Maxwell's Three-Charge Equilibrium Bound
Statement
How many nondegenerate equilibrium points can the potential of three positive point charges have? Gabrielov, Novikov and Shapiro had proved at most , and observed that their method would give if an auxiliary polynomial system had at least four solutions with multiplicity in each open quadrant. That four-solution statement holds, so the bound is , and six is attained for special charge values.
Record
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Andrei Gabrielov, Dmitry Novikov, T. Novikov and Boris Shapiro, using ClaudeThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The acknowledgement states that parts of the work, including the saddle-separation argument and the symbolic and numerical verification, were developed with the assistance of Claude, and that all results were independently verified by the authors. The abstract calls that separation argument at the unique saddle point of a separated-variable first integral the main new ingredient, so the model's contribution reaches the load-bearing step.
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