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, proves the six closure theorems, builds the seven physical bridges, calibrates to fundamental constants, and validates the framework through fourteen primary numerical experiments plus one starvation subtest. 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 native nine-channel complex carrier dynamics, and the resulting bridge layer connects to Lindblad correspondence, Landauer dissipation, emergent gravity, time dilation, holographic cosmology, the CMB acoustic oscillator, Born-compatible finite-substrate distribution, and joint torsion Bell/CHSH correlations. All sectors share one runtime currency: route cost. Version 5. 6 extends the runtime bridge layer with a joint torsion Bell/CHSH audit. The Bell angle dependence is computed from SO (3) rotation of a shared pure-gauge torsion link before exact largest-remainder microcell allocation. The framework is explicitly not local in Bell’s sense: it is a non-local realist topology that represents Tsirelson-level correlations with linear memory instead of exponential tensor-product storage. The Born bridge remains stated conditionally on finite microcell counting and no-label exchangeability, not as an unconditional proof that quantum probability is non-fundamental. The complete source package, including the PDF generator, closed-form simulator, generated numerical results, and audit charts, is available on GitHub: https: //github. com/alxspiker/Finite-Possibility-Mechanics-Complete. Readers can run the simulator directly to reproduce the derived constants, validation experiments, exact lattice-count audit, GFPM audit, Born-carrier runtime checks, and v5. 6 joint torsion Bell/CHSH audit.