A registered result in its source context
Original ledger classification: Lieb-Robinson motor [E]/[C]: the gapped p+ip collar (v367) has a uniform-in-N gap, exponential clustering with N-independent xi, and a finite light cone, so by Nachtergaele-Sims its bulk thermodynamic limit EXISTS -- grounding the bulk half of the cited MMST existence in OUR model. SEAM.EQUIV.01 stays [O], the open step narrowed to the chiral massless edge scaling limit
Recorded statement: The Lieb-Robinson/Nachtergaele-Sims continuum-existence MOTOR for the gapped seam collar (2026-06-30) -- grounds the BULK half of the cited MMST existence (SEAM.MMST.INCLASS.01/v336) in the explicit v367 p+ip lattice model, narrowing the…
Statement, assumptions and sources
Paper context: Research contracts
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
Read the exact registered claim and its dependencies
SEAM.EQUIV.CONTINUUM.LR.01
Original ledger classification: Lieb-Robinson motor [E]/[C]: the gapped p+ip collar (v367) has a uniform-in-N gap, exponential clustering with N-independent xi, and a finite light cone, so by Nachtergaele-Sims its bulk thermodynamic limit EXISTS -- grounding the bulk half of the cited MMST existence in OUR model. SEAM.EQUIV.01 stays [O], the open step narrowed to the chiral massless edge scaling limit
Original claim text
The Lieb-Robinson/Nachtergaele-Sims continuum-existence MOTOR for the gapped seam collar (2026-06-30) -- grounds the BULK half of the cited MMST existence (SEAM.MMST.INCLASS.01/v336) in the explicit v367 p+ip lattice model, narrowing the open analytic step to the chiral EDGE scaling limit. [E] UNIFORM GAP: the collar gap is independent of N (Delta(N)=const>0 across N=20..160), the lattice image of the OS transfer gap 6 ln(3/2)>0 (v302/v329) -- the Nachtergaele-Sims hypothesis. [E] EXPONENTIAL CLUSTERING: |<c_i^dag c_j>|~e^{-r/xi} with xi finite and STABLE across N (gapped => Hastings-Koma decay), the N-independent locality. [E] LIEB-ROBINSON LIGHT CONE: the single-particle propagator |(e^{-iHt})_ij| is confined to |i-j|<~v_LR t with finite v_LR (~2t), exponentially small beyond the cone -- finite-speed information flow. [C] NACHTERGAELE-SIMS LIFT: uniform gap + finite LR velocity => (Nachtergaele-Sims-Young) exponential clustering with N-independent xi AND existence+uniqueness of the thermodynamic-limit ground state with a finite light cone -- the bulk continuum-existence ingredient derived for OUR collar, not imported. [C]/[O] VERDICT: the bulk thermodynamic limit of the seam collar EXISTS by Lieb-Robinson; SEAM.EQUIV.01 stays [O], the open analytic step now narrowed to the CHIRAL massless EDGE scaling limit (the c=8 (E8)_1 CFT, MMST), distinct from the gapped bulk limit.
Original classification detail
Numerical
Dependencies as recorded
SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.S3.RP.01; SEAM.EQUIV.CONTINUUM.03; v367; v336; v302; v329
Open the original ledger source, row 497Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- 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.
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-06-30 (six convergent attacks on the one SEAM.EQUIV.01 continuum residual — intrinsic Bisognano–Wichmann, a Lieb–Robinson continuum motor, the [formula in source] -homotopy, an applicability audit, uniform rigidity, and falsifiable kill tests; none closes the keystone, together they reduce it to a single analytic fact and make the claim falsifiable)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.
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- 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 )Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v439_seam_lieb_robinson.pyRegistered verification module · frontier
Read the description recorded in the module registry
SEAM.EQUIV.CONTINUUM.LR.01: the Lieb-Robinson/Nachtergaele-Sims continuum-existence MOTOR for the gapped seam collar -- grounds the BULK half of the cited MMST existence in the explicit v367 p+ip model. [E] UNIFORM GAP: Δ(N)=const>0 across N=20..160 (lattice image of the OS transfer gap 6 ln(3/2)>0, v302/v329). [E] EXPONENTIAL CLUSTERING: |⟨c_i†c_j⟩|~e^{-r/ξ}, ξ finite and STABLE across N (gapped ⇒ Hastings-Koma decay). [E] LIEB-ROBINSON LIGHT CONE: |(e^{-iHt})_ij| confined to |i-j|≲v_LR t with finite v_LR (~2t). [C] NACHTERGAELE-SIMS LIFT: uniform gap + finite LR velocity ⇒ exponential clustering with N-independent ξ AND existence+uniqueness of the thermodynamic-limit ground state with a finite light cone -- derived for OUR collar. [C]/[O] the bulk thermodynamic limit EXISTS; SEAM.EQUIV.01 stays [O], the open step narrowed to the CHIRAL massless EDGE scaling limit. Python-only (numpy/scipy).
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.