When can an interpretability claim be trusted? Stability and certification of feature dimensionality, ridge leverage and the feature recovery rate

AI use statement: The literature search, research targets, novelty audits, proofs, experiment code and text were drafted by a pipeline of AI agents built on Anthropic's Claude models (the Opus- and Sonnet-tier models available in Claude Code in October 2026, including Claude Opus 5.5), run in Claude Code and directed by the authors. Every proof was checked by an independent blind AI reviewer and by numerical tests. No human mathematician other than the authors has verified the proofs. AI systems are not authors; the authors take full responsibility for the content.