The Bandelt-Dress Quartet Distance Conjecture
Statement
The quartet distance counts the four-leaf subsets on which two binary phylogenetic trees display different topologies. Bandelt and Dress conjectured the maximum over trees on leaves. Proved: it is , by reducing arbitrary pairs of trees to caterpillars through a common-root planarization and an identity on five-leaf trees.
Context
A 1986 conjecture calibrating the scale of the quartet distance, which is a standard metric for comparing phylogenetic trees in computational biology.
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The paper states plainly that the author used GPT-5.6 to prove the theorem and to draft an initial version of the manuscript.
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