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bibkey: barei2026solvable authors: Andres Barei (with Muse Spark via meta.ai; reviewed by Nicolás Jaramillo Torres) year: 2026 title: “On solvable evolution algebras and a conjecture by García-Martínez and Pérez-Rodríguez” doi: null url: https://ai.meta.com/research/publications/on-solvable-evolution-algebras-and-a-conjecture-by-garcia-martinez-and-perez-rodriguez/ claim: “Remark 3.5 records an unresolved search for idempotent subspaces of dimension greater than two without a nonzero proper idempotent subspace.” strata_touched:

  • D5/S3/QuadraticForms/EvolutionAlgebras/BareiRemarkThreeFive license: citation-only triage: anchor

On solvable evolution algebras and a conjecture by García-Martínez and Pérez-Rodríguez

§§2–3 define evolution algebras over an algebraically closed field, pair-product span V² and idempotent subspaces. Remark 3.5 is the external question answered here. Example 2.1 is a published counterexample and is not a formalization target in this delivery.

Verified locator

  • URL: https://ai.meta.com/research/publications/on-solvable-evolution-algebras-and-a-conjecture-by-garcia-martinez-and-perez-rodriguez/ (publication page and its linked PDF retrieved 2026-10-04; Meta AI, published 2026-10-02; no DOI).
  • Location: §1 (Conjecture 1.1, cited to García-Martínez and Pérez-Rodríguez), §2 (definitions, Example 2.1), §3 (Lemma 3.1, Theorems 3.2–3.3, Corollary 3.4, Remark 3.5 on PDF page 4, Remark 3.6).

Reading and scope

Fresh source retrieval on 2026-10-04 returned HTTP 200. The relevant passages were read for the bounded literature check in #12879. No higher-dimensional minimal idempotent-subspace answer was found in the inspected text. This is not-found-in-searched-scope, not exhaustive absence or a priority claim.