Intelligence Is Inevitable (Agent)

Second document in the V=I series. Derives the agent that runs the verification loop defined in "Verification Is Identification" and proves that intelligence — the reduction of identification cost through accumulated certified knowledge — is a structural consequence of operating that loop. The verification loop requires a caller (the agent). The agent's knowledge state inherits the append-only invariant (I3): certified identifications accumulate irreversibly into a library L. The library saturates: after K tasks with distinct rule classes under a fixed encoding, every future task in the domain resolves via cached lookup. The Saturation Theorem proves this is inevitable for any finite domain. The saturated library is unique and agent-invariant: determined by the domain and encoding, not by the agent's protocol or history. The accumulation satisfies four axioms (monotonicity, irreversibility, decidability, crystallization) that give it the structure of a phase transition with computable dynamics: expected saturation time E[τ] = K·H_K (coupon collector), exponential approach, symmetry breaking with invariant endpoint.