We present a discrete ontology of spacetime in which the continuum structure of general relativity emerges from a quantised causal graph G = (V, ≺) endowed with a local fermionic occupation density ρ̃ᵥ ∈ [0,1] per vertex. Four results of Tier-1 epistemic status are established from this minimal structure. (1) Discrete proper time and metric censorship. Proper time emerges as τ_γ = τ₀ Σ e^{−αρ̃ᵥ} along causal chains; classical metric singularities are structurally excluded by the Pauli bound. (2) Uniqueness of the pentachoron. In d = 4, the 4-simplex is the unique convex cell simultaneously satisfying algebraic rigidity (RC), metric completeness (MC: 10 edges = 10 independent components of g_μν), and causal rank (CC). The macroscopic arrow of time follows as an arithmetic necessity of n = 5, not an independent axiom. (3) Zero-parameter coupling. The coupling α* = 1/(4 ln 2) ≈ 0.3607 is fixed uniquely by a Bekenstein–Hawking correspondence principle with no free parameter. (4) Structural unification of gravity and scalar threshold. Gravitational curvature and the scalar saturation regime are two regimes of a single flux function F(ρ) = ρ e^{−αρ}, sharing one field and one coupling. The cosmological constant appears as an integration constant, not a fundamental parameter. A fifth result of Tier-1 mathematical status derives the complete spin spectrum {0, 1/2, 1, 3/2, 2} of the Standard Model from the stabiliser groups of the five geometric object types of the pentachoron, via a topological selection rule s = d/2. Twenty off-diagonal (dimension, spin) combinations are forbidden. Two corollaries follow: wave-particle duality is resolved as a vertex-edge distinction on the causal graph; the standard MSSM gravitino as a vertex-localised state is topologically excluded, constituting a falsifiable prediction accessible at the LHC. The model predicts |c_GW/c − 1| ≤ 10^{−76}, compatible with GW170817 by 61 orders of magnitude via quadratic — not linear — Lorentz-invariance suppression. Keywords: discrete quantum gravity, causal graph, 4-simplex, pentachoron, Regge calculus, spin spectrum, Bekenstein-Hawking entropy, Lorentz invariance violation, Standard Model, unimodular gravity, causal sets