Time-Varying Space-Fabric and Re-equilibration Dynamics: A Vector-Field Minimal Model of the Propagation, Superposition, and Re-equilibration of Space-Fabric Deformations

This study develops the principle of re-equilibration introduced in the first paper of the Mechanical Organism (MO) series into a minimal vector-field model. Its underlying premise is that an observable state resembling equilibrium is, at any given moment, the outcome of correction occurring concurrently with deformation and of continuous re-equilibration. The model distinguishes between the reference field derived from the mass distribution, the wave-like rearrangement associated with time-dependent changes in that distribution, and the local state variable representing the drive toward re-equilibration. The measurable acceleration is determined by the negative gradient of the potential-like state field. Within the model, the defined zero value is the conceptual counterpart of infinity at the opposite end of the interpretive range. It denotes neither absolute nothingness nor a precisely measurable smallest distance, but a value below the range resolvable at the applied physical resolution. Before the first separation becomes physically meaningful, neither spatial distance nor a measurable interval of physical time can be assigned to the state. Expansion denotes the emergence of separations; space and its dimensions arise from the system formed by the directions and distances of those separations. Once a path length has emerged, it determines a corresponding signal-propagation time. Interactions are mediated through the space-fabric, defined as the deformable structure of space arising from separations and tending toward re-equilibration. The minimal state description comprises the local separation scale, a vector field specifying the direction and rate of change, a reference field determined by the source distribution, and a perturbation describing the wave-like propagation of state changes. In the time-invariant, spherically symmetric limiting case, the model recovers Newtonian acceleration; in time-dependent configurations, it defines a hypothetical direction-dependent correction. The study does not present a model fitted to measurement data. It proposes a computable and falsifiable numerical framework rather than a new law of gravity. Standard physical relations are distinguished from model postulates throughout; the proposed field equation is a testable hypothesis, not a derived law of nature.