Axiomatic Exhaustiveness: Laplace's Demon and the Metaphysics of Law in Quantum-Geometry Dynamics

Laplace's demon articulates causal determinism as the joint sufficiency of a complete particle state and the governing physical laws for fixing the entire future (and past) of a system. This picture treats state and law as two independent ontological ingredients: the demon must possess both. This paper argues that Quantum-Geometry Dynamics (QGD) instantiates a structurally different form of determinism. In QGD the physical laws are not co-equal, externally supplied partners to the state but are themselves theorems derived from two axioms — a discrete space of preons(−) and kinetic matter of preons(+) propagating by preonic leaps. Via QGD's Uniqueness Theorem, the derivation is shown to be not merely sufficient but exhaustive: the axioms admit exactly one consistent set of derived theorems, including the dynamical laws (p-gravity and n-gravity), with no alternative or supplementary law-like structure compatible with them. This collapses the traditional two-component Laplacean picture into a single axiomatic source, sharpening the demon's epistemic burden to a fixed, closed body of axiomatic knowledge rather than an open-ended pair of independent facts. The uniqueness claim is distinguished from mere nomic necessity, situated against Humean and necessitarian accounts of lawhood, and defended against the principal objections it invites (axiom-status regress, formal versus constructive uniqueness, and the relationship to QGD's bounded-arithmetic results on internal derivability). The exhaustiveness claim is further shown to be compatible with, and clarified by, an independent philosophical argument (Ismael 2019) that no predictor embedded within the universe it predicts can occupy Laplace's original transcendent epistemic position; QGD's own Selector Opacity Criterion reaches a structurally related conclusion by an axiomatic route. A companion note situates this paper's Level 1 scope against P52's treatment of whether QGD's determinism constitutes an imposition of law on the universe it describes. The argument is conditional on the empirical validity conditions set out in P11 and does not itself constitute evidence that those conditions are met.