What was already known
Erdős 1040 asked whether transfinite diameter determines μ(F) and separately whether μ(F)=0 whenever the diameter is at least one.
AI involvement
Feng and coauthors report an autonomous Aletheia run for the first-question example. Human editors corrected the presentation while retaining its core logic.
The project's account classifies the model-origin first-question example as an autonomous partial solution; the later human edits preserved its core logic.
Importance
Answers the first Erdős 1040 question negatively.
Limitations
The model’s proposed reduction for the second question was rejected. A later separate paper answers that vanishing question; it is not part of this contribution. The exact expert reviewers and an exhaustive novelty search are undocumented.
Technical verification
Feng and coauthors report a completed expert vetting of the retained first-question example and explicitly distinguish the rejected second-question argument. This is source-reported human review, not a check reproduced here.
Formal checking
Feng and coauthors report a completed expert vetting of the retained first-question example and explicitly distinguish the rejected second-question argument. This is source-reported human review, not a check reproduced here.
- Checker
- Feng et al.'s internal domain experts and paper authors
- Scope
- The two countable compact sets have equal zero transfinite diameter but different μ(F)
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors give and explain the concrete two-set argument in §3.2 and identify why the other part fails. This supports understanding of this narrow contribution.
Correction and publication history
Answers the first Erdős 1040 question negatively.
Read this published revision