A registered result in its source context

TFPT4D.LATTICE.ACTION.01

Original ledger classification: Open (research contract; T1-T7 harness + Euclidean T2 kill + Hamiltonian-route T2 clearance executed at toy level; no gate closed)

Original claim text

THE EXPLICIT 4D LATTICE ACTION CONTRACT [O] (registered 2026-08-27 from the external bird's-eye review; route step (2) of the DIMENSION.UPLIFT.FIREWALL.01 ordering made concrete -- THE single object on which nearly all open 4D questions become simultaneously testable). DEMAND: exhibit ONE fully explicit finite family of 4D Euclidean lattice theories Z_a[J] = int DU Dpsi DPhi exp(-S_a[U, psi, Phi] + J O) with S_a = S_Wilson[U] + psibar D_GW[U, Phi] psi + S_Phi[U, Phi] + S_seam/top, where U are the fundamental holonomies (TFPT fixes representation content, charge lattice, coupling relations, boundary conditions), D_GW is a Ginsparg-Wilson/overlap operator for the TFPT chiral representation content (the CHIRAL4D.NOMIRROR.01 operator), Phi is the ONLY allowed relevant scalar/link-mixing sector (EWSB downstream), and S_seam/top is the boundary/topological module transporting the seam data into the bulk -- FIRST at finite lattice spacing a, deliberately WITHOUT continuum claims. FINITE GATES (all machine-checkable at finite size; the promotion criteria for any candidate): (T1) exact gauge invariance; (T2) a positive transfer matrix (RP at finite a); (T3) the seam boundary restriction reproduces the TFPT seam data EXACTLY (not merely dimensions or group labels); (T4) anomaly bookkeeping including the global SU(2) anomaly; (T5) the index/generation count; (T6) the mirror spectrum separated; (T7) at least one NONVANISHING connected four-point function (not free / generalized-free). KILL TESTS: no local reflection-positive action with the correct seam restriction exists (master route dead); every candidate is generalized-free (T7 unreachable); a hidden freely tunable dimensionless parameter is required (the strong parameter-freeness claim is refuted); the uniform twistor flat direction (v973: the sector-0 Okubo admixture) shifts NORMALIZED observables rather than only the vacuum normalization of Z (a genuine undetermined modulus). RELATION: the continuum limit is the SEPARATE contract QFT4D.OS.RECON.01; the unitary dilation is DYN.UNITARY.DILATION.01; d = 4 is typed by DIMENSION.SELECTOR.4D.01 [C]; the generating-functional collapse of the four transfer bridges is FTRANSFER.GENERATING.01. NOTHING in the corpus closes any gate. EXECUTED UPDATE (2026-08-28, v989): T4 exact SM one-generation anomaly bookkeeping (drop-L mutant fires); T5/T6 2D overlap index=q and GW circle (N=8); T7 Z2-cube kappa_4 != 0 at beta=0.4 (free control 0). EUCLIDEAN T2 KILL (Z2 N_t-exact): overlap |det D_ov|^2 violation ABSENT at N_t=2, APPEARS at N_t=4 (det-only -0.249); Wilson control PSD everywhere -- pinned on overlap time nonlocality. HAMILTONIAN ROUTE CLEARS T2 by construction (Gauss-law Hilbert space, H=H^dag, T=e^{-aH} SPD; seam intertwiner; background-field mu4 split k=1,3 degenerate; determinantal-law Gaussianity test). NOTHING closes the 4D contract. Python-only / Wolfram mirror deferred. See also QFT4D.LATTICE.FUNDAMENTAL.01 (registered route/typing).

Original classification detail

Open: one explicit finite 4D lattice family with seven finite gates T1-T7. EXECUTED (v989, toy level): T4 exact, T5/T6 2D mechanism, T7 toy, Euclidean T2 kill (N_t-exact), Hamiltonian route clears T2 by construction. No gate of the 4D contract closed; display marker stays Open.

Dependencies as recorded

DIMENSION.UPLIFT.FIREWALL.01; QFT4D.OS.RECON.01; CHIRAL4D.NOMIRROR.01; DYN.UNITARY.DILATION.01; DIMENSION.SELECTOR.4D.01; SEAM.BULK4D.RECON.01