What was already known
Bohman’s cited construction reached N≤0.22002·2^n. Dubroff, Fox and Xu proved a lower bound of order 2^n/sqrt(n); Erdős asked for a uniform positive multiple of 2^n.
AI involvement
GPT-6 Astra found the construction and wrote Lean code in a network-isolated run without human mathematical steering. Adamczewski packaged the repository; Bloom later explained the lattice view.
Benchmark and repository document no human guidance during the model proof search.
- Supporting source (erdosproblems.ai) — Dated 15 September dyadic-graph proof claim and linked Lean repository; separate proof
Importance
The construction disproves the proposed uniform exponential lower bound.
Limitations
Bloom reinterpreted the model’s rational-matrix proof as a lattice argument, but its detailed translation is not fully documented as a human 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 #1 compared theorem
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Bloom explains the lattice route but the detailed passage from the determinant construction to sum-distinct sets is not fully digested in a human proof.
Correction and publication history
The construction disproves the proposed uniform exponential lower bound.
Read this published revision