# Abstract and publication identity

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**Abstract.**

We study a deterministic hybrid model on a fixed finite configuration graph and prove convergence of its ordinary-configuration path law to the minimal Bell jump process in unchanged physical time. The model comprises a canonical complex field, passive bond coordinates, a bounded action exporter, charged carrier–packet reactions, finite-rate opposite-packet recombination, and a finite spatial gas. Its statistical premises are calibrated initial carrier populations and an independent product law for the gas. The entire marked contact history is within $(R_NT)^2/M_N$ in total variation of a Poisson comparison. Recombination contributes at most $\sum_e\kappa_e\mu_NB_e/(2a_e)$. A mass-action tracking argument, followed by a separate low-weight path localization, controls the remaining error, including nodes, current reversals and zero-current intervals. For a fixed engineered clock circuit, one explicit resource hierarchy gives an input-uniform $O(N^{-1/70})$ bound. A finite autonomous Hamiltonian carries preparation, measurement, fuel, pending and loss channels, reset receivers, an inaccessible reference and feedback. At monomial copying cuts, every fine current is forward on the first pass and the cut is crossed exactly once, making the archive a record of its own actual earlier configuration. The result depends on the specified interaction catalogue, including the exclusion of a direct pilot-ledger force on an ordinary pointer. It neither derives the initial statistical premises nor embeds the complete hybrid dynamics in a common smooth material Hamiltonian. A supplementary smooth construction applies only to isolated contact modules. This paper revises and consolidates previously disseminated work rather than asserting a new priority claim for the core construction. 

 **Keywords:** Bell jump process; deterministic hybrid dynamics; total variation; reaction networks; quantum records; autonomous clock