Anytime-Valid Answer Sufficiency Certificates for LLM Generation via Sequential Information Lift

We introduce Sequential-EDFL (Empirical Dynamic Formal Lift), which applies anytime-valid sequential testing to language model generation stopping. Our approach tracks information lift, defined as the log-likelihood ratio between the full model and deliberately weakened "skeleton" baselines, using self-normalized empirical-Bernstein e-processes that provide formal delta-level error control regardless of stopping time. This delta guarantee controls premature stopping when information lift is insufficient relative to the skeleton, and it does not imply delta control of factual incorrectness or hallucinations. We handle unknown centering through online mean estimation, combine multiple parameters via mixture e-processes, and support adaptive resets under distributional drift. On six benchmarks, Sequential-EDFL reduces generation length by 22 to 28 percent relative to sequential baselines while maintaining delta-level control with 12 percent computational overhead. We introduce automated skeletons (distilled submodels and randomized logits) and show robustness across skeleton families. Composing EDFL with a lightweight correctness gate (sentence boundaries plus a verifier) improves end-task correctness while preserving anytime-valid guarantees by only delaying stopping. Our certificates control information sufficiency, not factual correctness. Specifically, 10.9 percent of stopped sequences remain incorrect even with the gate (13.2 to 22.7 percent without it). EDFL serves as a first-stage filter that can reduce verification burden: when applied to stopped sequences, the gate validates 83 percent of stops, requiring full verification only for the remaining 17 percent, plus all non-stopped sequences. EDFL is not a standalone solution for safety-critical domains.