A registered result in its source context
Original ledger classification: Theorem stack [E] (citable composition) + [O] (one shared hypothesis)
Recorded statement: ROUTE A LITERATURE THEOREM STACK (2026-06-18): writes Route A's single import (v287 L3) as a precise, citable composition of three established theorems, isolating the one open hypothesis. [E] LIT-A: invertible/SRE gapped phase => trivial…
Statement, assumptions and sources
Paper context: Research contracts
The exact identifier, original classification and full claim are available below.
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SEAM.EQUIV.A.LIT.01
Original ledger classification: Theorem stack [E] (citable composition) + [O] (one shared hypothesis)
Original claim text
ROUTE A LITERATURE THEOREM STACK (2026-06-18): writes Route A's single import (v287 L3) as a precise, citable composition of three established theorems, isolating the one open hypothesis. [E] LIT-A: invertible/SRE gapped phase => trivial bulk topological order (no nontrivial anyons, trivial Drinfeld center). Refs: Kitaev, Ann. Phys. 321 (2006); Freed-Hopkins, Geom. Topol. 25 (2021). [E] LIT-B: the bulk modular category is the Drinfeld center Z(C) of the boundary fusion category; a trivial center forces the boundary chiral net to be completely rational with trivial representation category (holomorphic). Refs: Mueger, J. Pure Appl. Algebra 180 (2003); Kawahigashi-Longo-Mueger, Comm. Math. Phys. 219 (2001). [E] LIT-C: a holomorphic chiral net/VOA of central charge 8 is (E8)_1 (the rank-8 even unimodular lattice is unique = E8; the holomorphic c=8 net is its lattice net). Refs: Conway-Sloane (lattice uniqueness); Dong-Xu / Kawahigashi-Longo (holomorphic net = lattice net). [E] CHAIN COMPOSES: out(LIT-A)=in(LIT-B), out(LIT-B)=in(LIT-C), so 'invertible bulk => (E8)_1' is one logical chain; all three legs established (none is the open step). [O] THE ONE OPEN HYPOTHESIS: the input of LIT-A, 'the raw quasi-free seam bulk is invertible (SRE)', is the single open premise and is the SAME geometric input as Route B's Flat-Away. [E] NON-CIRCULAR: the stack uses only AQFT/topological-phase literature (no DtN/Steklov), meeting Route B only at the shared hypothesis (the v286 firewall holds).
Original classification detail
[E] the typed citable stack (LIT-A/B/C with statements + references) + the composition + the shared-hypothesis isolation + non-circularity; [O] the one open hypothesis (seam-bulk invertibility = Route B's Flat-Away). A documentation/typing module; it does NOT prove the hypothesis.
Dependencies as recorded
SEAM.EQUIV.A01; SEAM.EQUIV.01; FLATAWAY.RP.01; SEAM.EQUIV.B01
Open the original ledger source, row 397Location recorded in the ledger
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- Research contracts
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- 2026-06-18 (a [formula in source] closed form + Route A literature stack, v296– v297)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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.
- 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
- 2026-06-23 (Directions 3 \& 7 — the two hard functional-analysis residuals ADVANCED: the QG measure as one-loop fluctuations around the parameter-free saddle ( v365), and the seam collar verified IN MMST's free-fermion class so the scaling limit is [formula in source] ( v366))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
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v297_route_a_literature_stack.pyRegistered verification module · frontier
Read the description recorded in the module registry
SEAM.EQUIV.A.LIT.01 — Route A's 'one standard import' written out as a precise CITABLE theorem stack. [E] LIT-A invertible/SRE bulk ⇒ trivial bulk topological order (Kitaev, Ann.Phys.321 2006; Freed-Hopkins, Geom.Topol.25 2021); [E] LIT-B bulk MTC = Drinfeld center, trivial center ⇒ holomorphic boundary net (Müger, JPAA 180 2003; Kawahigashi-Longo-Müger, CMP 219 2001); [E] LIT-C holomorphic c=8 net ⇒ (E8)₁ (Conway-Sloane lattice uniqueness; Dong-Xu/Kawahigashi-Longo). [E] the three COMPOSE (out=in matches) into 'invertible bulk ⇒ (E8)₁', all legs established; [O] the ONE open hypothesis is the input of LIT-A, 'the raw quasi-free seam bulk is invertible (SRE)' = Route B's Flat-Away. [E] non-circular with Route B (no DtN/Steklov; the v286 firewall holds).
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.