Ω₀ Relational Generative Dynamics Finite Propagation, Self-Limiting Organization, State-Dependent Condensation, and Recursive Structural Generation

Can one inherited relational architecture generate qualitatively different regimes of organization without pre-specifying the objects that eventually emerge? This paper was developed specifically as a computational proof module of A2. It tests whether A2’s relational generation can survive a sequence of increasingly demanding dynamical requirements using a two-way strategy: reverse inference from established physical and systems-level phenomena to necessary constraints, followed by forward simulation under explicit controls, ablations and retained failures. Across a sequence of models, compatibility increases relational organization, cumulative history increases persistence, local accessibility produces a finite distance-ordered response front, and self-limitation suppresses unrestricted system-size scaling while exposing a failure of durable structure identity. A reality-informed extension with internal orientation, signed coupling, joint relational state, and state-dependent effective coupling produces rapid relational activation and a global condensation regime. A further multi-source model with stochastic local shocks and finite stress/recovery converts an otherwise nearly locked condensed state into an actively reorganizing regime with repeated observer-detected birth, fusion, fission, and transformation of relational components. The contribution is therefore not a single successful simulation, but a progressively constrained generative route in which both success and failure reduce the admissible mechanism space. We formulate recursive reification Γ_n→X_(n+1), generative-source multiplication, and k-order closure as the next falsifiable tests. The present results do not identify physical particles or cosmological events; they establish that a compact relational architecture can already support organization, finite propagation, explosive condensation, and shock-driven structural transformation within one inherited computational program.