Eventual categoricity for abstract elementary classes

Comments and discussion

• JesterOfAllTrades, Comments in “AI In Mathematics: October 10, 2026” (Reddit r/math, October 2026). A commenter describing previous research in AECs discusses the significance of the claimed ZFC result and reports difficulty following its exposition, without identifying a specific false lemma or providing a verification.

Formalization

• OpenAI math release, Shelah's eventual categoricity and the prescribed-threshold obstruction: Lean scope notes (lean/docs/240.md, 2026-10-06). The release's Lean formalization covers only the companion CH obstruction; the scope note says that "the separate eventual-categoricity theorem" of this paper is not included. [family-level]

Related prior literature mentioned by others

• Christian Espíndola, A proof of Shelah's eventual categoricity conjecture and an extension to accessible categories with directed colimits (arXiv:1906.09169v7, 2022-04-13; first posted 2019-06-21). Cited in the manuscript's introduction, this preprint separately claims eventual categoricity for arbitrary AECs in ZFC and an extension to accessible categories under SCH.
• Christian Espíndola, A complete classification of categoricity spectra of accessible categories with directed colimits (arXiv:2301.13167v1, 2023-01-30). Cited by both manuscripts, this preprint claims an explicit-threshold classification of AEC categoricity spectra, whose Theorem 4.1 and canonical-point argument are compared with the CH obstruction in the companion manuscript. [family-level]

Possibly relevant literature (found by the agent, not checked)

• Christian Espíndola, A short proof of Shelah's eventual categoricity conjecture for AEC's with interpolation, under GCH (arXiv:1909.13713, v3 28 December 2020). A further public claim by Espíndola, proving eventual categoricity for AECs with interpolation under GCH; the paper's comparison with Espíndola's claims cites only arXiv:1906.09169 and arXiv:2301.13167.
• Saharon Shelah and Andrés Villaveces, The Hart-Shelah example, in stronger logics (arXiv:math/0404258, Ann. Pure Appl. Logic 172 (2021) 102958). Builds AECs that are categorical in $\lambda^+,\dots,\lambda^{+k-1}$ but not in $\beth_{k+1}(\lambda)^+$ or above; these examples bear on how large the existential threshold $\mu(\lambda)$ in Theorem 1.2 must be.
• Sebastien Vasey, Building independence relations in abstract elementary classes (arXiv:1503.01366v6, 2016-03-29; Annals of Pure and Applied Logic 167, 2016). Its construction of good frames and, under additional locality hypotheses, global independence relations in tame AECs with amalgamation provides a comparison for the manuscript's Sections 5–7, which claim to construct a working-scheme independence calculus from the AEC axioms and unbounded categoricity.

Digests and expositions

• GitHub repository WBoney/AEC-categoricity-notes, Working Summary of the Eventual Categoricity Proof: Sections 2–4 and a Roadmap for Further Reading (LaTeX notes, revised 15 October 2026). Reading notes on this manuscript that treat Sections 2–4.1 in detail (EM foundations, strong-type reversal, comparison diagrams, amalgamation at selected cardinals) and outline the rest; the notes say they are "not an independent verification of the manuscript's proofs."