Original ledger status
SEAM.EQUIV.CONTINUUM.LR.01
SEAM.EQUIV.CONTINUUM.LR.01
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.
Recorded status: 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
Dependencies, status detail and source
Canonical status: Numerical
Dependencies: SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.S3.RP.01; SEAM.EQUIV.CONTINUUM.03; v367; v336; v302; v329
Scripts: v439_seam_lieb_robinson.py
Location: tfpt_research_contracts
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