A Hamiltonian cycle on the five-dimensional hypercube that maximizes a natural alternating parity functional is forced, up to symmetry, to follow a step-direction sequence governed by the 2-adic valuation of the step index. This determines the flip frequencies uniquely as (16, 8, 4, 2, 2) and produces a canonical three-tier hierarchy with normalized ratio 1:3:12. The structure is not assumed; it is derived entirely from the optimality condition established in the companion result on maximal parity alignment. This theorem establishes the tier structure as a combinatorial consequence of parity optimality on Q5.
Building similarity graph...
Analyzing shared references across papers
Loading...
Craig Edwin Holdway
Building similarity graph...
Analyzing shared references across papers
Loading...
Craig Edwin Holdway (Fri,) studied this question.
www.synapsesocial.com/papers/69e5c3ce03c2939914029805 — DOI: https://doi.org/10.5281/zenodo.19642822