Projective Thermodynamic Closure.

This work was carried out within the Theory of Structural Articulation (TSA). Corpus line: Foundations. Corpus ID: TSA-FOUND-PTO. This preprint develops the projective-thermodynamic front-end of TSA. Starting from the pre-geometric ontological minimum of Nett Space, N = (D, C, R), where D is the set of ontological differences, C is the structure of finite joint realizability, and R is the admissible distinguishability relation, the paper constructs a theorem-level bridge to the effective conflict functional Jₑff. The central result is that Jₑff is not introduced as a phenomenological postulate. It is obtained as a stabilized large-deviation rate functional generated by the thermodynamic closure of a projective incompatibility counter. The construction is carried out within the class of admissible physical projections N -> M1 and finite-type continuation grammars. The paper establishes the following chain of results: admissible physical projection from Nett Space to a coarse transport carrier; construction of the projective incompatibility counter; finite-volume Gibbs/LDP thermodynamic closure; coercivity and shortcut penalty of Jₑff; induced conductance law, resistance metric, and baseline/defect decomposition; construction of the projective thermodynamic arena; and emergence of a near-baseline proto-Onsager regime with an H-theorem and Gaussian identification of the physical temperature parameter. Within the TSA corpus, this work belongs to the Foundations line. Its role is to close the early pre-geometric layer: the transition from the ontological minimum N = (D, C, R) to the effective conflict functional, the transport background, and the projective thermodynamic arena used in subsequent TSA papers. The paper does not yet derive spatial dimension, spectral gap, heat-kernel asymptotics, causal speed, Newtonian gravity, mass generation, or full operator-geometric closure. These are treated as subsequent layers of the TSA program and are addressed in related works of the corpus.