mihalyimark

Solved 8

• Theorem 2, pp. 16–17, (15), no outliers — spectral rounding with (1+ε)-approximate k-means: Σ_k |S_k|/n_k ≤ 64(2+ε)‖X⁰ − X̂‖₁/n²_minProved

  Oct 2026

• Theorem 3 (Davis–Kahan, Yu–Wang–Samworth), p. 46, case s = 1 — ∃ orthogonal Ô, ‖U − ÛÔ‖_F ≤ 2^{3/2}‖Σ̂ − Σ‖_F / gProved

  Oct 2026

• (G.6), p. 46 — for the optimal rotation O, ‖Û − U⁰O‖²_F ≤ 8‖X̂ − X⁰‖₁/n²_minProved

  Oct 2026

• Lemma 5 (Lei–Rinaldo Lemma 5.3), pp. 45–46, (G.4) — Σ_k |S_k|δ²_k ≤ 4(4 + 2ε)‖V − V̂‖²_FProved

  Oct 2026

• MUB phase designs in dimension six are not subgroup cosets and must have a missing ternary productProved

  Oct 2026

• Proof of Theorem 2, p. 47 — for B* = Diag(1/√n_k)O with O orthogonal, ‖b*_l − b*_k‖ = √(1/n_k + 1/n_l)Proved

  Oct 2026

• Proof of Theorem 2, p. 46 — U⁰ = Z⁰Diag(1/√n_k) are top-r eigenvectors of X⁰ with eigenvalues n_k, and X⁰ vanishes on their complementProved

  Oct 2026

• (G.6)(iii), p. 46 — for A, B with entries in [0,1], ‖A − B‖²_F ≤ ‖A − B‖₁Proved

  Oct 2026

Posted 1

• MUB phase designs in dimension six are not subgroup cosets and must have a missing ternary productProved

  Oct 2026