A registered result in its source context
Original ledger classification: Dependency checker [E] (4/5 discharged) + [O] (the one external theorem)
Recorded statement: ROUTE A (AQFT) DEPENDENCY CHECKER (2026-06-18): for the open Gral arrow 'free Gaussian RP bulk => holomorphic single-sector boundary net', types the 5-lemma AQFT chain and isolates the ONE missing standard theorem (does NOT prove the…
Statement, assumptions and sources
Paper context: tfpt research contracts
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SEAM.EQUIV.A01
Original ledger classification: Dependency checker [E] (4/5 discharged) + [O] (the one external theorem)
Original claim text
ROUTE A (AQFT) DEPENDENCY CHECKER (2026-06-18): for the open Gral arrow 'free Gaussian RP bulk => holomorphic single-sector boundary net', types the 5-lemma AQFT chain and isolates the ONE missing standard theorem (does NOT prove the arrow). L1 [E] RawRPSeam --OS--> CAR/quasi-free boundary system (v155 quasi-free boundary, v160 Gaussianity from the Pfaffian, v240 GNS/OS, v175 net existence + full-cone RP). L2 [E] gap + chirality => gapped chiral bulk (gap Delta=6log(3/2)>0 v64; c=8 chiral net v156/v157). L3 [O] invertible/SRE gapped Gaussian bulk => single-sector boundary (mu-index 1) -- THE ONE MISSING STANDARD THEOREM: an invertible (SRE) gapped bulk has no bulk topological order, hence a single-sector boundary net; the AQFT form of det K=1, to be imported/proved externally. L4 [E] mu-index 1 + c=8 => holomorphic (v234 holomorphy<=>1 sector). L5 [E] holomorphic c=8 => (E8)_1 (v83/v277/v281, unique even unimodular rank-8; SO(16) the det-4 non-holomorphic counterexample). VERDICT: 4/5 lemmas discharged, so Route A reduces SEAM.EQUIV.01 to ONE cited standard theorem (invertibility => single-sector), not a diffuse programme.
Original classification detail
[E] the AQFT chain typing + the four discharged steps (L1/L2/L4/L5) + the single-missing-theorem isolation (L3); [O] the one external theorem 'invertible Gaussian bulk => single-sector boundary'. A dependency checker, not a proof.
Dependencies as recorded
SEAM.EQUIV.01; QFT.NETRP.01; GATE.HOLO.01; QGAMB.TIERB.01; QGAMB.ROUTEII.01
Open the original ledger source, row 382Location recorded in the ledger
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- Research contracts
Sections that explicitly cite this claim
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- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-06-18 (closing sprint: the Seam Equivalence Theorem named + both routes attacked, v286– v288)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- Front matter / supportResearch contracts
- 2026-06-18 (Route B sharpened: raw mark-locality decomposed + reviewer firewalls, v289 / v287– v288)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v287_free_rp_bulk_to_holomorphic_boundary.pyRegistered verification module · frontier
Read the description recorded in the module registry
SEAM.EQUIV.A01 — Route A (AQFT) theorem-dependency checker for the open Gral arrow 'free Gaussian RP bulk ⇒ holomorphic single-sector boundary net': types the 5-lemma chain and isolates the ONE missing standard theorem. [E] L1 RawRPSeam→OS→CAR/quasi-free boundary (v155/v160/v240/v175); [E] L2 gap+chirality ⇒ gapped chiral bulk (v64/v156); [O] L3 invertible/SRE Gaussian bulk ⇒ single-sector boundary (μ-index 1) — THE ONE MISSING STANDARD THEOREM (the AQFT form of det K=1); [E] L4 μ=1+c=8 ⇒ holomorphic (v234); [E] L5 holomorphic c=8 ⇒ (E8)₁ (v83/v277/v281). Verdict: 4/5 discharged, Route A reduces SEAM.EQUIV.01 to one cited theorem (invertibility ⇒ single-sector).
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