Given a point on the standard simplex, we calculate a proximal point on the regular grid which is closest with respect to any norm in a large class, including all <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\ell ^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math> </EquationSource> </InlineEquation>-norms for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$p\ge 1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>p</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>. We show that the minimal <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\ell ^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math> </EquationSource> </InlineEquation>-distance to the...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>