Timing and finite resources for autonomous memory

We prove two main quantitative results for specified autonomous memory architectures. Coherent endpoint-reset chains of dimension d satisfy the sharp fixed-mean bound λ/μ ≤ 2d-1, including detunings, where λ measures long clock silences and μ is the mean tick rate; arbitrary coherent reset states need not obey it. For any fixed finite consultation count and target error, a finite energy-exchange construction keeps local dimensions, interaction bounds and admitted defect strengths fixed as the access horizon grows. Two initially prepared controllers join unknown-input formation to delayed material answers; an explicit five-consultation certificate has error below 0.003329. Its O(T²) track volume and initial order are counted, and its conservation and bandwidth restrictions are explicit. For independent bit flips of rate κ and instantaneous renewal repairs, the logarithmic first-loss lifetime exponent is λ/(4κ). Combining a known counting bound with an approaching family gives the classical single-edge supremum λ=μ(2+Σ/4) at mean tick rate μ and entropy allowance Σ per tick. Stationary clock entropy alone can have minimum zero for a prepared finite task, while finite repair duration imposes a separate rate cost. A local autonomous timer/service model connects these benchmarks to noisy repair. A finite Hamiltonian implementation then joins quantum formation, retained banks, paid local decoding and stationary readers. Its complete reading-history bound includes timing resolution, preparation, continuing couplings, calibration and finite boundaries; an explicit 53-answer instance has joint error below 0.008454. A parameter-selection theorem covers prescribed finite durations and errors for every odd distributed memory size M ≥ 3. Its local reverse transitions can be retained inside the noise envelope, allowing a reference fuel gap independent of the requested duration. Locality is on a bounded-degree graph, with a restricted noise class and very large counted resources. Known record, control and protection mechanisms are attributed separately from the quantitative results. The construction establishes finite-task feasibility, not whole-device optimality, continuous Markov-trajectory equivalence or the origin of ordered preparation.