Symmetric ideal degree-3 PTE solutions are asymptotically counted as (4 log 2 / 3 π²) H³ log H + O(H³) due to the second moment of the sum-of-two-squares representation function.
Chiral Abelian gauge theories with few fermions,
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Arithmetic Symmetry in Ideal Prouhet-Tarry-Escott Solutions
Symmetric ideal degree-3 PTE solutions are asymptotically counted as (4 log 2 / 3 π²) H³ log H + O(H³) due to the second moment of the sum-of-two-squares representation function.