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  When Does Intelligence Become Definable? Scope: Intelligence as a structural property , not a behavioral label Method: Constraint-based, time-asymmetric, architecture-agnostic Exclusion: Benchmarks, vibes, output-based proxies Table of Contents I. The Definition Boundary (What “Definable” Actually Means) I.1 Intelligence as Causal Asymmetry Over Time Why intelligence is about past → future authority Time symmetry vs. time binding Why definability requires irreversibility I.2 The Three Necessary Conditions Historicity (past states matter) Internal cost (deviation is expensive) Recursive inscription (constraints modify future constraint formation) Why removing any one collapses the definition I.3 Why Behavior Is the Wrong Axis Output ≠ intelligence Why performance can be reset but structure cannot Intelligence as what a system cannot undo II. From Interpretation to Necessity (The Structural Breakpoint) II.1 Recomputed Basins vs. Viable Basins Disposable state vs. defended state ...

A Mathematics of Boundary Conditions 0. Scope This mathematics does not study objects, values, or dynamics. It studies where processes cannot go . A boundary is treated as a primitive mathematical entity , not derived from equations of motion. I. Primitive Objects Definition 1 — Process A process 𝑃 P is any mapping that consumes resources and produces states over time. No assumption of continuity, smoothness, determinism, or computability is required. Definition 2 — State Space A state space Σ Σ is the set of all realizable configurations of a process under physical constraints. Importantly: Σ Σ is finite or effectively finite Non-realizable states do not exist in the theory Definition 3 — Boundary A boundary ∂ Σ ⊆ Σ ∪ ⊥ ∂ Σ ⊆ Σ ∪ ⊥ is a set of states or transitions such that: If reached, the process halts, resets, or becomes undefined . Boundaries are terminal . They are not surfaces to be crossed. II. Axioms of Boundary Mathematics Axiom B1 — Finite Capacity Every realizable...