The Logon Framework (v3.16)

A formal framework for iterated selection on perception-action structures. Three definitions — the logon (perception-action dyad), the model (weighted configuration space with internal fitness function), and the carrier (instantiated configuration subject to adjudication) — connected by typed bridge maps and governed by eight explicit axioms. A universal scope declaration asserts all entities and processes are logons, with primitive base types at the bottom composition level.The framework gives a fully typed discrete dynamics on finite/countable spaces, derives results on on-policy identifiability, informational irreversibility, and falsification asymmetry, and defines truth-magnitude as a formal distance between a model's internal fitness map and its effective viability. Compositional structure via operads is deferred to a companion paper.Version history (v3.10 → v3.16)v3.11–v3.12 (from v3.10): First adversarial iteration. Fixed φ_t typing, J_E typing, U constraints, T formula. Added dyad derivation (§4.0) and irreversibility derivation from the dyad (§4.2).v3.13 (from v3.12): Response to first formal critique (countermodel-based). Fixed J̃_E to use model's own policy instead of best-action oracle. Formalized non-degeneracy conditions. Added compositional well-foundedness.v3.14 (from v3.13): Response to second critique ("fake formalism over metaphysics"). Added Technical Conventions section with explicit measure theory. Distinguished J_E dual role (formal vs ontological). Formalized non-degeneracy as three conditions.v3.15 (from v3.14): Response to third critique (17-section type-error teardown). STRUCTURAL SURGERY. Added bridge map ψ: C → 𝓛 connecting configurations to dyads. Added observation kernel Obs: E × C → Δ(S). Added explicit environment state e_t ∈ E. Fully typed 7-step dynamics. J now J(e_t, c_t, a_t). All axioms labeled [A1]–[A7]. "Actuality as instantiation" honestly labeled as axiom. Dyad argument moved to Motivation section. Expansion labeled Conjecture.v3.16 (from v3.15): All spaces committed to finite/countable with discrete σ-algebra. μ_t as weight function C → [0,∞). Added [A7] Feedback monotonicity (persist ≥ prior weight, eliminate = zero). Scope/base-case contradiction resolved (universal scope + explicit primitive base types at bottom level). Worked example (§TC.6) with explicit objects, multiplicative-weights U, and full cycle walkthrough. Removed underspecified model boundary sentence. Continuous extensions deferred to companion papers.