Formal Verification Certificate
All theorems formally verified in Lean 4 with zero sorry gaps.
Wolfram \u2194 Lean Bridge • Lean 4 + Mathlib • Apoth3osis Labs
The Central Question
Can Wolfram Physics computations be machine-verified without losing information? This project builds a bidirectional lossless bridge: hypergraph rules, states, and evolution traces translate to Lean 4 terms and back without information loss. A compact binary protocol serializes hypergraph data, and witness verification ensures that every Wolfram evolution step has a type-checked Lean proof. Round-trip fidelity is proved: translate then translate back is the identity.
Key Verified Results
roundtrip_fidelitytranslate ∘ translate⁻¹ = id (lossless)
Fidelity.lean
witness_typecheckEvolution witnesses are well-typed in Lean
Witness.lean
encoding_injectiveBinary encoding is injective
Hypergraph.lean
rule_translation_soundTranslated rules preserve rewriting semantics
Translate.lean