{"slug":"convergence-c08","verification":{"valid":false,"broken_at":0,"reason":"prev mismatch"},"count":5,"sources":[{"id":"godel-1931","type":"primary","url":"https://miscsubjects.com/a/godel-1931","title":"Gödel's Incompleteness Theorems (1931)","quote":"Gödel encoded arithmetic statements as numbers. He built a sentence that says 'I am unprovable.'","summary":"Gödel proved that any sufficiently powerful formal system contains statements that are true but unprovable within the system. The proof was constructive and arithmetic.","claim_ids":["c1","c2"],"quality_score":1},{"id":"turing-1936","type":"primary","url":"https://miscsubjects.com/a/turing-1936","title":"Turing's On Computable Numbers (1936)","quote":"Turing asked a machine to predict itself. The machine fails. It loops forever.","summary":"Turing defined computation via the universal machine and proved the halting problem is undecidable. Self-reference creates the limit that enables universality.","claim_ids":["c1","c3"],"quality_score":1},{"id":"von-neumann-1966","type":"primary","url":"https://miscsubjects.com/a/von-neumann-1966","title":"Von Neumann's Theory of Self-Reproducing Automata","quote":"Von Neumann designed a machine that builds copies of itself. The machine stores its own blueprint.","summary":"Von Neumann deduced self-replication from pure logic, sketching a 29-state machine that reads a tape describing itself. This predated the biological discovery of DNA's role.","claim_ids":["c1","c4"],"quality_score":0.95},{"id":"england-2013","type":"adjacent","url":"https://miscsubjects.com/a/england-2013","title":"England's Statistical Physics of Self-Replication","quote":"England derived a lower bound on the heat any replicator must dump.","summary":"England proved that self-replication burns entropy at a calculable rate depending on growth rate, internal order, and lifetime. The bound is thermodynamically hard.","claim_ids":["c5"],"quality_score":0.85},{"id":"maturana-1980","type":"adjacent","url":"https://miscsubjects.com/a/maturana-1980","title":"Maturana and Varela's Autopoiesis and Cognition","quote":"A cell does not process information. It produces itself.","summary":"Maturana and Varela defined autopoiesis: living systems as networks of processes that produce the components that produce the network. They built a computable model in 1974.","claim_ids":["c6"],"quality_score":0.85}]}