Formal Chemistry Definitions and Auditable Certificate Pipelines as Infrastructure for Trustworthy AI-Driven Materials Search

Abstract

AI-driven materials discovery has advanced rapidly, with projects such as Google DeepMind's GNoME identifying over 380,000 candidate stable crystals through graph-network predictions. Yet a persistent trust gap remains: surrogate models can hallucinate stability, and opaque screening pipelines make it difficult for downstream consumers—whether experimentalists, regulatory reviewers, or automated agents—to distinguish genuine predictions from silent errors. Industry surveys report that declining confidence in AI outputs, driven by hallucination rates of 3–30% depending on domain complexity, is a primary barrier to operational adoption across life sciences, chemistry, and materials engineering. This report presents HeytingLean, an integrated system that addresses this gap through two coupled layers. First, a Lean 4 chemistry formalization encodes the periodic table (all 118 elements with CIAAW 2024 standard atomic weights), bonding and molecular representations, chemical reactions with an automated balancing solver, crystal symmetry via space groups, and SLICES-based canonical structure identifiers—all backed by machine-checkable simp lemmas and compiled under strict –wfail (zero sorry) constraints. Second, an executable physics-constrained materials discovery pipeline (Computronium) operationalizes these definitions into a generate → certify → optimize → promote → archive workflow, where every candidate structure is evaluated against explicit physical-law proxies, every check is recorded in a schema-verifiable certificate, and every uncertain result triggers an ESCALATE signal to a higher-fidelity tier rather than being silently accepted. The pipeline supports fast surrogate backends (MACE, M3GNet, MatGL) for energy and force predictions, progressive stability gates (relaxation, bounded-force, gamma phonon, elastic tensor, convex-hull proximity), DFT-output attachment and formation-energy computation from CP2K and Quantum ESPRESSO, canonical deduplication to avoid redundant compute, cross-run caching keyed by structure identity and backend configuration, and optimization loops (random and Bayesian) over structure parameters with promotion of top candidates to heavier checks. The system is integrated into an agent ecosystem via MCP tool registration, producing standardized artifacts (JSONL leaderboards, certificate bundles, run directories) that other agents can discover and reuse. We position this work as infrastructure: the formal definitions and auditable pipelines are a substrate onto which neural proposal models, Bayesian optimization loops, or experimental feedback can be coupled with the guarantee that physical-constraint violations become explicit, traceable failures rather than hidden noise in a prediction stream. Published by The Institute for Applied Ontological Mathematics.