# Section 12: Conclusions and remaining obligations

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<a id="section-12"></a>

## 12 Conclusions and remaining obligations

 The conditional result has three quantitative comparison steps and one common output space. The independent spatial gas supplies a marked-history Poisson approximation; finite-rate recombination controls physical surplus service; the signed-queue estimates control the designated ordinary carrier through low weights and nodes. Combining these steps gives Theorem [8.1](/quantum-measurement/research/hybrid-bell-paths/the-complete-physical-time-bell-path-limit#thm:main) in physical time. The complete ordinary Hamiltonian then makes copying, retained reset outputs, reference-sensitive continuation and timing events common functionals of that same path. Their joint error is charged once.

Several boundaries are substantive. Calibration of the initial census does not follow from the tracking theorem, and independence of the gas is stronger than a uniform one-particle density. The excluded pilot-ledger read force is an explicit part of the interaction catalogue. Charge conservation does not itself exclude other charged species or multicarrier channels. Fixed scalar coefficients do not include arbitrary history-dependent response. Any alteration requires a new model or a new comparison argument. The basis-ready example removes random carrier preparation for that known input only; it does not construct a sampler for arbitrary unknown wave weights.

The ordinary gate Hamiltonian is finite, autonomous and semibounded after an irrelevant scalar shift. The complete microscopic model remains hybrid. Appendix [B](/quantum-measurement/research/hybrid-bell-paths/appendix-b-a-smooth-autonomous-realization-of-the-finite-contact-module#app:mechanical) proves a separate smooth contact-module theorem with its own output decoder and error estimate; it does not embed asynchronous export and all reactions in that Hamiltonian. The displayed polynomial hierarchy is an existence-scale construction with large finite resources, not a practical apparatus specification. No uniformity is claimed over growing graphs, unbounded retention times or arbitrary changes of reference resolution.

A focused independent review should check the low-population flux comparison, the preservation of the full microscopic marginal in the tagged coupling, and the fine-current condition at actual copying cuts. A material realization would additionally have to justify the interaction catalogue, manufacture the initial stock and bound its departures from the declared product law. These are distinct obligations. The separate continuous-configuration construction [[11](/quantum-measurement/research/hybrid-bell-paths/bibliography#bib-MassiveCompletion)] uses different dynamics and preparation premises and is not a missing step in the Bell-path proof.