Finite Possibility Mechanics: A Unified Information-Theoretic Framework

Finite Possibility Mechanics (FPM) is a candidate mathematical framework that models any system processing information under finite resources. This single self-contained paper presents the framework in full: it states the five axioms, derives every constant inline (zero fitted parameters, zero asserted calibration factors), proves the six theorems, builds the five physical bridges, calibrates to fundamental constants, and validates the framework through ten numerical experiments. The framework is organized as a single causal chain: five axioms generate a directed routing ledger, the ledger produces a viscosity field through a constitutive law, the viscosity field gates a per-tick Lagrangian whose closed energy ledger drives coherence dynamics, and the resulting theorems bridge to Landauer dissipation, emergent gravity, time dilation, particle mass, holographic cosmology, the CMB acoustic oscillator, and a calibrated sub-atomic tick, all sharing one runtime currency, route cost.