Re-emergence from Indistinguishability: Constraint Reset and New Admissibility Within the Paton System

This paper establishes the structural relationship between collapse and re-emergence within the Paton System. It demonstrates that collapse does not eliminate structure but removes distinguishability, dissolving identity and prior constraint relationships. Following collapse, constraint conditions reset to a minimal state from which new admissible configurations may arise. Re-emergence is therefore not recovery of prior structure but the formation of new structure under renewed constraint. This provides a unified structural interpretation of renewal across physical, biological, computational, and cognitive domains.