What was already known
Erdős established singularity when λ⁻¹ is Pisot. Fourier transforms at non-Pisot reciprocals tend to zero, so that method does not settle Salem parameters; the manuscript cites the existence of non-Pisot singular examples as open.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Supplies singular Bernoulli convolutions at non-Pisot reciprocal parameters.
Limitations
This selects the quartic Salem theorem rather than the manuscript’s general one-sided algebraic-unit approximation criterion. No completed independent check of this selected theorem was documented.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and precise Lean-scope or conditional-input review for non-notifying local inclusion.
Read this published revision