Hamilton Decompositions of the Directed 5-Torus, Odd Modulus

Precise statement

The directed five-dimensional torus $D_5(m)$ has a Hamilton decomposition for every odd $m \geq 3$, extending the decomposition program for directed tori beyond the three-dimensional case.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.5 Pro, GPT-5.5 Codex, Claude Opus 4.7

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.

Provider: OpenAI, Anthropic · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

A Lean 4 formalization draft exists (cited in the paper) but its completeness is not stated.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-04-29

   arXiv

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.