PULSE: Deterministic Release Gates for Safe & Useful AI

This record contains the preprint “PULSE: Deterministic Release Gates for Safe & Useful AI”. PULSE is a deterministic, fail-closed release-governance layer for large language model (LLM) applications. Policies are encoded as versioned, hashed gate maps that must be satisfied before shipping, across safety/consistency invariants (I2–I7), utility metrics (Q1–Q4) and SLO budgets on latency and cost. Undefined or missing checks default to violation (fail-closed), making release decisions auditable and reproducible. The paper provides a mathematical specification of the release rule, with Wilson score intervals and Newcombe deltas for all binomial rates, and introduces the Release-Decision Stability Index (RDSI) to quantify how stable PASS/FAIL outcomes are under small, structured perturbations (prompt shuffles, retrieval noise, cost/latency jitter, etc.). As a domain-specific extension, we define a Vacuum-energy Penalty Functional (EPF), inspired by the cosmological vacuum-energy problem but instantiated purely in detector space over archived logs, together with a paradox notation [(0 1)_P] and a paradox field over policies. These tools flag high-tension governance states where multiple constraints (safety, utility, fairness, SLOs, EPF) compete. This preprint complements the open-source PULSE software package (DOI: 10.5281/zenodo.17373002) and documents its design rationale, mathematical foundations, threats to validity and practical CI/CD integration.