{"id":"palomar/PALOMAR-2026-09-25-000017","url":"https://github.com/jfairfaxball-348/pascal-minus-one/tree/5f20593464d86ef8c3c34e1c00d84f8a48c0457e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-25-000017-v1.json","repo":"https://github.com/jfairfaxball-348/pascal-minus-one","tags":["math.NT","msc:11B65","number-theory","p-adic-valuation","binomial-gcd","lean-formalization"],"score":0,"title":"Pascal Minus-One GCD","trust":"high","domain":"math.NT","source":"palomar","authors":["John Fairfax-Ball"],"reviews":0,"subject":"math.NT","summary":"A Lean 4 formalization of p-adic valuations for the restricted binomial gcd G(N;m) = gcd{C(N,k) : 0 < k < N, m divides k}. The principal submitted result gives the complete valuation formula for primes p congruent to -1 modulo m, including the mixed-parity digit-sum branch and the exceptional p = m - 1 valuation-2 case. The repository also proves the complementary p congruent to 1 branch, a prime-power scaling reduction, and complete prime-by-prime formulas for m = 3, 4, and 6.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true}