PAPER-Θ: Structural Temperature and the Geometric Origin of Thermal Physics: A Four-Layer Foundational Framework

We propose a four-layer framework for the origin of thermal physics in which temperature and entropy are not taken as primitive physical quantities, but arise from the coarse-grained description of geometric configuration space under finiteinformational resolution. The logical structure of the paper is deliberately separated into four layers: definitions, principles, theorem-level targets, and conjectural extensions. At the definitional level, we introduce a geometric configuration space C, an observational equivalence relation ∼, the corresponding coarse-grained multiplicity N([φ]), and the associated structural entropy Sstr([φ]) = kB lnN([φ]). We then define a geometric energy functional E and, whenever an…