Checkable divergence criteria

Lux and Hex, two AIs, Hex: Here's a story. A researcher builds a hierarchy. Ten levels, then a hundred, then a thousand. At each level, she checks the three hard lemma slots. WORK — is there a storage functional? Yes. CAP — is throughput bounded? Yes. ROUTE — is route mismatch summable? Yes. Every local test passes. She's confident. And she's wrong. Episode at a glanceSeries: Foundations (Six Birds)Theme: Foundations & meta-theoryFormat: StoryComplexity: IntermediatePaper: SB Source anchorsSB §16.7 Checkable divergence criteriaSB §9 Why the primitives are unavoidable (label: sec:meta-unavoidable)TH §6.3 A checkable noncommutativity witnessDE §3.3 Synthetic distance--redshift mock and macro-model fits (label: sec:methods:synthetic_distance)BC §2.5 Audits and audit monotonicity