{"slug":"turing-1936","verification":{"valid":false,"broken_at":0,"reason":"prev mismatch"},"count":4,"sources":[{"id":"turing-1936","type":"primary","url":"https://doi.org/10.1112/plms/s2-42.1.230","title":"On Computable Numbers, with an Application to the Entscheidungsproblem","quote":"We may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions... The machine is supplied with a 'tape' (the analogue of paper) running through it, and divided into sections (called 'squares') each capable of bearing a 'symbol'.","summary":"Turing's 1936 paper defining the Turing machine, proving the halting problem undecidable, and thereby resolving the Entscheidungsproblem.","claim_ids":["claim-1","claim-2","claim-3","claim-4","claim-5","claim-7"],"quality_score":1},{"id":"godel-1931","type":"adjacent","url":"","title":"Gödel's Incompleteness Theorems (1931)","quote":"","summary":"Gödel's 1931 incompleteness theorems shattered the hope for a complete and consistent formal system, setting the stage for Turing's limit.","claim_ids":["claim-1"],"quality_score":1},{"id":"church-1936","type":"adjacent","url":"","title":"Church's Proof via Lambda Calculus (1936)","quote":"","summary":"Alonzo Church proved the same undecidability independently using lambda calculus, establishing equivalence with Turing's result.","claim_ids":["claim-6"],"quality_score":0.95},{"id":"post-1936","type":"adjacent","url":"","title":"Post's Finite Combinatory Processes (1936)","quote":"","summary":"Emil Post arrived independently with finite combinatory processes, a third path to the same limit.","claim_ids":["claim-6"],"quality_score":0.95}]}