Finite Carrier and Information Dynamics: Coherence, Resource-Gated Consolidation, and Exact Finite Allocation

Finite Possibility Mechanics represents local alternatives in a normalized nine-channel complex carrier rather than in independent scalar probabilities. Each carrier channel corresponds to one ordered pair of spatial route axes. Route cost acts on phase; carrier magnitudes determine immediate channel weights; coherence and binary probabilities are projections. When energy is sufficient, the carrier evolves continuously through phase rotation and dephasing. When available action falls below the consolidation gate, the runtime reduces maintainable alternatives, increases cache bias, quantizes channel weights onto a finite microcell population, and records the information discarded as a paid ledger term. The route-cost phase update preserves carrier norm exactly. The selected dephasing update is a contraction with the stepwise form of a zero-Hamiltonian Lindblad pure-dephasing channel. Largest-remainder allocation preserves the exact microcell total and bounds every channel-count error below one cell.