What was already known
The report presents this sharp pairwise total-variation asymptotic as a research-level probability question supplied by a domain expert. It does not document a precise earlier bound for these two starting states; a larger priority or numerical improvement cannot be inferred.
AI involvement
Minghao Pan supplied the problem statement. QED revised its proof plan and produced the proof without further human mathematical input; Pan then verified it.
The report documents problem-only human input and a model-driven proof search with substantial plan changes.
Importance
Obtains the sharp rate for this specified pair of lamplighter starting states.
Limitations
This concerns two starting states for the line walk, not the separately published tree return-probability result. The reviewed report gives no precise earlier bound for these states or detailed proof-checking steps.
Technical verification
The QED report and project README say Minghao Pan verified the resulting proof of the exact line-walk total-variation asymptotic. This is a source-reported human check, not a local reproduction.
Formal checking
The QED report and project README say Minghao Pan verified the resulting proof of the exact line-walk total-variation asymptotic. This is a source-reported human check, not a local reproduction.
- Checker
- Minghao Pan, probability researcher at Caltech
- Scope
- ||P_t^x-P_t^y||_TV asymptotic to within constants t^(-1/2) for the specified switch–walk–switch walk on Z_2 wr Z
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The expert reports technical difficulty but gives no explanation of the central proof mechanism; Few is the evidence default, not a positive finding of incomprehension.
Correction and publication history
QED produced the proof after problem-only input; Minghao Pan verified the result.
Read this published revision