E8) has det=1 (one primary => invertible); the gauged contrast D8=SO(16) has det(Cartan)=4 (anyons), which a free-fermion bulk cannot produce (output-consistency with the classification). [O] REDUCTION: LIT-A's 'invertible bulk' now FOLLOWS from 'gapped 16-Majorana quasi-free bulk' (v148 carrier + v160 quasi-free fixed point + the mass gap); the SEAM.EQUIV.01 residual changes character -- from 'is the bulk invertible (could it hide anyons)?' (now: a gapped free-fermion bulk cannot) to 'is the quasi-free bulk gapped?' (a spectral input). [O] VERDICT: with v300 (Route B = Route A's rationality), the WHOLE remaining open content of SEAM.EQUIV.01 is the single SPECTRAL statement 'the quasi-free seam bulk is gapped'; the topological-order obstruction (hidden anyons) is removed, the gap is NOT manufactured.
Original classification detail
[E] the carrier/c=8/embedding/det invariants; [C] the free-fermion invertibility import (Kitaev); [O] the reduced residual (gapped + quasi-free). Discharges the TOPOLOGICAL-ORDER part of Route A's last hypothesis, reducing it to a spectral input; does NOT manufacture the gap, does NOT close SEAM.EQUIV.01.
Dependencies as recorded
SEAM.EQUIV.A.LIT.01; FLATAWAY.RIGID.01; QGAMB.TIERB.01; SEAM.EQUIV.01
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- Research contracts
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- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
Navigation through a shared verification script
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- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)tfpt research contracts
- 2026-06-19 (Route A's last hypothesis discharged: the gapped quasi-free bulk is invertible by the free-fermion classification, v301)Research changelog; TFPT — Introduction and reading guide
- 2026-06-19 (the last lever: the seam mass gap is the derived Recovery gap [formula in source] , v302)Research changelog; TFPT — Introduction and reading guide
- 2026-06-23 (the two frontier walls attacked directly: Direction A assembles the continuum chain of SEAM.EQUIV.01 theorem-by-theorem and ties its residual to the seam one-sidedness; Direction B was found ALREADY closed by v40 (harmonic metric [formula in source] finite linear algebra, not a PDE): v356)Research changelog; TFPT — Introduction and reading guide
- 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
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)Research contracts
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)tfpt research contracts
Registered verification modules
- v301_route_a_invertible.pyRegistered verification module · frontier
Read the description recorded in the module registry
SEAM.EQUIV.A.INV.01 — discharge Route A's single open hypothesis (v297 LIT-A: 'the raw quasi-free seam bulk is invertible/SRE') via the free-fermion classification. Since v300 collapsed Route B into Route A, this is the LAST unconditional gap of SEAM.EQUIV.01. [E] carrier = 16 Majoranas, c=8: g_car+N_fam=5+3=8=16/2 (v148). [E] SO(16)₁ ⊃ (E8)₁: dim so(16)=120 currents + 128 spinor = 248 = dim E8 (v154). [C] free-fermion invertibility (Kitaev periodic table): a gapped Gaussian/quasi-free 2+1D fermion phase (class D) is Z-classified by the chiral Majorana number and is ALWAYS invertible (no intrinsic anyons; topological order needs interactions) — so a gapped quasi-free bulk is invertible automatically. [E] invariant |det K|=#anyons: E8 Cartan det=1 (invertible) vs the gauged contrast D8=SO(16) det=4 (anyons), which free fermions cannot produce. [O] reduction: LIT-A's 'invertible bulk' now FOLLOWS from 'gapped 16-Majorana quasi-free bulk' (v148+v160+the gap); the residual changes from a topological-order statement to the spectral input 'is the quasi-free bulk gapped?'. [O] verdict: with v300 the WHOLE open content of SEAM.EQUIV.01 reduces to the single spectral statement 'the quasi-free seam bulk is gapped'.
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