What was already known
The Moore bound gives nₖ(d)≤dᵏ+Oₖ(dᵏ⁻¹). The matching asymptotic was known only for selected diameters.
AI involvement
GPT-5.6 Pro suggested splitting complete flags into odd- and even-rank subflags. Wouter Cames van Batenburg and Samuel Korsky chose the setting, developed the construction and verified the arguments.
The model supplied the retained odd/even split central to the construction; humans directed the setting and completed the theorem and proof.
Importance
Settles the fixed-diameter asymptotic degree–diameter question for every k.
Limitations
The reported Lean development checks the central limit theorem and construction, but not every explicit error estimate or an auxiliary bipartite limit. The separate line-graph edge corollary is human-developed.
Technical verification
The authors report verifying the mathematical arguments, and their Lean 4 project reports kernel checks of the central theorem chain, including Theorem 1.1. The explicit quantitative O_k error estimates and an auxiliary bipartite exact limit lie outside its kernel-checked scope.
Independent checking
author verification of all mathematical arguments
- Checker
- Wouter Cames van Batenburg and Samuel Korsky
- Scope
- halved-flag construction and fixed-diameter theorem
- Basis
- Reported by the linked checker
Formal checking
pinned Lean build, axiom audit and writeup-alignment review
- Checker
- Lean kernel through the Cames van Batenburg–Korsky formalization
- Scope
- Theorem 1.1 fixed-diameter limit, Proposition 3.1 construction, and Corollary 1.2
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors derive the degree, order and diameter through flag counts and odd-even transposition routing and state how the AI suggestion became their construction.
Correction and publication history
The halved-flag construction proves the fixed-diameter asymptotic limit; auxiliary corollaries are outside this claim.
Read this published revision