A Python implementation of the Helfgott-Thompson algorithm for computing the Mertens function.
The singular spectrum of a sparse Mertens matrix: unit multiplicity, parent-degree upper values, compact-operator lower limits, and an unconditional equivalent for the smallest singular value.
Certified bounds on the oscillation of the Mertens function M(x)/sqrt(x)
The eigenvalue decay of the limiting kernel of a sparse Mertens matrix: lambda_r(K) ~ (6/pi^2)/(r log r), with the counting and cumulative laws, unconditionally.
The smallest singular value of a 2.6n-nonzero (0,1) matrix with determinant M(n): sigma_min = |M(n)| n^{-3/2+o(1)}, a two-sided Riemann-hypothesis criterion, via Alladi's estimates for the Mobius function over rough numbers.
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