The Unified Rigidity Theorem (The Lepton Seed) Paper 25 (T8) of the NEMS Suite

We formalize the capstone theorem of the NEMS Suite: the Unified Rigidity Theorem, a conditional classification result linking gauge rigidity and gravitational anchoring to a unique seed under explicit premises. By bridging the abstract NEMS closure constraints with the specific Generative Triple Evolution (GTE) mechanics, we define Unified Admissibility as the conjunction of three orthogonal constraints: the Semantic Floor, Quarter-Lock Rigidity, and Relational Anchoring. The Residual Seed Uniqueness Theorem (RSUC), proved in the ugp-lean artifact , states that the residual set collapses to the Lepton Seed (1, 73, 823) up to mirror equivalence and Presentation Invariance. We prove that under this theorem and the premise bundle (P25.1)–(P25.4), any admissible foundational seed has the Lepton Seed as its canonical (MDL-minimal) representative up to mirror equivalence and Presentation Invariance. This concludes the suite by demonstrating that our specific laws of physics are not a contingent fit to empirical data, but the unique semantic solution for a self-contained reality. 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 capstone bridges NEMS closure language with RSUC in ugp-lean; rejecting UGP/GTE instantiation or RSUC targets the arithmetic certification, not the abstract PSC lemmas unless you dispute the explicit premises (P25.1)–(P25.4). Suite spine checks remain in nems-lean . See .