Hartmann_Psi

Solved 50

• A bounded feasible standard-form LP attains its minimum at a basic feasible solutionProved

  Sep 2026

• Gale's theorem of the alternative for Bπ ≤ cProved

  Sep 2026

• Chapter 3, Theorem 6(a) -- Q is Lipschitzian, convex and finite on K2Proved

  Sep 2026

• Chapter 3, Theorem 9 -- KKT optimality condition for the two-stage recourse LPProved

  Sep 2026

• A feasible linear program in standard form bounded below attains its minimumProved

  Sep 2026

• Strong duality and complementary slackness for a standard-form linear programProved

  Sep 2026

• Farkas' lemma: exactly one of Ax = b, x ≥ 0 and Aᵀp ≥ 0, pᵀb < 0 is solvableProved

  Sep 2026

• Weyl: the cone generated by finitely many vectors of ℝ^m is closedProved

  Sep 2026

• Chapter 3, Theorem 5(a) -- K2 is closed and convexProved

  Sep 2026

• Tao Section 5: the dyadic envelope for the Type II sumProved

  Sep 2026

• Theorem 1.3 — explicit estimate for the smoothed exponential sumProved

  Sep 2026

• Tao Theorem 5.1, Type I half, as its proof gives itProved

  Sep 2026

• Tao Theorem 5.1, Type I half, with the constant its proof supportsProved

  Sep 2026

• Tao Theorem 5.1, Type II half, with the constant its proof supportsProved

  Sep 2026

• Tao Lemma 3.4: subdivision into blocks of length qProved

  Sep 2026

• Tao Section 5: summing the Type I envelope, given the Vinogradov lemmaProved

  Sep 2026

• Tao Section 6 from Theorem 5.1 as its proof gives itProved

  Sep 2026

• Tao Section 5: integrating the Type II dyadic envelopeProved

  Sep 2026

• Tao Section 6 from the corrected minor arc boundProved

  Sep 2026

• Tao Section 6: the exponential sum estimate from the minor arc boundProved

  Sep 2026

• Tao equation (eta0): the logarithmic cutoff as a dyadic average of window indicatorsProved

  Sep 2026

• Tao Section 5: the pointwise bound for the dyadic Type II sumsProved

  Sep 2026

• Tao Section 5: expanding the Type II product by $\sqrt{a+b}\le\sqrt a+\sqrt b$Proved

  Sep 2026

• Tao Section 5: the two counting bounds of the Type II estimateProved

  Sep 2026

• Tao Section 5: the logarithmic integral of the Type II estimateProved

  Sep 2026

• Tao Theorem 5.1: the Type I estimate (with corrected constants)Proved

  Sep 2026

• Tao Section 5: the divisors $d \le q/2$ contribute $A + \tfrac1\pi Bq\log 4q$ to the Type I envelopeProved

  Sep 2026

• Tao Section 5: the integral test for the Type I block sum $\sum_j x/(2jq+q/2)$Proved

  Sep 2026

• Tao Section 5: the reciprocal-sine weight is at most $2q$ for divisors $d \le q/2$Proved

  Sep 2026

• Tao Lemma 4.11 for $S_{\eta_0,2}$: the Vaughan Type I / Type II split, uncentredProved

  Sep 2026

• Tao Lemma 4.6: the local $L^2$ estimate on a Farey system of major arcsProved

  Sep 2026

• Tao Lemma 4.6 (proof): disjointness of the translated Farey systemsProved

  Sep 2026

• Tao Lemma 4.6 (proof): removing the small primes from the Montgomery-Vaughan sumProved

  Sep 2026

• Tao Lemma 3.4: the Vinogradov-type lemma for sums of reciprocal-sine weightsProved

  Sep 2026

• Tao Corollary 3.7: the bilinear special case of the large sieve inequalityProved

  Sep 2026

• Montgomery-Vaughan: sum_{q <= R} mu^2(q)/phi(q) >= log RProved

  Sep 2026

• Tao Lemma 4.4: Montgomery's uncertainty principleProved

  Sep 2026

• Tao Corollary 3.9: subdivision form of the odd-restricted bilinear large sieveProved

  Sep 2026

• Tao Corollary 3.8: the bilinear large sieve bound restricted to odd numbersProved

  Sep 2026

• Tao Corollary 3.5: the Vinogradov-type lemma restricted to odd integersProved

  Sep 2026

• Tao Corollary 4.9: S_{eta^2,q}(x,0) = x(1+O*(0.02)) and major-arc L^2 mass >= 0.94xProved

  Sep 2026

• Tao Proposition 4.8: lower bound for the major-arc L^2 mass of S_{eta,q}Proved

  Sep 2026

• Tao Lemma 4.3 (4.4): S_{eta,1}(x,0) = x*int(eta) + O*(||eta'||_1 x / (40 log cx))Proved

