Quantum Gravity from One Axiom

The Problem of Time — the apparent incompatibility between quantum mechanics' time parameter t and general relativity's proper time τ — has been treated as a fundamental obstacle to quantum gravity. I argue that this is a level-confusion: both theories define time within their own entity-theoretic frameworks, generating an apparent opposition that disappears when time is relocated to a meta-structural layer. Drawing on the meta-level temporal structure TSDT: = (VG, ≺) (Zeng 2026), the paper formalizes QM and GR time as two projections of a single Universal Time Formula, parameterized by entity-theoretic tokens. Four token specializations recover the corresponding time concepts. A Bridge Theorem establishes mutual compatibility of all token projections. A bidirectional QM-GR channel is constructed (forward: GR geometry → QM phase; reverse: discrete chain-pair → Lorentzian spacetime), composing into a self-consistent closed loop. Three further results move beyond dissolution toward unification. First, a Madelung-bridge construction derives the Schrödinger equation — Hilbert space, unitarity, Hamiltonian, quantum potential, Born rule — from the determination-graph axioms together with the continuum embedding (CL1), with no independent QM input; the derivation extends to Klein-Gordon. Second, a Planck-scale token μ = tP / |Aₕ'| is constructed on the discrete 𝒢D, where |Aₕ'| is the admissibility cardinality; under CL1, this single step-measure recovers QM (|A| ≫ 1) and GR (|A| = 1) as its two continuum limits, with Einstein's equation proved in the classical regime (|A| = 1) via a two-stage argument (Benincasa-Dowker action convergence + standard scalar-tensor variation). The exact quantum-gravitational correction is derived as a scalar-tensor equation with φ = 1/|A|. Third, the discrete determination graph without continuum embedding constitutes a self-contained Planck-scale quantum gravity theory: it has a well-defined path integral, a finite-dimensional S-matrix (unitary in the κ = 0 sector, isometric in the κ > 0 sector; no UV divergences), preserves information across black hole horizons, resolves singularities, derives the Past Hypothesis, and provides structural origins for gauge symmetry, Hawking radiation, spectral dimensionality, and the spin-statistics connection. The Problem of Time is not merely dissolved — it is replaced by a constructive framework in which QM and GR are unified as two limits of a single discrete structure.