The Universal Pisano Period of Second-Order Linear Recurrences in the Modulo-9 Ring

We generalize the Pisano period phenomenon to all second-order linear recurrence relations. Through computational brute-force and algebraic ring theory, we demonstrate that any sequence of this form fundamentally locks into a Pisano period of 24 in modulo-9 topology.Formal Verification & Source Code: The rigorous Lean 4 proofs and framework codebase are open-source and available at the Ouroboros GitHub Repository.