Withdrawn: "A p-adic Valuation Proof of the Beal Conjecture"

Retraction (2025-10-22). The key lemma misused the p-adic valuation of sums and ignored cancellation cases; the finite computational sweep cannot substitute for a proof. I withdraw the proof claim.
Context. First-year paper; any future claim will include a correct lemma chain or be clearly marked as a conjecture with code and logs.