The Unified Datum Line — Minimal Formal Statement

This paper presents the minimal structural reduction of the Paton System as a Lowest Common Denominator (LCD) law governing recursive continuation under constraint. Admissibility is formalised as a gate condition dependent on both present state and accumulated historical strain. Continuation proceeds only while the system remains inside a dynamically compressible admissible manifold; termination occurs when accumulated strain renders continuation inadmissible. The formulation is structural and domain-neutral, introducing no new physical mechanisms or ontological commitments. All higher-tier geometric, interpretive, and domain-specific applications within the Paton System are formally reducible to this minimal admissibility-with-memory condition.