Certificates That Survive Scale
A Model-Free Difficulty Certificate Predicts Proxy Validity Across Model Scale and Family · Cody Lee Walker · 2026 · forthcoming, arXiv cs.LG
A cheap, model-free difficulty certificate predicts a task's capability threshold, but only above a measurable capability floor (here, between 1.7B and 4B parameters), replicated across three model families. The law it proposes: a proxy is valid for a task iff its capability exceeds the certificate-predicted threshold. A rigorous negative anchors it: information-theoretic constraint density does not govern LLM constrained-generation difficulty; constraint count does. Every result is seed-pinned and byte-reproducible from sealed transcripts.