What was already known
Atanasov and Ranganathan had proved existence through genus five. Earlier tropical and subdivision results did not establish the discrete genus-six statement on the original graph.
AI involvement
Nathan Pflueger supplied direction, notes and sources. The project credits agents with devising the decisive odd-subdivision descent and formal proof.
Agents supplied the decisive odd-subdivision descent within Pflueger's human-directed research.
- Supporting source (github.com) — Rank proof and tripod-subtraction explanation
Importance
Extends Baker’s graph Brill–Noether existence conjecture by one genus.
Limitations
The reported Lean proof covers existence through genus six. Separate rank and once-marked results in the project require their own assessments; no completed human check or human explanation of this descent is documented.
Technical verification
The repository reports a sorry-free Lean proof of the exact genus-six statement with only standard axioms.
Formal checking
Repository reports a sorry-free Lean theorem with standard axioms for the exact genus-six existence statement.
- Checker
- Lean 4 kernel, as reported by the project
- Scope
- GenusSix.brill_noether_existence_through_six for finite connected loopless multigraphs
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human author checked the statement against published definitions, but a named human explanation of the central descent proof is not documented; Few is the evidence-gap default.
Correction and publication history
The genus-six existence proof includes an agent-origin descent argument; separate rank and marked results are outside this claim.
Read this published revision