Causal Propagation, Persistent Relational Structure and Emergent Dynamics: An Integrated Physical Bridge in the Ω₀/A2 Framework

We integrate causal propagation, persistent relational identity, adaptive recovery and cross-scale emergence within the Ω₀/A2 programme. Causal influence is defined interventionally before any speed is assigned, and is separated from pattern displacement and identity-preserving object propagation. Persistent Γ is promoted only through the non-compensatory admission gate of prediction, intervention, History, recovery and causal ancestry. Five framework laws characterize viability and recovery under changing constraints. We prove finite-cycle Dynamic Viability–Recovery Compatibility and, after explicitly fixing cross-scale lineage, History transport, Mapping and re-admission conditions, prove a finite-cycle Cross-Scale Self-Maintenance theorem: same-scale recovery failure need not imply lineage-preserving maintenance failure. We further prove a quotient criterion for co-generation of effective state, evolution law and coupling map. Physical identifications with c, ħ or Standard-Model entities remain open regression targets. The revision adds a Local-to-Global Causal-Speed Bound, a finite-speed existence criterion and a cross-scale propagation-bound transport theorem, while explicitly firewalling detector traversal and coarse scheduler timing from genuine causal propagation.