From Axioms to Master Action in Information–Pressure Theory: The Spectral Generator, Interaction Existence Kernel, and Admissibility Maximum Principle

Description: Information–Pressure Theory (IPT) reconstructs physics from boundary data by elevating entropy bounds to dynamical generators. This paper derives the complete logical structure connecting the three IPT axioms—capacity bound (A-1), flux bound (A-2), and overload instability (A-3)—to physical outputs. We prove that these axioms force a unique constrained variational principle (the Master Action S₀⁽ᴰ⁾[ω,b]) and identify the boundary spectral anomaly ΔW as the single generator controlling all capacity, coupling, and selection phenomena through λ² = exp(ΔW). The Interaction Existence Kernel E(i) is defined as the canonical bridge between continuous boundary thermodynamics and hard selection rules; we prove E > 0 is necessary and sufficient for physical realizability. The Admissibility Maximum Principle (AMP) establishes that Π_adm is the unique maximal projector satisfying all constraints. Together, these results close the IPT framework: dynamics, constants, interactions, and admissibility are fully determined with no free parameters. Standard QFT structures—RG flow, scattering amplitudes, partition functions—emerge as theorems from boundary data rather than postulates. The framework provides a unified treatment of gravity (s = 2) and quantum field theory within a single boundary-first formalism. Keywords: Information-Pressure Theory, Master Action, boundary thermodynamics, entropy bounds, spectral anomaly, holographic principle, interaction selection rules, gauge invariance, admissibility projector, variational principle, quantum gravity, theory of everything, Bekenstein bound, capacity coefficient, renormalization group, Standard Model, cosmological constant, fine-structure constant