The Minimal Universal Model Framework. A Reader-Facing Synthesis. From primitive distinction to quantum structure, arithmetic realization, and emergent geometry.
This document presents the defensible core of the Universal Model Framework (UMF), isolating the minimal set of structural assumptions and derivations that remain logically coherent, mathematically motivated, and empirically falsifiable. As stated in the text, the goal is to extract “the smallest segment that is logically structured, mathematically motivated, and empirically vulnerable,” while ensuring that “every load‑bearing claim is paired with an explicit failure condition.” It is a deliberately falsifiable research program investigating whether quantum structure, arithmetic regularity, and emergent spacetime geometry can arise from a common relational foundation. It separates three logically distinct questions: whether relational systems can reconstruct quantum-theoretic structure; whether ordinary prime-number organization is physically selected rather than merely mathematically available; and whether a stable continuum geometry with causal and gravitational dynamics can emerge under refinement. The work reports exact finite results for recursive graph constructions, discrete geometry, cochain-based fermionic operators, local frames, symmetry tests, and numerical-reproducibility controls, while documenting failed frame-transport and continuum candidates. Crucially, it does not claim established fundamental physics: no continuum limit, Lorentzian causal structure, gravitational field equation, physical mass scale, complete quantum reconstruction, or prime-specific empirical signal has yet been derived. The framework’s contribution is therefore methodological as well as mathematical: it provides a transparent architecture for distinguishing theorem, model assumption, numerical fit, negative result, and falsifiable prediction in foundational physics. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.