The d=6 Exact-Base Branch for E677 Magmas

We isolate and formalize a d=6 exact-base branch in finite E677 magmas. In the branch considered here, a distinguished element x has left orbit c_0 = x, c_1 = x ◇ x, c_2 = x ◇ c_1, ..., c_5 = x ◇ c_4, together with an outsider element A satisfying the exact-base rows A ◇ A = c_1, A ◇ x = c_3, c_3 ◇ c_3 = c_1. Under the d=6 gap-1 context hypotheses, these rows force c_4 ◇ x = x, and therefore ((x ◇ x) ◇ x) ◇ x = x. The Lean formalization exposes this result through D6ExactBasePacket.fixer in lean/E677/D6Publication.lean. The theorem is independent of the large gap-1 dispatcher and verifies with only standard Lean axioms (propext, Classical.choice, Quot.sound).