The Sandier-Serfaty conjecture: the triangular lattice minimizes planar Coulomb renormalized energy

Theorem 1.1: for every admissible curl-free field with unit background, $W(E)\ge W(E_\triangle)$ , and $\inf W=W(E_\triangle)$ is finite, with no separation, periodicity or Voronoi assumption on the competitor. Theorem 1.2 gives the finite version: on every square torus with $n\ge2$ points the renormalized energy is at least $nW(E_\triangle)$ . The proof builds one trial potential from Voronoi sectors on a minimizing torus configuration, with an exact identity leaving a nonnegative square, plus interval-arithmetic estimates. It does not classify minimizers (compact changes keep the energy per area) and does not treat the Riesz or higher-dimensional cases.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Sandier-Serfaty conjecture: the triangular lattice minimizes planar Coulomb renormalized energy · Sandier-Serfaty conjecture

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VibeMathed record: The Sandier-Serfaty conjecture: the triangular lattice minimizes planar Coulomb renormalized energy

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No independent mathematician has checked this yet. Checked here: Theorem 1.1 of the principal manuscript was read against Sandier-Serfaty Conjecture 1. It states $W(E)\ge W(E_\triangle)$ for every cutoff family and every field in the admissible class $\mathcal A_1$ (density-one normalization, which the manuscript matches to the conjecture's background $m=2\pi$ ), with the triangular value finite and equal to the infimum. The proof was not refereed and the interval certificate was not re-run here. No Lean formalization in the release covers this manuscript (lean/docs/090.md lists only the universal-optimality and circle-packing statements). The manuscript itself notes the minimum statement does not classify all minimizing configurations.

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The Brauchart-Hardin-Saff conjecture on the linear term of optimal logarithmic energy on the 2-sphere

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Related in family: Universal optimality of the triangular lattice

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VibeMathed record: The Sandier-Serfaty conjecture: the triangular lattice minimizes planar Coulomb renormalized energy evidence for this event

The Brauchart-Hardin-Saff conjecture on the linear term of optimal logarithmic energy on the 2-sphere evidence for this event

Related in family: Universal optimality of the triangular lattice evidence for this event

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