Abstract

This monograph introduces the Λ–Ψ Operational Framework, a complete formal system for the quantification and governance of meaning. The framework is presented through four integrated documents: a core theoretical framework, a set of eight operational principles, a rigorous mathematical calculus (v8.0), and an implementation-ready runtime charter ("The Engine" v1.26). The system is built upon a foundational triadic axiom set: Existence (the observer as a boundary condition), Definition (entropy contraction through information compression), and Longing (goal-directed force as a gradient in state-space). From these axioms, we derive the core equation of the framework: Λ = J · ∇Ψ, where Meaning (Λ) is operationalised as the projection of an effort vector (J) onto a performance gradient (∇Ψ). The accompanying Λ–Ψ Operational Calculus (v8.0) provides a tiered, falsifiable specification for measuring these quantities, incorporating psychophysical primitives (E_psy, t_psy), a chaos coefficient (χ), and entropy-energy reconciliation. The Runtime Charter translates these principles into an enforceable governance system for autonomous and socio-technical systems, featuring cryptographic stamps, WORM logs, and boundary enforcement mechanisms. We demonstrate the framework's universality through its application across scales: from micro-level cognitive acts to a novel cosmological prediction, deriving an upper bound for cosmic entropy production (σ_cosmic ≤ 4.82 × 10⁻⁵⁸ nats/s). The Λ–Ψ Framework thus establishes a unified, operational basis for a science of meaning, with direct implications for artificial intelligence, cognitive science, complex systems, and philosophy.