Spacetime from First Principles: Free-Energy Foundations on the Infinite-Clique Graph (Draft)

This paper derives the foundational structures of modern field theories from a principled minimalist framework. We begin with two postulates: (1) a substrate consisting of a single, real-valued field on an infinite-clique graph representing a geometrically unstructured ``single substance''; and (2) a simple, volume-normalized free-energy functional governing node interactions. From these minimal assumptions, we derive the key elements of physical continuum field behavior: light-cone structure, metric universality, a Newtonian $1/r$ limit, and an effective action scale $\hbar_{\mathrm{eff}}$. Our central contribution is a complete, bottom-up derivation path, showing how the core apparatus of modern physics, from the complex nature of the wavefunction to the structure of spacetime, emerges as a collective phenomenon from a pre-geometric substrate.

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