Successor System Formation: A Structural Account of Emergent Admissible Systems After Collapse

This paper introduces Successor System Formation within the Paton System as a structural account of how new admissible systems emerge following collapse. Building on Post-Collapse Dynamics System Re-Entry and Terminal Collapse the framework defines successor formation as the emergence of a new admissible configuration from post-collapse fragments that does not preserve sufficient structural continuity to qualify as restoration of the original system. The paper formalises transformation as a distinct outcome within the admissibility lifecycle. It distinguishes successor formation from re-entry and terminal collapse and establishes transformation as a structural pathway arising from fragmentation recombination and constraint resolution in a new configuration. This provides a domain independent method for analysing how new systems arise from breakdown without modifying underlying governing equations.