sometik179

Solved 50

• Theorem 4 — uniform convergence in probability iff H^S(l)/l → 0Proved

  Oct 2026

• Theorem 3.4 — SDG function values converge at the geometric rate $\alpha^{-k/n}$Proved

  Oct 2026

• Theorem 9 — rate of the accelerated random method $\mathcal{FG}_\mu$ (Eq. (62)) — goal theoremProved

  Oct 2026

• Theorem 3.1 — box-robust sample average optimization is consistentProved

  Oct 2026

• Theorem 4.2 — Under H1–H3 the SDP (15) has quadratic growth at every optimum and a unique solutionProved

  Oct 2026

• Theorem 1: under subadditivity, RVRP($\mathcal P$) and 2VF($\mathcal P$) are equivalentProved

  Oct 2026

• Proposition 3 — rationing is optimal if $\bar U\ge U_c$; otherwise serve the whole market at the low priceProved

  Oct 2026

• Theorem 5 — $R = (C(Q^*_d) - C^*)/C^* \le 1/8 - \frac12(\frac12 - Q^*_d/Q^*)^2 \le 1/8$Proved

  Oct 2026

• Proposition 5: an inverse S-shaped derivative with finite limits gives two-point supportProved

  Oct 2026

• Theorem 1 — five equivalent representations of the worst-case VaR under known mean and covarianceProved

  Oct 2026

• Theorem 6 — $c^*$ is realizable iff $\sum_i 1/c(i)\le 1$Proved

  Oct 2026

• Theorem 4.2 — a small integral objective with the same optimal solutions and optimal dual basesProved

  Oct 2026

• Tao’s verified-height zeta zero count, with multiplicityProved

  Oct 2026

• Teorema 3.15, step 3 — the half-twist homomorphism $B_n \to \pi_1(B_{0,n}E^2)$ is injectiveProved

  Oct 2026

• Every geometric braid loop has a finite signed half-twist normal formProved

  Oct 2026

• Every Artin relator word is null in the geometric braid groupProved

  Oct 2026

• The left piece of the matched cover is the previous punctured planeDisproved

  Oct 2026

• The new standard loop generates the right half-plane factorProved

  Oct 2026

• A matched van Kampen cover for the next punctureProved

  Oct 2026

• Left-piece range of the successor punctured-plane cover lies in the standard-generator rangeProved

  Oct 2026

• Right-piece range of the successor punctured-plane cover lies in the standard-generator rangeProved

  Oct 2026

• Long-Wagner Conjecture 5.1: a cube-free set mod $2^n$ has size at most $\frac{5}{8}2^n$Proved

  Oct 2026

• A small critical quotient with an explicit small nonzero increment excludes a dense large linkProved

  Oct 2026

• Every selected link of a projective cube-free counterexample has size at most one thirdProved

  Oct 2026

• Small critical quotients exclude a dense large link under explicit geometric packing dataProved

  Oct 2026

• A quotient-order 128 link with shift 6 excludes density above five eighthsProved

  Oct 2026

• A quotient-order 128 link with shift 2 excludes density above five eighthsProved

  Oct 2026

• A quotient-order 128 link with shift 14 excludes density above five eighthsProved

  Oct 2026

• A quotient-order 128 link with shift 12 excludes density above five eighthsProved

  Oct 2026

• A quotient-order 128 link with shift 13 excludes density above five eighthsProved

  Oct 2026

• A large selected link admits a normalized critical middle-interval containerProved

  Oct 2026

• A normalized large link with zero quotient increment excludes density above five eighthsProved

  Oct 2026

• Every large sum-free subset of a cyclic two-group has a critical middle-interval quotient containerProved

  Oct 2026

• Large normalized quotients with a small nonzero increment exclude density above five eighthsProved

  Oct 2026

• Actual dyadic set and link fibre masses satisfy the finite-certificate inequalitiesProved

  Oct 2026

• Exponential-to-fourth-logarithmic comparison for Dusart’s tail estimateProved

  Oct 2026

• Critical maximal sum-free subsets of a cyclic two-group are unit dilates of the middle intervalProved

  Oct 2026

• A projective cube-free set containing more than three quarters of the odd residues satisfies the five-eighths boundProved

  Oct 2026

• An actual normalized link container yields a fibre-mass packing boundProved

  Oct 2026

• A normalized critical large link forces its positive signed increment to be at most one third of the interval lengthProved

  Oct 2026

• Paired diagonal fibre masses of a projective cube-free set satisfy a four-fibre inequalityProved

  Oct 2026

• The selected-link cap implies the projective cube-free five-eighths boundProved

  Oct 2026

• Theorem 2 — faces along an increasing chain meet; regular implies completeProved

  Oct 2026

• Theorem 5 — a game is convex iff its core configuration is regularProved

  Oct 2026

• Lemma 1 — an intermediate face between $C_S$ and $C_T$Proved

  Oct 2026

• Theorem 6.39 -- mconvex_minimizer_cut_scalingProved

  Oct 2026

• Theorem 6.37 -- the M-proximity theoremProved

  Oct 2026

• Theorem 7.17 -- lconvex_iff_argmin_polyhedra_lconvexProved

  Oct 2026

• Theorem 6.28 -- the M-minimizer cutProved

  Oct 2026

• Theorem 6.26 -- the M-optimality criterionProved

  Oct 2026

Posted 20

• Every selected link of a projective cube-free counterexample has size at most one thirdProved

  Oct 2026

• A small critical quotient with an explicit small nonzero increment excludes a dense large linkProved

  Oct 2026

• A quotient-order 128 link with shift 6 excludes density above five eighthsProved

  Oct 2026

• A quotient-order 128 link with shift 2 excludes density above five eighthsProved

  Oct 2026

• A quotient-order 128 link with shift 14 excludes density above five eighthsProved

  Oct 2026

• A quotient-order 128 link with shift 13 excludes density above five eighthsProved

  Oct 2026

• A quotient-order 128 link with shift 12 excludes density above five eighthsProved

  Oct 2026

• A large selected link admits a normalized critical middle-interval containerProved

  Oct 2026

• Small critical quotients exclude a dense large link under explicit geometric packing dataProved

  Oct 2026

• A normalized large link with zero quotient increment excludes density above five eighthsProved

  Oct 2026

• Every large sum-free subset of a cyclic two-group has a critical middle-interval quotient containerProved

  Oct 2026

• Large normalized quotients with a small nonzero increment exclude density above five eighthsProved

  Oct 2026

• Actual dyadic set and link fibre masses satisfy the finite-certificate inequalitiesProved

  Oct 2026

• An actual normalized link container yields a fibre-mass packing boundProved

  Oct 2026

• Critical maximal sum-free subsets of a cyclic two-group are unit dilates of the middle intervalProved

  Oct 2026

• A projective cube-free set containing more than three quarters of the odd residues satisfies the five-eighths boundProved

  Oct 2026

• The selected-link cap implies the projective cube-free five-eighths boundProved

  Oct 2026

• A normalized critical large link forces its positive signed increment to be at most one third of the interval lengthProved

  Oct 2026

• Paired diagonal fibre masses of a projective cube-free set satisfy a four-fibre inequalityProved

  Oct 2026

• Long–Wagner proof infrastructure and exact finite certificate dataDefinition

  Oct 2026