An Elementary Zero-Freeness Certificate for an Order-Six Linear Recurrence

We establish an unconditional zero-freeness certificate for a specific non-simple, non-degenerate integer linear recurrence of order six, identified as unresolved in the 2025 dissertation of Joris Nieuwveld and a 2026 survey of the Skolem Problem. The proof uses congruences modulo 3, 4, 16 and 23 and a binomial lifting lemma valid for all positive indices. It does not depend on a numerical search bound or number-theoretic conjectures. The result concerns a fixed instance and does not settle the general Skolem Problem. This is an author preprint, not yet peer-reviewed; independent A.K/79 W04 audit and Lean 4.35.0 formal verification are pending. Licensing (AK79 / A.K/79): Research materials are available under CC BY-NC 4.0; code is available under PolyForm Noncommercial 1.0.0. Science, research and other non-commercial uses are permitted under the applicable licences. Any commercial use requires a separate written licence from AK79 (A.K/79): [email protected].