IGNATIUM: Lean 4 Formalization (Technical Supplementary Preprint)

This technical preprint presents the complete Lean 4 formalization of the core invariant calculus of IGNATIUM, the foundational structural layer of the Ignatian corpus. The formalization includes the inductive syntax of invariants, the sub‑invariant relation, the structural equivalence system, and the δ‑rule governing invariant reduction. A semantic model is defined to interpret invariants, together with structural prohibitions such as non‑contradiction, acyclicity, and total interpretation. Within this framework, the Lean development proves that δ preserves structural identity, semantic interpretation, and all admissibility constraints required by IGNATIUM. The resulting Master Theorem establishes δ as a sound and safe reduction rule across all valid models. This preprint serves as supplementary material to the conceptual exposition of IGNATIUM and provides a machine‑checked foundation for subsequent developments in ONTESIS, ONTESIA, and the broader Ignatian system.