From Gödel to Lloyd: A Lattice of Finite-Rate Constraints in Physical Law

This preprint articulates a finite-rate closure conjecture for physical law, motivated by a lattice of independently established constraints: quantization of action, causal speed limits, rate-bearing local consistency terms, quantum speed limits, the absence of a global time function in Gödel's rotating universe, information-capacity bounds, thermodynamic gravity, and physical limits to computation. The paper proposes a minimal covariant toy model of finite local closure and identifies high-energy astrophysical dispersion as an empirical falsifier. No theorem deriving the conjecture is claimed. A compile-clean ancillary Lean 4 file is included to pin the operational definitions, the toy-model ODE solution, and the lattice enumeration; it does not prove the conjecture, the τ → 0 limiting interpretation, or the empirical physics.