Admissibility-First Materials Discovery: Collapse-Surface Gating, Corridor Non-Emptiness, and a Reproducible 3D Percolation–Spectral Validation for a Paradox Ceramic Class

Description This paper presents an admissibility-first contraction framework for multi-objective materials discovery. Microstructures are represented as graphs/voxel fields. Collapse surfaces are defined via deterministic predicates: film spanning (percolation) and free-backbone spectral continuity. A constructive 3D lattice instantiation proves corridor non-emptiness and enables reproducible contraction analysis. A numerical sweep on a 3D cubic lattice (N=20, 40 trials per p) reports spanning probabilities and spectral radius behavior, replacing speculative threshold scalings with empirical gates. The contribution is a falsifiable admissibility certificate framework, not a materials recipe.