An Autonomous Realization of a Single M-Event Detection Cycle: Writing, Retention, and Reset Within One Hamiltonian

A detector records an event through a succession of physical changes, from its initial response to the recovery of its working state. We construct a complete finite cycle on the local physical--observation phase space of PODA. An incoming carrier traverses fixed interaction regions, with its arrival, speed, and energy transfer governed by an autonomous Hamiltonian bounded below. Six canonical gates write a smooth event profile, amplify the pointer separation, export the record, reverse the working displacement, and exchange the remaining pointer state with a prepared blank. Their exact reference map identifies the selector and mechanical recoil left by record export. The retained core returns on the event-cell plateaus; narrow transition strips contribute a bounded probability of failure and a recoil that depends on the resolution. With a positive free Hamiltonian present throughout the passage, energy conservation and a finite-time perturbation estimate establish faithful writing, finite retention, and return within prescribed tolerances. An explicit binary realization admits nonzero preparation errors, and independent trajectory integrations check the equations and the endpoint map. These results complete the single cycle for the specified local model and incoming family. The calculation follows the archive, carrier, and waste through the output section, making explicit the resources consumed by reset. Preparation of fresh blanks, replenishment of those resources, and storage beyond the proven holding interval remain physical requirements of continued operation.