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Aletheia

This directory contains prompts and responses from Aletheia on research level math problems.

Note that 2 outputs, one in Erdos problems and one in LeeSeo26, are not from Aletheia. The latter is for illustration purposes only (a correct solution was obtained by various models, including Aletheia).

  • A generalization of Erdos-1051, proving irrationality of certain rapidly converging series: tex, pdf (full paper).
  • Results from a semi-autonomous case study on applying Gemini to open Erdős problems: tex, pdf (full paper).
  • Computations of eigenweights for the Arithmetic Hirzebruch Proportionality Principle of Feng--Yun--Zhang: tex, pdf (full paper).
  • An initial case of a non-trivial eigenweight computation: tex, pdf (full paper).
  • A mathematical input to the paper "Strongly polynomial iterations for robust Markov chains" by Asadi–Chatterjee–Goharshady– Karrabi–Montaseri–Pagano. It establishes that specific bounded combinations of numbers are in polynomially many dyadic intervals: tex, pdf (full paper).
  • Generalizations of bounds for independence sets, used to help produce the paper "Lower bounds for multivariate independence polynomials and their generalisations" by Lee and Seo: tex, pdf (full paper).
  • Solutions to FirstProof challenge:
  • Proof that the Hodge bundle on the moduli space of genus g curves is simple, i.e., admits no non-trivial sub-bundles. : tex, pdf (full paper).

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