The Classification Cascade for Foundational Universes: Survivor Selection from Closure to Physics Architecture Paper 80 of the NEMS Suite

Paper 79 proved that closure compatibility and foundational viability are equivalent, establishing closure compatibility as the first sieve. This paper formalizes the next arrows in the classification cascade with structure-tied predicates: survivor compatibility ⇒ probabilistic admissibility ⇒ physics-architecture admissibility. We define the composite predicate (\CascadeCompat(U)), the narrowing predicate (\NarrowSurvivor(U)), and prove that survivor-compatible frameworks with nonvacuous worlds land in the narrow survivor class. The main results are proved in Lean in NemS/Cosmology/ClassificationCascade.lean and FoundationalAdmissibility.lean: \beginflushleft ClosureForcedProbabilityStructure ClosureCalibratedLawStructure survivor_filter_narrows_class survivor_compatible_implies_cascade_compatible \endflushleft Foundational viability is not the end of classification; it is the beginning of survivor selection. The present paper proves the first post-admissibility filters in a structure-tied form, but does not yet yield a final narrow-survivor or near-categoricity theorem. Risk of being oversold as the final survivor theorem. 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. Cascade lemmas and structure-tied predicates named in the abstract are in nems-lean (NemS.Cosmology.ClassificationCascade and related). Near-categoricity and final survivor classes are explicitly not claimed here; see .