The PATON Continuity Architecture

This paper consolidates two completed bodies of work within the PATON System: the spacetime/cosmology stack and the physical-scale closure ladder. The spacetime/cosmology stack describes how admissible relation becomes an observable arena for spacetime, field possibility, cosmological reconstruction and large-scale structure. The physical-scale closure ladder describes how persistent structure forms, stabilises, transforms and hands continuity across scale within that arena, from quark–gluon relations through hadrons, nuclei, atoms, molecules, materials, cells and macroscopic systems. The paper argues that these are not separate projects. They are two views of one larger continuity architecture. The spacetime papers answer where the admissible arena comes from. The physical-scale papers answer how structure persists once that arena is available. When joined, they produce a continuous PATON account running from Original Datum to macroscopic physical continuity. The central claim is not that the PATON System replaces established physics, cosmology, chemistry, biology or materials science. Rather, it provides a structural continuity account that clarifies how admissibility, closure, persistence, identity, recovery, failure and scale handover recur across otherwise distinct domains. Spacetime is interpreted as an admissible continuity condition. Matter is interpreted as localised persistence within that condition. Scale is interpreted as repeated continuity handover. Macroscopic continuity is interpreted as the cumulative result of nested admissible closure, coordinated persistence, recovery or failure boundary. The paper provides a bounded, non-interfering synthesis from Original Datum to macroscopic structure, supported by the SFM 2.0 mathematical interface and Recursive Continuity Geometry.