What was already known
Earlier packing catalogs listed candidate arrangements for these cases without cited optimality proofs. Results for one to four squares are separate claims.
AI involvement
The project credits ChatGPT with the n=5 and n=7 proofs and the analytical n=6 proof, with Claude models supplying the occupied-arc idea, certificates and formalization support. The-Anh Vu-Le directed and reviewed the statements.
The source assigns the central proofs and six-square certificate-to-analysis step to the models; the owner set scope and reviewed statements.
Importance
Establishes exact optimality and classification for three previously open small packing cases.
Limitations
The reported Lean checking covers the n=5,6,7 radii and classifications. The n=3 exactness claim and n=4 priority overlap are outside this assessment. No independent human mathematical review is documented.
Technical verification
The source reports sorry-free Lean proofs of the exact radii and optimal-packing classifications, Comparator statement comparison, and independent kernel replay.
Formal checking
Repository reports sorry-free Lean proofs and statement comparison for the selected cases.
- Checker
- Lean 4 kernel and reported Comparator replay
- Scope
- SquaresInCircles.optimal_radius and optimal_packings for n=5,6,7
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The owner reviewed the statement and documentation, but no person's explanation of the central arc and six-square separation proofs is identified; this is the evidence-gap default.
Correction and publication history
The reported Lean proofs cover optimal radii and classifications for five, six and seven squares.
Read this published revision