Endogenous Generation of Causal-Organizational Order

This paper is Part III of the CoG research sequence and investigates the endogenous generation of causal-organizational order in finite autonomous deterministic systems. A constructive witness demonstrates a transition from a recurrent precursor organization to a forward-invariant terminal regime in which the persisting organization becomes constitutively necessary for another recurrent organization. The paper then derives general deterministic pre-target structural constraints, establishes a witness-specific participatory-generation result under a fixed binary constant-interface replacement class, and proves a sharp class-relative auxiliary embedding-cardinality minimum of ∣SG∣=3, with equality forcing τ=6. The results are explicitly limited to the stated deterministic finite-state framework. They do not establish global minimality, robustness, inevitability, provenance sensitivity, stochastic analogues, or a universal law of hierarchical causal organization. Three executable verifier scripts accompany the manuscript and independently audit the constructive witness, the participatory-generation proposition, and the class-relative minimality result.