Triangular-lattice minimality for planar Coulomb renormalized energy
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Does the density-one triangular lattice minimize planar Coulomb renormalized energy among all admissible full-plane configurations? The formulation uses a unit neutralizing background and the manuscript’s admissible square-cutoff families.
Why it matters and what counts as progress
Why it matters: The minimum determines a crystallization target and, through a prior equivalence, the linear term of optimal spherical logarithmic energy.
What counts as progress: A matching lower bound for the entire admissible class, rather than only lattices or periodic configurations, or an admissible configuration with smaller energy.
How the problem developed
- 2012 · Conjecture [1]
Étienne Sandier and Sylvia Serfaty Introduced the planar Coulomb renormalized energy and conjectured that its minimizer is the Abrikosov triangular lattice; triangular minimality among lattices was known, but the unrestricted problem remained open.
- 23 Sept 2026 · Reported claim [2]
OpenAI The preprint claims triangular-lattice minimality over the stated admissible curl-free fields with unit uniform background.
AI contribution
Triangular minimality for planar Coulomb renormalized energy
For the manuscript’s unit-background planar Coulomb renormalized-energy class and admissible square-cutoff families, every admissible field has energy at least that of the density-one triangular lattice. A prior equivalence then identifies the linear term of optimal spherical logarithmic energy.
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Publication dates and editorial changes.
OpenAI claims triangular minimality for planar Coulomb energy