Finite Possibility Mechanics: A Unified Information-Theoretic Framework

Finite Possibility Mechanics (FPM) is a mathematical framework for finite-resource information-processing systems. This paper defines the model through five axioms, derives its constants inline, proves six executable closure results, develops its physical correspondence bridges, and reports sixteen numerical experiments plus a starvation subtest. It is presented as a reproducible theoretical and computational framework, not as an established theory of physics. The model follows a single update chain. The axioms define a directed routing ledger. The ledger produces a viscosity field, which controls a per-tick Lagrangian. That Lagrangian updates a native nine-channel complex carrier. The bridge layer then tests correspondences with Lindblad dynamics, Landauer dissipation, gravity, time dilation, holographic cosmology, the CMB acoustic oscillator, finite-substrate Born distributions, joint-torsion Bell/CHSH correlations, and a bare fine-structure coupling. Route cost is the common accounting variable across these sectors. Version 6.2 runs its main audit on a periodic 5×5×5 cubic lattice with 125 nodes and six neighbors per node. Ordinary interior replenishment obeys exact local conservation. When capacity boundaries, starvation, Landauer erasure, or explicit torsion-link operations occur, the expanded signed ledger remains conserved. The matching source package is maintained in the GitHub repository Finite-Possibility-Mechanics-Complete. It includes the paper generator, simulator, JSON results, and audit charts. The supplied scripts reproduce the derivations, lattice-count and G_FPM checks, numerical experiments, Born and Bell runtime tests, fine-structure calculation, SPARC gas-boundary audit, and active-boundary resolver audit.