Ortropy Dynamics: Recursive Construction, Formation–Loss, and Conditional Accumulation

Previously formed organization can alter the conditions of further formation. Persistence alone, however, does not establish that an organization remains usable, that its use improves a resource-constrained process, or that the improvement increases what remains afterward. This paper develops a within-level dynamics of selected readouts of ortropy, understood as a theoretical characterization of realized ordered complexity, including its historical formation and continuity. Structural spectra are treated as selected structural projections, while reliable construction costs describe capabilities under explicit resource, information, and completion requirements. We connect paid preparation, contextual complementarity, and retention to formation–loss dynamics without identifying minimum construction cost with an actual transition rate. Finite-state generator methods yield conditional accumulation criteria, a limitation on globally nonnegative drift in recurrent systems, and comparisons between alternative generative arrangements. An exact finite-horizon identity separates changes in transition rates from their consequences for later organization. A fully specified four-state model then joins endogenous scaffold formation, finite persistence, resource competition, and downstream reuse. At equal cumulative activity budgets, investment in the scaffold reduces early downstream availability but can increase its long-run value; a general investment threshold separates an availability obstruction from the reuse efficiency needed for a long-run benefit. Blocking reuse while preserving the scaffold process separates persistence from causal contribution. The resulting framework distinguishes economical continuation, increased capability, growth through time, and improvement relative to a counterfactual. Its contribution is an explicit, mechanism-dependent connection between historically continued organization and subsequent accumulation, rather than a universal law of increasing complexity.

The manuscript and accompanying documentation are licensed under CC BY 4.0. Verification code in the supplementary archive is licensed under the MIT License.

Correspondence: fengli@eudavia.org.