Zero-Parameter Quantum Gravity from Discrete Recognition Calculus

We derive classical and quantum gravity from a minimal information-theoretic axiom—a recognition event requires non-empty data—with parameter-fixed, gauge-rigid displays (dimensionless quantities invariant under admissible units moves). The discrete recognition calculus yields conserved ledger dynamics on graphs, forcing exact integer 1-forms, a unique convex cost functional J(x) = 1/2 (x+ x^(-1))−1, and an 8-tick minimal period in three dimensions. These results dictate a discrete light-cone bound Δr ≤ c Δt and a parameter-free Planck normalization λ_rec = ℏG/(πc^3). Mesh refinement recovers the continuity equation ∂_t ρ + ∇·J = 0 and Einstein's field equations with emergent Lorentz invariance. The unique scale-recursion fixed point is the golden ratio φ = (1 + √5)/2, proven to be the only positive solution satisfying four independent physical constraints; we machine-verify that common alternatives (e, π, √2, √3, √5) fail. Beyond the linearized regime, we present an interacting, BRST-consistent quantum theory of gravity under the RS bridge: we derive the constraint algebra and gauge fixing, construct the Faddeev–Popov/BRST sector, and give a background-field renormalization with an RS-compatible UV mechanism expressed entirely in dimensionless displays. We further construct the nonperturbative gauge-fixed path integral as a discrete-exterior-calculus (DEC) limit that is background independent in the mesh refinement, and we reproduce black-hole semiclassics (Hawking temperature and entropy) with the RS normalization. Structural theorems (T2–T7, bridge identities, completeness) are machine-verified in Lean 4; the expanded interacting/UV/nonperturbative/semiclassical results are presented as classical proofs with explicit audits and falsifiers. Key testable predictions: galaxy rotation curves with zero per-galaxy tuning (median χ^2/N = 2.75 vs. MOND 2.47), subtle scale-dependent weak-lensing residuals, Solar-System PPN bands, gravitational-wave speed bands consistent with GW170817, and pulsar timing signatures at ~10 ns. Nanoscale-G claims are withdrawn in this manuscript pending external constraints.