The Thermodynamic Laws of Information Physics A Law-by-Law Mathematical Reconstruction from Zeroth to Third Law

This paper reconstructs the four laws of classical thermodynamics (zeroth, first, second, third) as a single law-by-law extension within an information-physics framework, building on the eleven preceding papers of the Information Physics Series (Papers 4-16). The reconstruction proceeds from two foundational axioms — Ω₀ (information conservation as the closed-system axiom, dI(S,t)/dt = 0) and Ω₁ (erasure-as-transfer) — and derives each thermodynamic law as a consequence rather than a postulate. Three central results are established: (i) the Mutual-Closure Theorem (Theorem 17.5), which proves four-directional consistency among the laws — each can be reconstructed from the others through Ω₀, with no adjustable parameter introduced by the closure relation itself; (ii) Bridging Lemma 17.3.1, connecting the equilibrium structure of the zeroth law to the dynamical structure of the second law via a shared equilibrium index; (iii) three formal lemmas — Lyapunov stability (§A.4.1), the logistic closed-form solution (§C.5.1, after Verhulst-Paper 11), and well-posedness of the sharpness measure W (§D.6.1). Empirical consistency is checked against 78 IVP datasets spanning quantum erasure, biological condensation, neuronal dynamics, black-hole entropy, ethical relaxation, and optical-singularity ensembles, with zero contradictions across cross-validation between Papers 13 (Karma), 14 (Qi), and 15 (Superluminal). Appendix G specifies 10 falsifiable thresholds (F17 series) and Appendix H presents a 40-cell consistency matrix across the framework's claims. The framework yields zero free parameters at the closure level. Connections to Landauer (1961), Bekenstein (1973), Hawking (1975), Page (1993), Jaynes (1957), Bennett (1973), Wheeler (1990), and Almheiri et al. (2020) are explicit. The work positions itself as foundations-of-physics meta-paper rather than a derivation of new measurable quantities; its primary contribution is structural — demonstrating that the four thermodynamic laws admit a unified information-theoretic reconstruction with explicit falsification criteria.