Listen and ask questions on NotebookLM: https://notebooklm.google.com/notebook/b4184a0f-d71c-4a9f-b594-ad19e86d45ed?authuser=1 Catholic Invariant Grammar (CIG v1.3) is a relational compression framework for theological reconstruction. It identifies recurring structures across Scripture, Tradition, sacramental theology, ecclesiology, anthropology, prayer, doctrine, and reasoning systems, then tests whether those structures can reconstruct Catholic doctrine without replacing it. The framework proposes that Catholic theology contains discoverable invariant relations such as Being, Distinction, Relation, Participation, Nature, Intelligibility, Source, Reception, Transmission, Fidelity, Continuity, Communion, and Person. CIG v1.3 documents the discovery method, primitive layer, roles, operations, derived structures, validation history, continuity topology, limits, future work, and explanatory appendices, including a child-accessible explanation and a biographical appendix on Gottfried Wilhelm Leibniz.