2-adic zeta value ζ2(7) is irrational

We prove that the Kubota–Leopoldt 2-adic zeta value \(ζ_2(7)\) is irrational. A 2025 result could only prove that at least one of four 2-adic zeta values ζ₂(7), ζ₂(9), ζ₂(11), ζ₂(13) is irrational. This preprint claims to isolate the first of those values and prove ζ₂(7) itself irrational. The proof constructs Hankel determinants from moments of an explicit Volkenborn integral whose values lie in \(Q+Qζ_2(7)\). A quadratic 2-adic valuation bound, an archimedean logarithmic-energy estimate, and explicit control of odd denominators yield the required contradiction, while nonvanishing follows from strict \(p\)-adic dominance at a suitable auxiliary prime.