States of Matter and Phase Transitions: The Emergence of Collective Topological Organization — Volume IV of the Axiomatization of Chemistry in the Global-Realism Framework

This manuscript is Volume IV of the program that seeks to axiomatize chemistry within the established global-realist framework. Its purpose is to derive the macroscopic states of matter and the laws of phase transitions from the previously admitted microscopic ontology, without introducing "phase," "liquid," "solid," "equation of state," or "phase change" as primitive empirical notions. Building directly upon the corrected Boltzmann framework of the earlier physical papers and the molecular and reaction-theoretic closures of the first three chemical volumes, a phase is defined as a stable macroscopic organization mode of the collective intermolecular disturbance field under given preparation variables. The ideal-gas and real-gas equations of state, the statistical meaning of temperature and pressure, and the first retained transport coefficients of dilute gases are derived from first principles. The condensed-phase descent for liquids and solids is then constructed: radial and direct-correlation structure, variational liquid functionals, diffusion and viscosity, electrolyte thermodynamics, crystalline order, lattice dynamics, elasticity, defects, and amorphous arrest. On that basis, a unified phase-transition sector is derived containing coexistence conditions, latent heat, nucleation barriers, Avrami growth laws, Landau–Ginzburg order-parameter theory, critical exponents and scaling relations, dynamic critical slowing, hysteresis, and phase-diagram constructions. The volume closes by compressing these results into a finite output layer and a lawful forward interface for later anisotropic, glassy, and refined-critical developments. Throughout the manuscript, definitions precede use, all effective approximations are marked by control regimes, no later macroscopic verdict is allowed to define the underlying structure from which it is derived, and no circular dependence is permitted between observables, constitutive laws, and ontological claims.