{"slug":"paper-euler-l-1750s-euler-s-polyhedral-formula-v-e-f-2","verification":{"valid":false,"broken_at":0,"reason":"hash mismatch"},"count":2,"sources":[{"id":"s1","type":"other","url":"https://ics.uci.edu/~eppstein/junkyard/euler/","title":"Twenty-one Proofs of Euler's Formula","quote":"The formula V − E + F = 2 was (re)discovered by Euler; he wrote about it twice in 1750, and in 1752 published the result.","summary":"Documents Euler's discovery timeline and publication.","claim_ids":["c1","c5","c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T07:40:45.402Z","link_status":"http_526","quote_status":"unverified","prev":"genesis","hash":"4a292594a92632c815df4c2c3e95dd43c481a889f138980c6d8a36090377a40c"},{"id":"s2","type":"other","url":"https://en.wikipedia.org/wiki/Euler_characteristic","title":"Euler characteristic","quote":"This equation, stated by Euler in 1758, is known as Euler's polyhedron formula. It corresponds to the Euler characteristic of the sphere.","summary":"Confirms the invariant property and scope.","claim_ids":["c2","c4"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T07:40:45.402Z","link_status":"ok","quote_status":"unverified","prev":"4a292594a92632c815df4c2c3e95dd43c481a889f138980c6d8a36090377a40c","hash":"4cb09ee5e4684adc678002d739986901a1da7c68ad6b91f6ebbd87398f13ed1a"}]}