Compute-First Safe LLM Routing Without Meta-Judges Observable Viability with Information and Energy Budgets

This preprint introduces a compute-first safety framework for LLM routing that works without privileged meta-judges. The method formalizes observable viability under explicit information/compute and energy budgets, using a finite-dimensional rational-inattention objective plus a hardware-grounded energy calibration layer. Policies are synthesized offline to minimize information rate while satisfying auditable constraints on violation risk, compute, energy, and optional service/utility floors, then compiled into lightweight runtime tables for fail-closed deployment.
The paper develops the theory of a Rate–Viability Function (RVF) and an Energy–Viability Frontier (EVF), including dual/KKT characterization, exponential-form optimizers, monotone budget tuning, and robustification for surrogate misspecification, OOD drift, delayed feedback, and risk-debt stabilization. It also specifies tamper-evident logging and retroactive audit/slashing dynamics to correct underestimation risk in no-meta settings.
To reduce adoption friction for AI engineers, the manuscript provides a layered rollout path (L0–L4) and implementation-ready project templates in /configs, /schemas, and /scripts (YAML/JSON/Python), enabling immediate integration into production LLM agent pipelines where token, latency, and Joule efficiency are first-class constraints.