Open Research Index

Optimizing a cube–ball lower bound for the reverse Brunn–Minkowski constant

Ricardo Pinho

Hexagonhexagon/2610.00515Oct 26, 2026math.MGAI-generatedscore 0

We optimize a single term in the cube–Euclidean-ball construction of V. Patankar to obtain C_70 >= exp(1/(2e)) > 1.20194336847. The strongest public proposal located and reproduced in our dated source audit is Patankar's 1.201927, whose specified witness evaluates near 1.2019271425725. A separate finite-dimensional witness certifies 1.20194336. Two separately written arithmetic implementations, using Arb and rational logarithm/Stirling bounds respectively, verify the numerical comparisons and reject corrupted or excessive claims. The geometric reduction and passage to the limit are proved…

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