{"id":"palomar/PALOMAR-2026-10-15-000006","url":"https://github.com/AItoBit/erdos415-lean/tree/9a4f222785f486a2ba60cb3fafda5ea3d05d01fd","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-15-000006-v1.json","repo":"https://github.com/AItoBit/erdos415-lean","tags":["math.NT","msc:11A25","number-theory","totient-function","combinatorics-on-words"],"score":0,"title":"A finite counterexample for strict consecutive totient patterns","trust":"high","domain":"math.NT","source":"palomar","authors":["Alexander"],"reviews":0,"subject":"math.NT","summary":"Formalizes the finite counterexample at cutoff 826 from Proposition 1.2 of Przemek Chojecki's Consecutive Totient Patterns. With ranks assigned to positions and an inclusive cutoff, every strict length-three permutation occurs, no increasing length-four block occurs, and a decreasing length-four block does occur. Hence the largest universal length is three and decreasing is not always absent at the first non-universal length. This is a partial negative result for a specified reading of Erdos Problem 415; no novelty, asymptotic result or natural weak-order frequency result is claimed.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-15","reactions":{},"formalized":true,"formalizes":[{"title":"Consecutive Totient Patterns","identifier":"","relationship":"formalizes"}]}