A Machine-Verified, Parameter-Free Framework Deriving Physics from a Single Axiom

We present a certificates-first, machine-verified framework in Lean 4 that derives a discrete recognition calculus from a single axiom ("nothing cannot recognize itself") and exposes only dimensionless observables through a gauge-quotiented bridge. The master statement RSRealityMaster(phi) conjoins (i) a reality-facing bundle—unique calibration, units quotient and K-gate route identity, and a non-empty, cross-domain certificate family—with (ii) a spec-level closure that, parameterized by phi, compels counting/causality consequences and a model-level recognition-computation separation. Each claim is a Lean proposition with a one-line #evalreport on a pinned toolchain and no external I/O.

Representative verified consequences include: exact 8-tick minimality in 3D, a discrete light-cone bound with slope c, a Planck normalization c^3 * lambda_rec^2 / (hbar * G) = 1/pi under mild positivity, and phi-power mass-ratio ladders at the matching scale. The bridge is gauge-rigid (dimensionless displays invariant under admissible units rescaling) and route-locked (time-first = length-first via the K-gate), eliminating tunable continuous parameters on the reported surface; a single-inequality audit provides a units-aware falsifier for route equality. We prove a Minimal Axiom Theorem (provenance-based): there exists an environment that uses only this axiom and derives RSRealityMaster(phi), and any environment that derives it must include this axiom; hence the axiom-only environment is minimal in the axiom lattice. We also prove phi-selection at the algebraic level: among positive reals, the unique solution of x^2 = x+1 is phi; within the instrument, phi-selection together with the closure holds uniquely. We distinguish formal truths inside the instrument from empirical alignment: the former are machine-checked theorems; the latter are unit-aware comparisons and ablation tests. The repository acts as an auditable instrument: running the manifest prints "OK" per certificate or fails deterministically if any obligation is not met.