Lume‑Gov: Deterministic Governance for Public‑Sector Administrative Systems Using Lume‑V and Lume‑X

Public‑sector administrative systems increasingly rely on automated decision pipelines to process high‑volume, high‑impact determinations across domains such as benefits adjudication, licensing, compliance verification, resource allocation, and public‑facing service delivery. These systems frequently incorporate probabilistic models, heterogeneous data sources, and multi‑agent workflows, resulting in nondeterministic behavior that undermines auditability, fairness, reproducibility, and institutional trust. Existing governance frameworks lack the formal guarantees required to ensure that automated administrative decisions remain stable, explainable, and verifiably compliant with domain‑specific constraints. I introduce Lume‑Gov, a deterministic governance substrate for public‑sector administrative systems built on the DAIGS foundation, integrating the single‑organism safety layer of Lume‑V with the multi‑agent cognition and arbitration capabilities of Lume‑X. Lume‑Gov provides domain‑specific invariants, certificate schemas, arbitration rules, and deterministic override mechanisms tailored to public‑sector workflows. I formalize the Lume‑Gov governance pipeline, define its operational semantics, and present constructive proofs demonstrating invariant preservation, deterministic override correctness, multi‑agent convergence, and replay‑identical execution. Results show that Lume‑Gov enforces deterministic safety envelopes, maintains certificate‑chain integrity, and ensures reproducible outcomes under adversarial and degraded conditions.