What was already known
The directed three-torus was known. Older product results and surveys did not give this five-dimensional decomposition for all odd moduli.
AI involvement
Park credits GPT-5.5 Pro with retained zero-set selector design and block-recurrence case analysis. Park designed and completed the construction, checked the paper and Lean theorems, and explained the return-map proof.
The author identifies model-origin selector design and recurrence case analysis as retained central pieces of the five-torus construction.
Importance
Extends the return-map construction to a new infinite five-dimensional family.
Limitations
Even moduli and higher dimensions remain outside the theorem. The reported Lean theorem covers every odd m≥3 with finite certificate branches, alongside Park’s stated human check.
Technical verification
Park reports a Lean 4 theorem for the same directed Cayley-edge statement for every odd m≥3, with finite certificate branches, and explicitly reports human verification of all mathematical content. Appendix C identifies the theorem, commit and build command. Neither check was reproduced here.
Independent checking
Author verification of all mathematical content and formal theorems, expressly stated in the AI disclosure
- Checker
- Sanghyun Park
- Scope
- The paper's complete odd-modulus directed five-torus construction and Lean theorems
- Basis
- Reported by the linked checker
Formal checking
Top-level D5Odd.D5_odd_cayley_unconditional and lake build D5Odd at the cited commit
- Checker
- Lean 4 type checker on Park's D5Odd development
- Scope
- Hamilton decomposition of Cay((Z/mZ)^5,{e0,…,e4}) for every odd m≥3 and finite m=3/matching branches
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Park explains the Latin-table selector, layer matching, normalized return map and block recurrence that produce a single cycle in each colour.
Correction and publication history
Extends the return-map construction to a new infinite five-dimensional family.
Read this published revision