Pre-Reeb graphs are the 1-skeleta of cubes or zonotopes and their augmented versions have total-order reachability posets, giving combinatorial uniqueness for compatible order-embedding cubic coordinates on deletion towers of weak orders in types A and B.
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Lifting Cubic Realizations of Weak Orders in Types A and B
Pre-Reeb graphs are the 1-skeleta of cubes or zonotopes and their augmented versions have total-order reachability posets, giving combinatorial uniqueness for compatible order-embedding cubic coordinates on deletion towers of weak orders in types A and B.