The Theorem of Semantic Terminality Paper 18 (T1) of the NEMS Suite

Traditional physics often assumes an infinite reductionist regress: an endless hierarchy of deeper micro-theories. In this paper, we prove that in any universe satisfying Perfect Self-Containment (PSC), this hierarchy must terminate. We introduce the notion of a PSC-optimal theory—one that minimizes descriptional complexity while fully capturing all macroscopic record facts. We then establish the Theorem of Semantic Terminality: any "deeper" theory extending a PSC-optimal description either fails PSC (by requiring new external selectors) or is physically redundant (by adding unforced complexity without altering record-truth). This implies that a foundational theory achieving record-level closure (such as the Standard Model at its appropriate scale) is not merely an effective approximation, but represents the logical limit of semantic closure. All definitions and theorems are formalized and machine-checked in Lean 4. Trust boundary. Terminality is relative to the formalized complexity/optimality predicates and PSC definition in nems-lean ; SM mentions are illustrative. See .