{"id":"palomar/PALOMAR-2026-10-17-000002","url":"https://github.com/AItoBit/erdos-662-proof/tree/91f70364bf88c9ae8181aa82a703a7ba2d369901","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-17-000002-v1.json","repo":"https://github.com/AItoBit/erdos-662-proof","tags":["math.MG","math.CO","msc:52C15","msc:52C10","discrete-geometry","erdos-problems","lattices","counterexample"],"score":0,"title":"Erdos 662: corrected global threshold conjecture","trust":"high","domain":"math.MG","source":"palomar","authors":["Colin Snyder","AItoBit"],"reviews":0,"subject":"math.MG","summary":"Disproves an explicitly corrected global threshold formulation of Erdos problem 662. For each radius, the conjecture bounds the average number of nearby points in every sufficiently large one-separated planar set by the unit triangular lattice's neighbor count. An exact rational oblique lattice and separated finite replicas violate the bound at radius six.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-17","reactions":{},"formalized":true,"formalizes":[{"title":"Erdos 662 Star Fleet verification archive","identifier":"https://www.starfleetmath.com/downloads/verify/erdos-662/erdos-662-solution.zip","relationship":"adapts"}]}