What was already known
Swanepoel disproved the conjecture for 1<p<2, while Ge, Xu and Zhou proved it for 2≤p≤4. A separate construction refuted it at p=5 and nearby values.
AI involvement
Xiong credits GPT-6 Astra with finding the construction; Xiong wrote and explained the published proof.
The acknowledgments identify GPT-6 Astra as finder of the central equilateral-set construction, while Xiong supplied the published proof and presentation.
Importance
Closes the remaining p>4 range of Kusner’s equilateral-set conjecture.
Limitations
Xiong explains the Hadamard-block coordinates, distance cases and parameter existence. His responsibility statement does not document a completed proof check, and none was found.
Technical verification
The manuscript proves the claim on paper but documents no separate completed human proof check, machine certificate or exact computation; Reported is the evidence default.
Human understanding
Xiong explains the front/back coordinate design, all pairwise distance cases and the parameter-existence step for every p>4.
Correction and publication history
If correct, closes the remaining p>4 range of Kusner’s equilateral-set conjecture.
Read this published revision