First-Principle Derivation of the Information–Pressure Axioms

Description: Information–Pressure Theory (IPT) is founded on three axioms: a maximum entropy bound per causal surface, an instantaneous entropy–flux bound, and an overload instability criterion. This paper presents the original first-principles derivation of these axioms, written to stand independently of modern field theory, semiclassical gravity, or horizon thermodynamics. The derivation begins from eight standalone logical constraints on any finite, self-consistent universe—finite and conserved information content, discreteness of information and addressability, finite propagation speed, interface-mediated influence, global self-agreement, exclusion of overlapping storage, and mode-exclusivity of interface flow—and shows that these constraints uniquely force the IPT entropy–area structure up to a single resolution scale. The 1/4 coefficient in the entropy bound emerges from the geometry of 2D boundaries: normal flux (Gauss) and tangential circulation (Stokes) each carry a sign, yielding four mutually exclusive mode-channels per boundary slot. By elevating the first-principles derivation to the primary foundation of IPT, the axioms become prior to (rather than derived from) any particular physical mechanism, removing concerns about circularity in subsequent gravitational and quantum-field reconstructions. Keywords: information theory, entropy bounds, holographic principle, black hole thermodynamics, Bekenstein bound, causal surfaces, discrete spacetime, quantum gravity, entropy–area relations, first principles, Information-Pressure Theory, IPT