A registered result in its source context
Original ledger classification: edge existence forced by the invertible bulk (anomaly inflow) -- realised non-gappable chiral edge on the lattice strip [E]/[C]/[O]
Recorded statement: Track 1 (2026-06-23): the bulk-edge / anomaly-inflow leg (S4 of the v356 chain) made CONCRETE on the v367 lattice model -- a finite STRIP of the gapped p+ip model has a REALISED, non-gappable chiral edge, so edge EXISTENCE is a CONSEQUENCE…
Statement, assumptions and sources
Paper context: Research contracts
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SEAM.S3.INFLOW.01
Original ledger classification: edge existence forced by the invertible bulk (anomaly inflow) -- realised non-gappable chiral edge on the lattice strip [E]/[C]/[O]
Original claim text
Track 1 (2026-06-23): the bulk-edge / anomaly-inflow leg (S4 of the v356 chain) made CONCRETE on the v367 lattice model -- a finite STRIP of the gapped p+ip model has a REALISED, non-gappable chiral edge, so edge EXISTENCE is a CONSEQUENCE of the bulk being a nontrivial invertible phase (anomaly inflow), NOT a separate assumption. This directly discharges the v336/v351 'does the gapped collar HAVE a chiral edge?' residual on the lattice. [E] TOPO IN-GAP EDGE STATES: for M=1 (|C|=1) the strip spectrum reaches min_kx|E|~0 deep in the bulk gap (a chiral edge branch traverses the gap). [E] TRIVIAL CLEAN GAP (neg control): for M=3 (C=0) min_kx|E|>0.3 stays well above zero. [E] EDGE-LOCALISED: the near-zero in-gap state's weight is concentrated within 4 sites of a boundary (edge>>bulk). [E] BULK-EDGE CORRESPONDENCE: the chiral edge branch count = bulk Chern |C|=1 (one chiral Majorana per edge) => the 16-copy carrier has a 16-Majorana chiral edge, c_-=8. [C] ANOMALY INFLOW: a gapped invertible phase with c_-!=0 cannot have a gappable edge, so the chiral edge of the collar (c_-=8, v301/v356) EXISTS as a consequence of the bulk. [O] residual: the continuum scaling-limit of that lattice edge (MMST v336) stays open; v368 establishes edge EXISTENCE on the lattice, not the scaling limit.
Original classification detail
[E] the strip edge spectrum + localisation + bulk-edge correspondence + the trivial neg control; [C] the anomaly-inflow edge-existence argument; [O] the continuum scaling limit. Discharges the S4 'edge exists' leg on the lattice; does NOT close SEAM.EQUIV.01.
Dependencies as recorded
SEAM.EQUIV.01; v367; v356; v336; v351; v301
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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.
- 2026-06-23 (Track 1 — the S3 input made CONCRETE: an explicit gapped chiral-Majorana ( [formula in source] ) lattice model with numerical Chern [formula in source] realises the [formula in source] edge ( v367), and a strip shows the chiral edge exists by anomaly inflow ( v368))Research changelog; TFPT — Introduction and reading guide
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.
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)tfpt research contracts
- 2026-06-30 ( v449– v453 + Lean + Wolfram — the edge CFT named end-to-end: uniform-in- [formula in source] convergence, three independent reads of [formula in source] , the Ising operator tower, the [formula in source] modular data, and [formula in source] -symmetry derived from the four marks)Research changelog; TFPT — Introduction and reading guide
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
- Front matter / supportResearch contracts
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- 2026-06-23 (Status propagation: the v365– v380 [formula in source] FORM.SEAM.MMST.01 status carried into the remaining papers, the README and the Zenodo description)Research changelog; TFPT — Introduction and reading guide
All 37 linked sections
- Research Contract 1 — [formula in source]
- Honest status
- =150 2026-08-20 (CXI) (the externalization contracts — the two open non-RH kind-(A) external-math targets SEAM.EQUIV.01 and ALPHA.QUILLEN.EXACT.01 packaged as short, self-contained EXTERNALIZATION CONTRACTS for outside specialist mathematicians (conformal nets/VOA/AQFT for the seam; determinant lines/ [formula in source] -invariants/index theory for alpha), added as two new sections at the end of tfpt_research_contracts (before ``Certifiability and recommended order''), plus a one-sentence pointer in the head keybox; DOCUMENTATION ONLY — no module touched, no number changed, no status marker moved, no gate closed or narrowed, NO RH claim: (1) the SEAM.EQUIV.01 contract states the minimal theorem (the scaling limit of the gapped [formula in source] -equivariant CAR collar exists in local-net topology; the index-4 simple-current extension functor commutes with the limit; the OS reconstruction is the holomorphic [formula in source] lattice net) broken into the four review-named lemmata L1 (uniform energy/nuclearity bounds — honestly typed: NO uniform nuclearity estimate exists in the corpus), L2 (convergence of local algebras, the cited Osborne–Stottmeister scaling-limit theorem with the [formula in source] -equivariant structure retained), L3 (crossed product commutes with the limit; the finite index-4 Q-system is explicit, v125/ v154/ v469) and L4 (uniqueness of the holomorphic [formula in source] reconstruction; [formula in source] vs the same- [formula in source] rival [formula in source] ), with the complete typed hypothesis list (12 PROVEN-FINITE rows citing v302/ v113/ v155/ v160/ v356/ v366/ v367/ v368/ v461/ v376/ v377/ v378/ v379/ v125/ v154/ v216/ v286, 5 CITED-CLASSICAL rows, 1 OPEN target), the runnable finite models, the HONEST Lean axiom surface ( SeamScalingLimit.lean kernel-proves only the arithmetic hypotheses by decide; the analytic content is named cited axioms over opaque Props; no sorry; explicitly flagged: L1–L4 have ZERO Lean content beyond the composition audit), five must-fail controls (MF-S1: [formula in source] alone must NOT suffice — the red-team point; MF-S2: index-2 glue must yield [formula in source] ; MF-S3: the trivial [formula in source] collar must give no chiral limit; MF-S4: non-order-4 clock breaks the marks; MF-S5: the v286 import firewall) and four acceptance tests; (2) the ALPHA.QUILLEN.EXACT.01 contract states the two-step theorem T1 (gap-stable continuum limit [formula in source] under norm-resolvent convergence with the Fermi gap uniformly open over the twist torus — the Dai–Freed section has no zero; finite side computed, v472) and T2 ( [formula in source] [formula in source] Bismut–Freed curvature [formula in source] inflow response with the exact corpus coefficients [formula in source] , [formula in source] , [formula in source] , [formula in source] , exponent [formula in source] ), the two named open faces (the analytic diagonal- [formula in source] /multiplicity face v484/ v485 and the topological EM1 lemma v48/ v435), the typed hypothesis list (10 PROVEN-FINITE rows citing v3/ v48/ v341/ v382/ v434/ v470/ v435/ v342/ v367/ v472/ v484/ v485/ v391/ v433, 5 CITED-CLASSICAL rows, 1 OPEN target), the runnable finite models, the HONEST Lean statement (there is NO Lean formalisation of this target — stated plainly), four must-fail controls (MF-A1: no experimental [formula in source] anywhere in the construction; MF-A2: deck/carrier/Chern-level ablations must destroy the CODATA match; MF-A3: [formula in source] , [formula in source] ; MF-A4: the [formula in source] [formula in source] -power/metric-independence partition) and the review's three acceptance tests verbatim (no experimental [formula in source] input; unique physical fixed point [formula in source] ; ablations destroy the hit) plus one structural test; (3) the website paper mirror of tfpt_research_contracts ( papers.ts) gains one section entry covering both contracts; tfpt_research_contracts.pdf and changelog.pdf recompiled and mirrored via bash build.sh website; maps and changelog.ts regenerated via bash build.sh gen; bash build.sh audit [formula in source] AUDIT OK; manifests regenerated LAST. Both targets stay [O]; NO RH claim anywhere)
- What this means for the theory-of-everything question
- Outcome
- The hard reduction: the live residual as typed interfaces
- Honest status
- Front matter / support
- The unique attractor: a gapped transport selects ONE fixed point
- Front matter / support
- Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)
- 2026-06-23 (S3 closure stack — the target of the seam scaling limit pinned at EVERY computable level: central charge [formula in source] from the lattice ( v376), the [formula in source] character ( v377), the genus-1 torus count [formula in source] ( v378), and reflection positivity ( v379); only the abstract continuum existence (cited MMST) stays external)
- Front matter / support
- Honest status
- Front matter / support
- Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)
- The [formula in source] compiler: [formula in source] as a closure, not an input
- 2026-06-30 (the chiral-edge scaling motor v444 — the edge half of the one SEAM.EQUIV.01 continuum residual: the lattice edge already carries the conformal data of a chiral [formula in source] Majorana CFT and converges under refinement, grounding the EDGE the way v439 grounded the BULK; the keystone stays )
- The [formula in source] compiler: [formula in source] as a closure, not an input
- Research Contract 1 — [formula in source]
- The compact status formula: three honest layers
- Research Contract — SEAM.SIMPLECURRENT.GENERATOR.01 (one generator instead of 128 currents)
- Front matter / support
- The [formula in source] compiler: [formula in source] as a closure, not an input
- Full quantum gravity — induced from the boundary kernel
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
- The unique attractor: a gapped transport selects ONE fixed point
- In plain words
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
Registered verification modules
- v368_seam_s3_inflow.pyRegistered verification module · core
Read the description recorded in the module registry
Track 1: the bulk-edge / anomaly-inflow leg (S4 of the v356 chain) made CONCRETE on the v367 lattice model -- a finite STRIP of the gapped p+ip model has a realised, non-gappable chiral edge, so edge EXISTENCE follows from the invertible bulk (anomaly inflow), NOT a separate assumption. [E] topo in-gap edge states (M=1 strip min_kx|E|~0) vs trivial clean gap (M=3, neg control); [E] the near-zero state is edge-localised (weight within 4 sites of a boundary, edge>>bulk); [E] bulk-edge correspondence (edge branch count = bulk Chern |C|=1) => 16-Majorana edge, c_-=8. [C] anomaly inflow: a c_-!=0 invertible bulk cannot have a gappable edge => discharges the v336/v351 'does the edge exist?' residual on the lattice. [O] residual: the continuum scaling limit (MMST v336). Establishes edge EXISTENCE on the lattice; does NOT close SEAM.EQUIV.01.
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