The Coralia Sequence: A Unique Finite Integer Set Under Fibonacci-Lucas Terminal Constraints

We introduce the Coralia Sequence C = {0, 1, 2, 3, 5, 7, 9, 12, 15, 23, 30, 35}, a 12-element integer set characterized by nine axioms (C1–C9). The sequence is generated by four arithmetic zones with non-decreasing initial gaps, followed by a strictly descending terminal gap triple drawn from the Fibonacci and Lucas numbers. We prove that C is the unique 12-element completion of a 10-element seed satisfying the stated axioms. In particular, the terminal gap triple (8, 7, 5) = (F_6, L_4, F_5) is shown to be the unique strictly descending triple from the Fibonacci–Lucas set whose elements sum to 20 and are all at least 5. Exhaustive verification code supporting the uniqueness result is publicly available.