Boundary-Maintaining Self-Organizing Systems under Finite Capacity: Maintenance Load, Phase-C Collapse, and Invariant Selection

This paper(FDS-N1) develops a complex-systems bridge for Active Finite Distinction Systems. The FDS formal core defines active finite systems as systems that maintain boundaries through state-dependent updates under finite representational capacity and finite resource budgets. This paper translates that core into a normal-form account of boundary-maintaining self-organization. A self-organizing system, in this paper, is not merely a system that becomes structured. It is a finite system whose internal updates are causally relevant to future boundary-maintenance loss. The revised model distinguishes structural complexity K(t) from maintenance load LM(t), operationalizes effective organizational capacity Corg(t), adds resource-gated pruning, treats externalization as an accounting boundary shift that can clog the environment, and introduces a Phase-C catastrophic-feedback regime in which boundary loss reduces resource intake and accelerates collapse. Invariant-supported persistence is connected to a T3-style survival score based on maintenance cost, verification cost, refresh cost, boundary utility, and predictive utility. The main theorem states that an activeboundary finite system with positive deficit-driven load pressure, finite resource input, and eventually resource-exceeding maintained load cannot remain indefinitely in unbounded Phase-A growth without pruning, compression, externalization, task relaxation, invariant stabilization, resource expansion, automation, or collapse. Deterministic simulations illustrate Phase-A/Phase-B/Phase-C trajectories, operational organizational capacity, pruning viability windows, externalization clogging, bounded self-organization regimes, invariant-residue selection, active-boundary ablation, and domain bridge templates. The paper does not claim that all self-organizing systems are alive, intelligent, conscious, optimal, or oscillatory; it provides a normal-form and mapping protocol for later domain-specific applications.