The Bandelt-Dress Quartet Distance Conjecture
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.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Combinatorics
- Posed by
- Hans-Jurgen Bandelt, Andreas Dress
- Year posed
- 1986
- Years open
- 40y
- Solved
- 2026-08-04
- Model
- GPT-5.6
- Vendor
- OpenAI
- Collaborators
- Lior Pachter
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper states plainly that the author used GPT-5.6 to prove the theorem and to draft an initial version of the manuscript.
Verification
arXiv preprint, not yet peer-reviewed.
Source
arXiv:2608.03542 - The maximum quartet distance between phylogenetic trees