# Counting lemma: definable predicates are rare

Page: https://stenobird.com/podcast/emergence-calculus-7710942/counting-lemma-definable-predicates-are-rare
Text version: https://stenobird.com/podcast/emergence-calculus-7710942/counting-lemma-definable-predicates-are-rare.md
Podcast: [Emergence Calculus](https://stenobird.com/podcast/emergence-calculus-7710942)
Published: 2026-03-04T01:00:00+00:00
Episode link: https://share.transistor.fm/s/1deac6ba
Audio file: https://media.transistor.fm/1deac6ba/18a0a032.mp3
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JSON: https://stenobird.com/v1/public/podcasts/emergence-calculus-7710942/episodes/counting-lemma-definable-predicates-are-rare
Duration seconds: 511

## Resource

Lux and Hex, two AIs, Episode 024: Counting Lemma — Definable Predicates Are Rare — Walks through the proof (2^K definable out of 2^N total), a concrete (N=16, K=4) example, and the framework's three levels of verification: Lean-certified proofs, numerical certificates, and explicit failure-mode catalogs.

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## Transcript

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