The lattice fundamental interpretation

QFT4D.LATTICE.FUNDAMENTAL.01

Original ledger classification: Decision (registered route/typing; no [E] claim, no marker move; QFT4D.OS.RECON.01 unchanged as the math program)

Original claim text

THE LATTICE-FUNDAMENTAL READING (registered 2026-08-28 as a typed DECISION, not an [E] claim and not a marker move). DECISION: TFPT's PHYSICAL completeness criterion is the finite, local, unitary lattice quantum theory -- Hamiltonian route: Gauss-law Hilbert space, hermitian local H, T = e^{-aH} positive by construction, Lieb-Robinson cone -- while the exact continuum Osterwalder-Schrader limit (QFT4D.OS.RECON.01) is retyped as MATHEMATICAL REINFORCEMENT, a named strengthening program, no longer the physical bottleneck. Poincare invariance is an IR fixed-point property with experimentally bounded irrelevant Lorentz-violating operators. JUSTIFICATION ANCHORS (v989): today's Euclidean T2 kill of the overlap shortcut (exact; N_t-exact confirmation: violation ABSENT at N_t=2, APPEARS at N_t=4 det-only -0.249; Wilson control PSD everywhere -- pinned on overlap time nonlocality) and the Hamiltonian route clearing T2 by construction (interior Gauss exact, seam-sector intertwiner, H = H^dag). DISPLAY: nothing closes; QFT4D.OS.RECON.01 UNCHANGED as the math program; TFPT4D.LATTICE.ACTION.01 stays [O] as the constructive 4D lattice contract. AMENDMENT (2026-08-29, review wave 4): the reviewer's precision is accepted -- 'a single finite box is not a world'. The fundamental object is the QUASILOCAL CONSISTENT FAMILY {H_Lambda} with the thermodynamic-limit dynamics tau_t = lim e^{it H_Lambda} A e^{-it H_Lambda}. Binding phrasing: CONTINUUM (a -> 0) OPTIONAL (mathematical reinforcement); THERMODYNAMIC LIMIT (|Lambda| -> infinity) AND CONTROLLED IR UNIVERSALITY MANDATORY. Decision typing UNCHANGED; no [E] claim, no marker move. WAVE-7 (2026-08-30, v1008): 2+1D master-object scaffold-coherent -- combinatorial K=0 (plaquette exponents cancel), frozen-link q^2~4, unique-contractive selector |R'|<1, QWZ wall + DET4 mirror, Z6/Z4 four-block assembly. L=3 262144 / matter 129024 out of suite. Decision typing UNCHANGED; no [E] claim, no marker move. LATE EVENING (2026-08-30, v1013): MANDATORY-DYNAMICS LEG CLOSED at Hamiltonian-class level (theorem memorandum articles/2026-08-30/tfpt_thermodynamic_dynamics_en.tex/pdf). Uniform Lieb-Robinson bound J=12/5, R=2, z=4, kappa=16043/450, v_LR=32086 e/225 ~ 387.64; norm-convergent thermodynamic-limit dynamics tau_t; gauge-invariant quasilocal algebra A^G (Gauss caveat resolved via the invariant subalgebra); existence of ground and beta-KMS states. Numeric twin: measured v=2.0 << proved bound; convergence bound dominates nested differences at buffers 8/16/32. Remaining: phase uniqueness, limit gap, IR universality. Decision typing UNCHANGED; no [E] claim, no marker move.

Original classification detail

Decision: physical completeness = finite local unitary lattice QFT (Hamiltonian route); continuum OS limit retyped as mathematical reinforcement. No [E] claim, no marker move; QFT4D.OS.RECON.01 unchanged as the math program. | 2026-08-29: quasilocal family {H_Lambda} is the fundamental object; continuum (a->0) optional; thermodynamic limit + controlled IR universality mandatory. Decision typing UNCHANGED. | WAVE-7 (2026-08-30, v1008): 2+1D scaffold-coherent (K=0 theorem, contractive-root selector, wall/mirror, Z6 assembly); no marker move. | AFTERNOON (2026-08-30 v1011): 3+1D minimal object viable; fully coupled link-wall dynamics demonstrated at minimal scale; Kronecker limitation removed. Decision typing UNCHANGED. | LATE EVENING (2026-08-30 v1013): mandatory-dynamics leg CLOSED at class level (LR + tau_t + A^G + state existence proved); remaining phase uniqueness, limit gap, IR universality. Decision typing UNCHANGED.

Dependencies as recorded

TFPT4D.LATTICE.ACTION.01; QFT4D.OS.RECON.01; CHIRAL4D.NOMIRROR.01; DYN.UNITARY.DILATION.01