# Triangular lattice energy benchmark

Family 090: Triangular-lattice optimality, long-range Riesz and Coulomb energies, and spherical logarithmic energy. First review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Materials and geometric-design researchers can compare ideal planar arrangements against a triangular-lattice energy reference.

## Applicability and commercial boundary

The result concerns infinite density-one configurations and a specific completely monotone potential class. Finite boundaries, anisotropy, substrates and manufacturing constraints require separate modeling.

## Initial business decision

Conditional research. Commercial demand and profitability remain hypotheses.

## Next verification action

Build a finite-boundary sensitivity study and verify whether the modeled potential meets the theorem's assumptions.

## Evidence scope

The catalog statement was individually reviewed. Main-paper and selected formal-scope passages were additionally inspected for families 090, 093, 094, 097, 325, 328 and 332; this record does not claim a full proof audit or independent Lean verification. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).