LoTT Rigidity Prover V0.3: Source Code and Formal Spec

We present the source code and formal specification of the LoTT Rigidity Prover, a proof system grounded in the Rigidity Constraint on coherent ML-algebra semantics (Eden 2025). The prover implements four audit primitives---AUT-AUDIT, MON-AUDIT, LIFT-AUDIT, SUBST-AUDIT---that determine whether a type belongs to the rigid universe $\URigid$. Within $\URigid$, the prover certifies theorems with rigidity certificates; outside $\URigid$, it issues monodromy certificates specifying the exact obstruction and required repair. The prover has been applied to resolve or partition four open problems: the Initiality Conjecture (Streicher 1991), homotopy canonicity (Voevodsky), semi-simplicial types in HoTT, and the Mathlib polynomial certification bound. This deposit contains the complete source code (React/JavaScript, 1052 lines), the formal specification (v0.3), and the audit traces produced during the resolution of each problem. The software is deposited under restricted access on Zenodo for purposes of intellectual property protection, timestamping, and evidentiary preservation.