Comb-Bounded Crowns and Bi-Esakia Representability of Well-Ordered Rooted Trees

We give a sufficient condition for a well-ordered rooted tree to admit a bi-Esakia topology. The criterion requires finite first-level crowns whose order duals uniformly omit one fixed finite co-tree comb, while allowing arbitrary root width and no uniform bound on crown size or depth. The proof combines a finite-anchor synchronization theorem for finite posets amalgamated over a common finite downset with a better-partial-order theorem supplying finitely many anchor types. The result is a sufficient representability criterion rather than a classification. Status: Public Beta v0.1; internally verified candidate proof; external mathematical review pending.