Learning Dense Ising Models from Deterministic Snapshots without Mixing

We study parameter recovery for a dense Ising model from one arbitrarily initialized heat-bath trajectory observed only at a fixed deterministic time grid. The unknown interaction matrix is symmetric, and each field-plus-interaction row width is bounded by a known Lambda. Every site has a known unit-rate heat-bath attempt clock, including attempts that leave the spin unchanged. The learner receives only exact full-state snapshots X(c), X(2c), ..., X(Nc) at a known positive rational lag c. No update attempts, intermediate flips, stationary initialization, degree bound, minimum interaction strength, or mixing-time bound are required. Joint symmetric pseudolikelihood recovers all fields and interactions with an epsilon^(-2) sample dependence and absolute polynomial exponents in dimension and inverse accuracy. For fixed width and lag, a conservative explicit sample bound is O(n^6 epsilon^(-2) + n^5 epsilon^(-2) log(n/delta)), with constants exponential in the width and polynomial in the inverse lag; no dimension-optimality is claimed. Total physical acquisition time is Nc, distinct from the data-processing runtime. The proof combines reversible generator-coboundary concentration with uniform dense conditional excitation. A fixed-iteration rational conditional-gradient algorithm gives an all-outcome finite-bit runtime bound for rational width, lag, target accuracy, and confidence inputs; the true model parameters may be arbitrary real numbers. A one-spin lower bound establishes the necessity of the accuracy exponent two. The result concerns symmetric heat-bath models with known clock normalization and exact observations. It does not provide an efficient sampler or partition-function algorithm for the learned low-temperature model. Full proofs, an explicit finite-bit implementation, and comparisons with earlier trajectory-learning and pseudolikelihood methods are included.