The Theorem of the Semantic Floor (The Minimal Reflexive Seed) Paper 24 (T7) of the NEMS Suite

We formalize an information-theoretic constraint on the initial conditions of a Perfectly Self-Contained (PSC) universe. We prove the Theorem of the Semantic Floor: a PSC universe cannot originate from an underspecified initial boundary that requires external completion data to determine record-truth. Instead, any admissible initial state must possess a "Semantic Floor"—a structural capacity to host or internally generate Diagonal Capability (Arithmetic Self-Reference) and Internal Adjudication () without relying on an external model selector. We show that classical singularities, which represent states of infinite underdetermination requiring external initial conditions, are non-foundational under PSC. The theorem does not directly refute GR singularity models as effective descriptions; it says that an underspecified initial boundary requiring external completion cannot serve as a foundational PSC origin. The universe must begin as a discrete, self-interpreting "Reflexive Seed. " All definitions and conditional theorems are formalized and machine-checked in Lean 4. This overview presents the core NEMS theorem engine and selected applications; stronger domain-specific derivation and ontological synthesis claims belong to separate release surfaces with their own premise bundles and formal artifacts. Trust boundary. The semantic-floor claim targets foundational PSC origins and underspecified boundaries, not every effective use of singularities in classical GR. Cross-suite formalization is nems-lean. See.