What was already known
Green’s original question concerned complex-valued functions. A separately solved real-valued formulation did not answer it.
AI involvement
DeepMind researchers and Green clarified the question; the team found a numerical candidate and formalized the target. AlphaProof Nexus then produced the formal proof.
The agent produced the proof autonomously, but humans supplied a mathematically substantive numerical candidate and formal target.
Importance
The finite counterexample resolves the intended complex-valued question.
Limitations
The report does not publish the exact Lean declaration or a full human mathematical explanation of the counterexample.
Technical verification
The paper reports formalizing the corrected complex-valued counterexample and the agent proving that statement in its Lean-validated proof-search pipeline. The exact Lean source was not independently located or rebuilt here.
Formal checking
Agent-generated formal proof checked through the paper’s Lean compilation and integrity pipeline
- Checker
- AlphaProof Nexus Lean validator, as reported by the DeepMind authors
- Scope
- The Z/3Z separating functional is a counterexample to the intended complex-valued Green Problem 57
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The report explains the real-versus-complex correction and candidate but does not give a human explanation of the central formal proof; Few is the evidence default.
Correction and publication history
The finite counterexample resolves the intended complex-valued question.
Read this published revision