A Deterministic Hybrid Medium for Bell Jump Paths and Autonomous Records

How can deterministic microscopic dynamics reproduce quantum jump histories, including their timing, while creating records faithful to actual earlier events? This paper constructs a conditional realization of the minimal Bell jump process using a deterministic hybrid model on a fixed finite configuration graph. The model combines a canonical complex field, conservative packet production, carrier–packet reactions, finite-rate recombination, and a finite spatial gas. Under explicit initial calibration and gas-independence assumptions, the ordinary-configuration path law converges in total variation to the Bell jump process without rescaling physical time. Quantitative estimates control the gas contact history, recombination error, and population tracking, including wavefunction nodes, current reversals, and zero-current intervals. An autonomous quantum clock carries a finite measurement circuit that retains fuel, loss channels, copied archives, reset receivers, feedback, and an inaccessible reference. At specified copying gates, the Bell path crosses the gate exactly once during the first pass. The archive therefore records its own actual earlier configuration and preserves that record under subsequent label-preserving operations. An explicit resource hierarchy provides an input-uniform polynomial convergence bound for a fixed engineered circuit. The theorem depends on the stated interaction catalogue and statistical preparation premises. It does not derive those premises, establish laboratory realization, or embed the complete hybrid dynamics in a single smooth material Hamiltonian. A supplementary smooth construction covers isolated contact modules.