Finite-Resolution Quantum Gravity: Certified Integer-Length Causal Regge Ensembles, Exact Cutoff Composition, and an Executed Falsification Program

Abstract

Finite-Resolution Quantum Gravity (FRQG) formulates a candidate theory of quantum gravity at finite cutoff as a family of amplitudes over time-oriented causal simplicial geometries whose invariant edge intervals are integer multiples of a fundamental resolution scale. The construction separates discrete geometry from continuous gauge, bosonic, and fermionic fields; establishes certified nonempty integer-length causal Regge sectors; proves exact cutting, gluing, and duration-resolved kernel composition at fixed cutoff; and develops explicit reflection-positivity and transfer-kernel criteria.The monograph distinguishes exact cutoff results from continuum claims and replaces several heuristic arguments common in discrete-gravity models with explicit mathematical conditions. It provides a canonical instance, FRQG₀, together with a staged falsification program testing reflection positivity, continuum scaling, Lorentz and diffeomorphism symmetry restoration, chiral matter, and regulator-independent observables. The first executed calibration computation finds link-reflection positivity in the canonical two-dimensional sector and agreement in a matched-measure correlation-length comparison. The continuum viability and physical identification of FRQG remain open and are deliberately left to the declared tests.