Hamilton Decompositions of the Directed 5-Torus, Odd Modulus
The directed five-dimensional torus has a Hamilton decomposition for every odd , extending the decomposition program for directed tori beyond the three-dimensional case.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Graph decompositions
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-04-29
- Model
- GPT-5.5 Pro, GPT-5.5 Codex, Claude Opus 4.7
- Vendor
- OpenAI, Anthropic
- Collaborators
- SangHyun Park
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
GPT-5.5 Pro "contributed to proof exploration, including selector design and block-recurrence case analysis"; GPT-5.5 Codex drafted the Lean 4 formalization; Claude Opus 4.7 contributed exposition. All mathematical content author-verified.
Verification
A Lean 4 formalization draft exists (cited in the paper) but its completeness is not stated.