VibeMathedMath problems solved by AI
All problems

Hamilton Decompositions of the Directed 3-Torus

For D3(m)=C⃗m□C⃗m□C⃗mD_3(m) = \vec{C}_m \square \vec{C}_m \square \vec{C}_m, can the full arc set be partitioned into three directed Hamilton cycles for every integer m≥3m \ge 3?

Result
Proved
Status
Resolved
AI contribution
AI co-developed
Method
Argument
Field
Graph decompositions
Posed by
—
Year posed
2026
Years open
0y
Solved
2026-03-25
Model
Claude Opus 4.6, GPT-5.3 Codex, GPT-5.4 Pro
Vendor
Anthropic / OpenAI
Collaborators
—
Verification
Lean-verified
Publication
Preprint
Significance
5 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

The return-map and odometer reduction, the Kempe-swap constructions for odd mm, and the clock-and-carry analysis for even mm were developed across three frontier models.

Verification

A Lean 4 formalization accompanies the construction; arXiv preprint.

Source

arXiv:2603.24708 - Hamilton decompositions of the directed 3-torus

Discussion