What was already known
Earlier tables gave weaker lower bounds for these covering numbers. The 25-point bound follows from the new 24-point bound and a known derivation inequality.
AI involvement
James Chang selected the target and directed an OpenAI Dots campaign. Astra agents developed the contradiction excluding 19 blocks and wrote the original Lean proof; the 25-point derivation is standard.
Agents supplied the core mathematical argument and first formal proof while Chang set the task, directed the campaign and later rewrote the presentation; this is not autonomous research.
- Supporting source (github.com) — Final indexed and Finset theorem statements
Importance
Excludes a 19-block (24,14,4) covering and improves a related 25-point lower bound.
Limitations
These are lower bounds, not exact covering numbers, and they do not decide whether 41 blocks suffice for C(25,15,5). The reported machine check covers both finite-set statements; no complete human mathematical check is documented.
Technical verification
Palomar v2 records two matching Finset declarations at commit 401d986 and reported mechanical verification, including Comparator replay through Lean and independent kernels. No human proof check is documented.
Formal checking
Registry v2 reports compared finite-set declarations and mechanical verification at the pinned commit.
- Checker
- Palomar mechanical verifier and Comparator
- Scope
- C(24,14,4)≥20 and C(25,15,5)≥34 for finite-set covering families
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Chang's later paper and companion exposition explain the central incidence, rigidity and counting mechanism; this documents author understanding without implying independent human verification.
Correction and publication history
The AI-found 24-point lower bound and its standard 25-point consequence match the reported machine check.
Read this published revision