What was already known
Frankl, Kupavskii and Swanepoel asked the general 2d+1-vertex unit-distance question. Their lower bound gives the matching dimension when d=3.
AI involvement
Dishant Shah chose the d=3 target and signed the statement. AI agents wrote the central graph proofs and integrated the Lean development; Claude Opus 5.5 managed the work and made mathematical fixes. No named human explanation of the graph-classification proof is documented.
The public run log metadata attributes most central proof leaves and the accepted ten-edge theorem to AI agents; the human owner fixed the target and statement, and the managing AI integrated and repaired work.
Importance
The proof settles the seven-vertex case of a broader open dimension question.
Limitations
Priority for the seven-vertex case against earlier proofs is unestablished; Shah’s sign-off checked the target statement, not the full proof.
Technical verification
The cited development reports Lean and NanoDa acceptance of questionAt3 via Comparator; statement fidelity was separately checked and signed by the owner. This review did not rerun the build.
Formal checking
Kernel checks, Comparator statement match and standard-axiom audit
- Checker
- Lean 4 and NanoDa kernels, reported in repository Comparator record
- Scope
- FKSProblem2.Palomar.target = questionAt3
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The owner’s sign-off documents statement understanding, not explanation of the central graph-classification and placement proof. The README outline and agent review do not establish a human explanation; Few is the evidence default.
Correction and publication history
The proof settles the seven-vertex case of a broader open dimension question.
Read this published revision