NIP2 implies almost strongly quadratically atomicity
NIP2 implies almost strongly quadratically atomicity
Let an elementary -group property (epGP) be a property of elementary abelian -groups, and let denote the stated second-order independence-property condition. An epGP is almost strongly quadratically atomic when the required high-rank quadratic factors have bounded complexity and provide the stated approximate atomic decomposition. NIP2 atomicity conjecture. If an epGP is , then it is almost strongly quadratically atomic. This strengthens the preceding structural result from almost quadratic atomicity to its strong variant; the supplied text gives no resolution.
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Primary source
C. Terry and J. Wolf, “Higher-order generalizations of stability and arithmetic regularity”, arXiv:2111.01739 (2025).
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