NIP2 implies almost strongly quadratically atomicity

Let an elementary pp-group property (epGP) be a property of elementary abelian pp-groups, and let NIP2\mathrm{NIP}_2 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 NIP2\mathrm{NIP}_2, 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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