Prospective Health in Organized Dynamical Systems

Scientific abstract and context

From prospective capacity to an interacting physical system

This seventh paper constructs a physical-time stochastic law for finite populations of reversible mechanochemical transporters. Each transporter has Langevin position and momentum dynamics and guarded chemical reactions; all transporters are coupled through one shared ionic and chemical inventory. The initial population is prepared from the invariant single-transporter distribution of a maintained resource environment.

The complete stochastic history admits a stopped-time restart law. Uninterrupted residence of normalized charge within a declared operating band becomes an exact demand-indexed prospective Health capacity. A separate productive demand requires both a completed transport cycle and forward ATP regeneration while the charge band is maintained.

At each fixed finite population size the analysis establishes strictly positive productive continuation at positive finite horizons, a fifth-order short-time probability law, an attained positive maximum at finite time, and eventual operating-band exit with finite expected lifetime. In the same one-label preparation, continuously positive ATP reserve has zero capacity while regenerative transport has positive capacity.

Prospective observability: an instantaneous reporter retaining position, phase, shared resources, kinetic energy and reaction rates can still lose the sign of momentum. It determines the initial exit hazard, but the omitted direction changes the second-order future likelihood, including on the prepared ensemble's support. Ideal continuous position history reconstructs kinetic direction, whereas simultaneous transporter-label permutations preserve unlabeled future probabilities.

The mathematical conclusions are specific to the declared stochastic source. Calibrated physiological sensing, clinical applications and independent empirical validation remain separate scientific questions.

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Citation

James, Z. (2026). Prospective Health in Organized Dynamical Systems: Lawful stochastic continuation and constitutive maintenance in interacting kinetic populations. Zenodo. https://doi.org/10.5281/zenodo.24143821.

Preprint v1.0 · November 11, 2026 · Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International.

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