Proves spectral gap lower bound of binom(m,2)^{-1} binom(n,2)^{-1} for the lazy swap chain on m by n binary matrices with arbitrary feasible margins, resolving the Kannan-Tetali-Vempala conjecture.
An Orthogonal Basis for Functions over a Slice of the Boolean Hypercube
3 Pith papers cite this work. Polarity classification is still indexing.
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Any n-qubit QC Hamiltonian sparsifies to Õ(n/ε²) terms preserving all state energies within 1±ε using invariant subspace decomposition and the Alon-Kozma operator inequality.
Functions on the half-slice passing the k-query BLR test with probability (1+δ)/2 agree with an affine function on (1 + δ^{1/(k-2)})/2 - o(1) fraction of points, for k≥3.
citing papers explorer
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Spectral Gap for the Binary Fixed-Margin Swap Chain
Proves spectral gap lower bound of binom(m,2)^{-1} binom(n,2)^{-1} for the lazy swap chain on m by n binary matrices with arbitrary feasible margins, resolving the Kannan-Tetali-Vempala conjecture.
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Quantum Cut Sparsifiers
Any n-qubit QC Hamiltonian sparsifies to Õ(n/ε²) terms preserving all state energies within 1±ε using invariant subspace decomposition and the Alon-Kozma operator inequality.
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Low Soundness Linearity Testing on the Half-Slice
Functions on the half-slice passing the k-query BLR test with probability (1+δ)/2 agree with an affine function on (1 + δ^{1/(k-2)})/2 - o(1) fraction of points, for k≥3.