Lume-Fin introduces a deterministic governance substrate for nondeterministic AI systems operating in financial environments. It unifies invariant-based validation, deterministic explainability, cryptographically verifiable audit trails, safety-dominant arbitration, and deterministic natural-language interfaces into a single reproducible pipeline purpose-built for banking, trading, credit, fraud detection, risk management, compliance, AML/KYC, and systemic risk monitoring. I define a nine-layer financial governance architecture, introduce LTC-Fin v1.0 — a cryptographically signed trust certificate standard for financial AI — formalize five financial invariant classes (risk, fraud, compliance, fairness, temporal-domain), establish five deterministic arbitration classes (multi-model risk, fraud, credit, trading signal, cross-market), and specify a complete multi-agent coordination layer with five coordination agents and two system governance agents. Lume-Fin aligns deterministic governance with major regulatory frameworks (Basel III, OCC, CFPB, SEC, CFTC, FinCEN, OFAC, EBA, ESMA, ECB, GDPR, FATF, IOSCO, MAS, HKMA) and establishes a new scientific and regulatory category: Deterministic Financial AI Governance (DFAG). This work positions Lume-Fin as the financial instantiation of Deterministic Autonomous Infrastructure Governance Systems (DAIGS) — the second major vertical after Lume-Med — built on the Lume programming language and the Lume-V governance engine.