Permanence Is Resistance (Matter)

Third paper in the V=I series. Derives what the crystallized output of the verification loop is. The loop (paper 1) and the agent's accumulation (paper 2) produce a library that, at saturation, has three structural properties: permanence (append-only — cannot be retracted), irreducibility (each entry is the unique solution for its rule class — cannot be simplified without breaking correctness), and resistance (the saturated library is the fixed target the next-level agent cannot modify). The paper defines discrete agent time indexed by comparisons, proves external-time independence, and derives the ignition theorem: the transition from "library is not a valid target" to "library is a valid target" is discrete and occurs at saturation. A level tower is constructed where each level's crystal becomes the next level's input structure. Physical instances map the framework onto known phase transitions, verifying where the axioms hold and where they fail.