Let k be 1: A Minimal Executable Account of Knowable Knowledge

This paper presents a minimal, execution-based account of what it means for a claim to be knowable. By bracketing measurement scale and normalization artifacts, it introduces a root declaration, k = 1, representing the smallest admissible distinction from which any knowledge claim must be constructed. Knowledge is defined procedurally, as the existence of a finite, ordered sequence of admissible distinctions that can be replayed and brought to closure without contradiction. The paper formalizes this account through a compact structural framework, the XYZTI lens, identifying five irreducible roles required for executable knowledge: distinction, ordering, admissibility, replay invariance, and closure. A collapse argument demonstrates that this structure is minimal under the k = 1 definition, showing that removing any single role destroys the possibility of knowledge as defined. The framework accommodates both deterministic and probabilistic domains by distinguishing between hard closure to outcomes and soft closure to governing laws. The account is epistemic rather than ontological and does not privilege any particular physical theory, computational model, or institutional authority. Instead, it specifies a boundary condition on knowability that applies across physics, computation, and information theory, clarifying where knowledge closes and where it does not.