feat: add Golod-Shafarevich inequality eval problem#386
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Add the Golod-Shafarevich inequality for finite p-groups: a nontrivial finite p-group Q satisfies d(Q)^2 < 4 r(Q), where d(Q) is the generator rank and r(Q) = dim H^2(Q; F_p) the relation rank (both fixed by trusted helper definitions). This is one of the two external inputs taken as a hypothesis in Logical Intelligence's formalization of the disproof of Erdos's unit-distance conjecture (Hyp_GolodShafarevichInequality), and is not yet available in Mathlib. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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This PR adds the Golod–Shafarevich inequality for finite
p-groups as an eval problem: every nontrivial finitep-groupQsatisfiesd(Q)^2 < 4 r(Q), whered(Q)is the generator rank andr(Q) = dim_{𝔽_p} H²(Q; 𝔽_p)the relation rank. The two trusted helper definitionsgeneratorRankandrelationRank(non-holes) fix the meaning ofdandr, presenting a finitep-group as a discrete topological group so that topological generation and continuous cohomology agree with their abstract counterparts; they followErdosUnitDistance.Defs.ProPGroups.This is one of the two external inputs taken as a hypothesis in Logical Intelligence's formalization of the disproof of Erdős's unit-distance conjecture (erdos-unit-distance,
Hyp_GolodShafarevichInequality), and is not yet in Mathlib. The statement was checked for faithfulness against NSW Theorem 3.9.7 and Serre by an independent review, and the module builds with only the expectedsorry.🤖 Prepared with Claude Code