Finite Possibility Mechanics: A Unified Information-Theoretic Framework

Finite Possibility Mechanics (FPM) is a candidate mathematical framework that models the dynamics of any system processing information under finite resources. The central thesis is that bounded route-cost dynamics -- the thermodynamic pressure on a finite computational substrate to consolidate, choose, and remember -- can serve as a single bookkeeping system spanning decoherence, gravitational attraction, time dilation, mass-equivalent energy, and cosmological perturbation. This report presents the framework in full: it dismantles the assumptions of standard physics that FPM replaces, establishes the formal axiomatic foundation, derives the core theorems (dispersion contraction, Lindblad correspondence, starvation theorem, finite lag ceiling), builds the physical bridges (Landauer energy, mass ladder, acoustic metric, emergent gravity), extends to cosmology (holographic horizon, ledger inertia, stripped Boltzmann oscillator), and validates the framework through ten numerical experiments covering dispersion contraction, Lindblad correspondence, closed-universe energy conservation, spectral-gap weight derivation, mean-field consensus closure, Point-Pair coefficient convergence, bounded asymptotic behavior, semantic-entropy conservation, finite lag ceiling consistency, and galaxy rotation curves with derived kernel exponents. All ten experiments pass their pre-registered criteria. The framework is classified as a phenomenological information-theoretic topology: viable as an interpretive framework for understanding classicalization and emergent gravity, productive as a source of falsifiable predictions (finite redshift ceiling, split-source rotation curves, CMB source spectrum), and honest about its divergences from standard physics (no Born rule, no Einstein field equations, energy as thermodynamic potential rather than Noether charge).