{"type":"rich","version":"1.0","provider_name":"Transistor","provider_url":"https://transistor.fm","author_name":"Emergence Calculus","title":"Counting lemma: definable predicates are rare","html":"<iframe width=\"100%\" height=\"180\" frameborder=\"no\" scrolling=\"no\" seamless src=\"https://share.transistor.fm/e/1deac6ba\"></iframe>","width":"100%","height":180,"duration":511,"description":"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.","thumbnail_url":"https://img.transistorcdn.com/-k4twdYpQ3zWC7xasY79j2kROCLhELHd05EVQiVwRhU/rs:fill:0:0:1/w:400/h:400/q:60/mb:500000/aHR0cHM6Ly9pbWct/dXBsb2FkLXByb2R1/Y3Rpb24udHJhbnNp/c3Rvci5mbS9jOGY4/MzRhODFiYWE4Y2I0/MWVlYmQzODE3YjA5/YjUxOC5qcGc.webp","thumbnail_width":300,"thumbnail_height":300}