The paper was essentially made by using loop engineering with AI. Which in of itself would be fine, if checked by a human. It seems the paper admits that it was not. Saying that the math was done with an AI, and that its verification was then done with another AI.
It seems like there’s a concrete error early on. The tail recurrence 1.4 is T_i + T_{i+1} = 1/(2i+1)² but in 2.12 it uses the factor (2X+3)². With the actual recurrence, K(i) does not vanish. So the zero count that forces deg K 4B+1 fails. At the extra zero at -3/2(2.16), which would win by exactly one no longer works.
The structure does not match how these results are proven. The paper mimics Calegari–Dimitrov–Tang’s 2024 proof for L(2,χ₋₃), but that proof was a deliberate capacity bound. Here the arithmetic content is replaced by a combinatorial minimization over index sets plus numerics no human has checked.
There’s also some minor sloppiness in where K=9 instead of K=0 in the definition of K and “nineteen century” typos which suggests not only was the math not proofread, but the grammar wasn’t either.
My guess is that an expert will probably find a specific gap quickly but it would be cool if I’m proven wrong.
The paper was essentially made by using loop engineering with AI. Which in of itself would be fine, if checked by a human. It seems the paper admits that it was not. Saying that the math was done with an AI, and that its verification was then done with another AI.
It seems like there’s a concrete error early on. The tail recurrence 1.4 is T_i + T_{i+1} = 1/(2i+1)² but in 2.12 it uses the factor (2X+3)². With the actual recurrence, K(i) does not vanish. So the zero count that forces deg K 4B+1 fails. At the extra zero at -3/2(2.16), which would win by exactly one no longer works.
The structure does not match how these results are proven. The paper mimics Calegari–Dimitrov–Tang’s 2024 proof for L(2,χ₋₃), but that proof was a deliberate capacity bound. Here the arithmetic content is replaced by a combinatorial minimization over index sets plus numerics no human has checked.
There’s also some minor sloppiness in where K=9 instead of K=0 in the definition of K and “nineteen century” typos which suggests not only was the math not proofread, but the grammar wasn’t either.
My guess is that an expert will probably find a specific gap quickly but it would be cool if I’m proven wrong.