Research correspondence

Selected exchanges with researchers concerning results from my autonomous AI-assisted mathematical research experiments. These discussions range from mathematical feedback and identification of prior work to potential collaborations. Correspondence does not imply independent verification or endorsement.

Exchanges

Paata Ivanisvili — Keller–Klein Conjecture

30–31 October 2026

Discussed complementary approaches to the Keller–Klein Berry–Esseen conjecture. Ivanisvili proposed combining the results into a unified manuscript and Lean formalization. The correspondence developed into a collaborative effort to check and consolidate the candidate proof, with formal statement verification remaining essential.

Carlos Martins da Fonseca — q-Permanent Conjectures

29–31 October 2026

Shared an AI-generated counterexample to extended q-permanent monotonicity. After examining the manuscript, da Fonseca provided mathematical and bibliographic feedback and offered to collaborate on reviewing, refining, and extending the work, with transparent acknowledgment of AI involvement.

Yair Lavi — Gyires's Permanent Inequality

25–27 October 2026

Discussed a proposed proof of Gyires's inequality for order-five circulant matrices. Lavi considered the result potentially new and independently examined the manuscript's analytic arguments, reporting no errors in the portions reviewed. The computational certificates and Lean formalization were outside the scope of his review.

Pierre Letouzey — Generalized Hofstadter Functions

29 October 2026

Shared explicit counterexamples to a conjectured ordering of generalized Hofstadter iterates. Letouzey confirmed the failure of the proposed universal inequality and explained how the counterexample, together with known asymptotic behavior, establishes incomparability between the relevant iterated functions.

Eric Rowland — Power Ranks of Recursive Sequences

29 October 2026

Discussed candidate counterexamples concerning power ranks of recursive sequences. Rowland described related independent experiments using an LLM that produced infinite families of rank-three recurrences, supporting the failure of a finiteness assertion. He also mentioned an ongoing revision of the original paper.

Sam Ferguson — Spectral Tiles and Aperiodic Complements

30 October 2026

Exchanged findings concerning spectral tiles in finite binary vector spaces without periodic tiling complements. Ferguson discussed related counterexamples already known to him and his coauthor and shared a preliminary AI-assisted comparison of the constructions. The exchange highlighted mathematical overlap and differences without establishing independent verification of the candidate proof.

Priority questions raised in correspondence, including the exchanges with Eric Rowland and Sam Ferguson, are recorded in detail in PRIORITY_AND_NOVELTY.md.