The Logon Framework: Three Definitions, Zero Additional Axioms

A formal framework built from three definitions and universal scope. No additional axioms are introduced. Definition 1 — Logon: A perception-action dyad ℓ = (p, π), where p maps states to representations and π maps representations to a distribution over actions. Definition 2 — Model: An iterating approximation M_t = (C, μ_t, φ_t) consisting of a configuration space, weight measure, and internal fitness function. The model produces carriers and updates through adjudication. Definition 3 — Carrier: An instantiated configuration c_t ~ μ_t, drawn from the model's weight measure and tested against the external fitness function J_E. Carriers that fail are eliminated. When no carrier can be produced, the model is falsified. From these three definitions, the following properties are derived (not assumed): the structural necessity of the perception-action dyad, non-determinism, irreversibility, entropy increase, falsification asymmetry, truth-magnitude T ∈ [0,1), the Logos limit, compositional nesting via Γ, and the fitness landscape as mutual adjudication among logons. The framework is Popperian: models can be permanently falsified (T → 0) but never permanently validated (T < 1). Universality is a scope declaration, not a fourth axiom.