What was already known
Erdős, Hajnal and Szemerédi suspected infinitely chromatic examples for every arbitrarily slowly divergent f.
AI involvement
GPT-6 Astra found the proof and wrote Lean code in a network-isolated run without human mathematical steering. Adamczewski packaged the repository; Bloom later explained its approach.
Benchmark and repository document no human guidance during the model proof search.
Importance
The result settles the local-versus-global chromatic question in the opposite direction.
Limitations
The compared theorem does not provide an explicit rate for f. Bloom sketches the core argument but does not document a line-by-line proof check.
Technical verification
Source-reported Lean build and Comparator match to the trusted challenge in a pristine environment; no broader informal theorem is silently inferred.
Formal checking
compiled proof, trusted statement comparison, and standard-axiom check
- Checker
- Lean 4 kernel and FrontierMath Erdős Comparator
- Scope
- Problem #74 compared theorem
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Bloom describes the core induction, while the formal-to-informal details and claimed explicit rate remain undigested.
Correction and publication history
The result settles the local-versus-global chromatic question in the opposite direction.
Read this published revision