A Finite Discrete Alternative to Renormalization (with Null-Tested π–ϕ–e Framework)

This deposit contains the final version of The Finite Discrete Standard together with a complete computational validation suite. The work introduces a finite, discrete framework for fundamental physics in which physical constants, mass ratios, and scale hierarchies emerge from geometric and arithmetic structure rather than from renormalization or parameter fitting. The paper demonstrates that independent mathematical and physical constructions converge on a small set of invariant constants, and that this convergence is statistically non-accidental. All central claims are supported by explicit numerical tests, Monte Carlo baselines, and reproducible scripts included in the accompanying validation archive. The validation suite implements the full analysis pipeline used in the paper, including constant generation, convergence testing, statistical controls, and robustness checks. No external datasets or fitted parameters are required. The archive is provided to enable independent verification, replication, and extension of the results. This upload establishes a stable, citable reference version of the Finite Discrete Standard and its validation infrastructure. Future applications and extensions are intentionally separated from this deposit to preserve conceptual clarity and auditability.