Formal Verification Certificate
All theorems formally verified in Lean 4 with zero sorry gaps.
OmegaProof • Lean 4 + Mathlib • Apoth3osis Labs
The Central Question
Can neural network properties be formally verified with machine-checkable proofs? OmegaProof expresses neural network properties — robustness, fairness, monotonicity — as algebraic constraints over weight matrices and activation functions. These constraints are verified in Lean 4, and the results are packaged as CAB v2 certificates with IPFS-pinned evidence for auditability. The goal: move neural network verification from empirical testing to mathematical certainty.
Key Verified Results
weight_norm_boundWeight matrix norms bounded for stability
WeightNorm.lean
activation_lipschitzActivation functions are Lipschitz continuous
Activation.lean
composition_boundLayer composition preserves norm bounds
Composition.lean
property_propagationInput property propagates to output
EndToEnd.lean