Fourier Entropy-Influence constant: determine C 71 or improve its bounds; the repository records 6.278 (6.521845710923046575 ) (lower) and infty (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12056Computational complexityOpen

Maximal number of relevant variables in Boolean functions of degree $d$ ( $C_{44}$ )

Maximal number of relevant variables in Boolean functions of degree d : determine C 44 or improve its bounds; the repository records 1.5 (lower) and 4.394 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12047Computational complexityOpen

The degree--sensitivity exponent ( $C_{37}$ )

The degree--sensitivity exponent: determine C 37 or improve its bounds; the repository records log 3 (6) approx 1.63093 (lower) and 2 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12034AnalysisOpen

Bohnenblust--Hille constant on the Boolean cube ( $C_{26a}$ )

Bohnenblust--Hille constant on the Boolean cube: determine C 26a or improve its bounds; the repository records 2 (lower) and infty (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12012CombinatoricsSolved

Critical exponent for isoperimetric inequality on the Hamming cube ( $C_{11b}$ )

Critical exponent for isoperimetric inequality on the Hamming cube: determine C 11b or improve its bounds; the repository records 0.5 (lower) and 0.5 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12011ProbabilityOpen

$L^1$ Poincaré constant on the Hamming cube ( $C_{11a}$ )

L^1 Poincaré constant on the Hamming cube: determine C 11a or improve its bounds; the repository records sqrt pi/2 approx 1.2533 (lower) and pi/2 - 0.00013 approx 1.5707 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11950Computational complexityOpen

Sensitivity versus Degree for Boolean Multilinear Polynomials

Sensitivity versus Degree for Boolean Multilinear Polynomials. Solid result problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

Classifying finite universality

Finitely universal joins of small varieties

Large lattices without finite universality

Small varieties with large covers

Small finitely generated varieties

Fourier Entropy-Influence constant (C71C_{71}C71​)

Maximal number of relevant variables in Boolean functions of degree ddd (C44C_{44}C44​)

The degree--sensitivity exponent (C37C_{37}C37​)

Bohnenblust--Hille constant on the Boolean cube (C26aC_{26a}C26a​)

Critical exponent for isoperimetric inequality on the Hamming cube (C11bC_{11b}C11b​)

L1L^1L1 Poincaré constant on the Hamming cube (C11aC_{11a}C11a​)

Sensitivity versus Degree for Boolean Multilinear Polynomials

Fourier Entropy-Influence constant ( $C_{71}$ )

Maximal number of relevant variables in Boolean functions of degree $d$ ( $C_{44}$ )

The degree--sensitivity exponent ( $C_{37}$ )

Bohnenblust--Hille constant on the Boolean cube ( $C_{26a}$ )

Critical exponent for isoperimetric inequality on the Hamming cube ( $C_{11b}$ )

$L^1$ Poincaré constant on the Hamming cube ( $C_{11a}$ )