{"id":"palomar/PALOMAR-2026-09-30-000033","url":"https://github.com/jfairfaxball-348/Pascal-Extremes/tree/a7e414a9e5bcf931c79b2bd4d4ffa81eeb6cfc22","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000033-v1.json","repo":"https://github.com/jfairfaxball-348/Pascal-Extremes","tags":["math.NT","msc:11B65","number-theory","binomial-coefficients","p-adic","lean-formalization"],"score":0,"title":"Pascal Extremes","trust":"high","domain":"math.NT","source":"palomar","authors":["John Fairfax-Ball"],"reviews":0,"subject":"math.NT","summary":"A Lean 4 formalisation of sharp p-adic extremal behaviour for the restricted binomial gcd G(N;m) = gcd{C(N,k) : 0 = 2 with p not dividing m, it proves that the maximum of v_p(G(N;m)) over admissible rows is the least r >= 1 with m = 2, the exact least-row formula T_p(p^a+1) = p^(3a)+1.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true}