Collatz conjecture: every positive orbit reaches one

Starting from any positive natural number n, repeatedly replace an even value x by x/2 and an odd value by 3*x+1. Prove that a finite number of iterations reaches 1. The exact Lean target uses Nat.rec to iterate this map, including zero iterations for n = 1. Almost-all results and finite computational checks do not establish the universal claim. Research status checked 8 October 2026: no accepted general proof identified in the cited literature. This is a proposed formal statement; independent correspondence review is requested. A successful statement check establishes well-formedness, not the conjecture.

∀ n : Nat, 0 < n → ∃ k : Nat, Nat.rec n (fun _ x => if x % 2 = 0 then x / 2 else 3 * x + 1) k = 1

OA_statement : Prop