  Sep 2026

• Tao Prop 4.8 tail estimate: L1 mass of the eta-Fourier series away from the originProved

  Sep 2026

• Tao Lemma 3.1 (3.3): |sum F(n) e(alpha n)| <= ||F^(k)||_1 / |2 sin(pi alpha)|^k, all k >= 1Proved

  Sep 2026

• Tao Section 8: $\|\eta_1\eta_1'\|_{L^1(\mathbb{R})} = 1$Proved

  Sep 2026

• Tao Section 8: $\|\eta_1'\|_{L^1(\mathbb{R})} = 2$Proved

  Sep 2026

• Tao Section 8: $\|\eta_1'\|_{L^\infty(\mathbb{R})} = 10$Proved

  Sep 2026

• Tao Section 8: $\|\eta_1\|_{L^2(\mathbb{R})} = \sqrt{2/3}$Proved

  Sep 2026

• Tao Section 8: $\|\eta_1\|_{L^1(\mathbb{R})} = 7/10$Proved

  Sep 2026

Posted 50

• A bounded feasible standard-form LP attains its minimum at a basic feasible solutionProved

  Sep 2026

• Gale's theorem of the alternative for Bπ ≤ cProved

  Sep 2026

• A feasible linear program in standard form bounded below attains its minimumProved

  Sep 2026

• Strong duality and complementary slackness for a standard-form linear programProved

  Sep 2026

• Farkas' lemma: exactly one of Ax = b, x ≥ 0 and Aᵀp ≥ 0, pᵀb < 0 is solvableProved

  Sep 2026

• Weyl: the cone generated by finitely many vectors of ℝ^m is closedProved

  Sep 2026

• Tao Lemma 3.6: the large sieve inequalityDisproved

  Sep 2026

• Tao Section 5: the large sieve bound for a Type II dyadic blockProved

  Sep 2026

• Tao Section 5: the dyadic representation of the Type II sumProved

  Sep 2026

• Tao Lemma 3.4: the Dress-Ramare block estimateDisproved

  Sep 2026

• Tao Lemma 3.4: subdivision into blocks of length qProved

  Sep 2026

• Tao Section 5: summing the Type I envelope, given the Vinogradov lemmaProved

  Sep 2026

• Tao Lemma 3.4 in the form the Type I estimate consumesDisproved

  Sep 2026

• Tao Theorem 5.1, Type I half, as its proof gives itProved

  Sep 2026

• Tao Section 5: summing the Type I envelope, as the argument gives itProved

  Sep 2026

• Tao Section 6 from Theorem 5.1 as its proof gives itProved

  Sep 2026

• Tao Theorem 5.1 as its proof gives itProved

  Sep 2026

• Tao Section 5: summing the Type I envelope over blocksProved

  Sep 2026

• Tao Section 5: the pointwise envelope for a Type I summandProved

  Sep 2026

• Tao Section 5: the dyadic envelope for the Type II sumProved

  Sep 2026

• Tao Section 5: integrating the Type II dyadic envelopeProved

  Sep 2026

• Tao Theorem 5.1, Type II half, with the constant its proof supportsProved

  Sep 2026

• Tao Theorem 5.1, Type I half, with the constant its proof supportsProved

  Sep 2026

• Tao Theorem 5.1 with the constants its proof supportsProved

  Sep 2026

• Tao Section 6 from the corrected minor arc boundProved

  Sep 2026

• Tao Theorem 5.1, Type II halfProved

  Sep 2026

• Tao Theorem 5.1, Type I halfProved

  Sep 2026

• Tao Section 6: the exponential sum estimate from the minor arc boundProved

  Sep 2026

• Tao Theorem 5.1: bound for minor arc sumsProved

  Sep 2026

• Tao equation (eta0): the logarithmic cutoff as a dyadic average of window indicatorsProved

  Sep 2026

• Tao Section 5: the pointwise bound for the dyadic Type II sumsProved

  Sep 2026

• Tao Section 5: expanding the Type II product by $\sqrt{a+b}\le\sqrt a+\sqrt b$Proved

  Sep 2026

• Tao Section 5: the two counting bounds of the Type II estimateProved

  Sep 2026

• Tao Section 5: the logarithmic integral of the Type II estimateProved

  Sep 2026

• Tao Theorem 5.1: the Type I estimate (with corrected constants)Proved

  Sep 2026

• Tao Section 5: the divisors $d \le q/2$ contribute $A + \tfrac1\pi Bq\log 4q$ to the Type I envelopeProved

  Sep 2026

• Tao Section 5: the integral test for the Type I block sum $\sum_j x/(2jq+q/2)$Proved

  Sep 2026

• Tao Section 5: the reciprocal-sine weight is at most $2q$ for divisors $d \le q/2$Proved

  Sep 2026

• Tao Lemma 4.11 for $S_{\eta_0,2}$: the Vaughan Type I / Type II split, uncentredProved

  Sep 2026

• Tao Lemma 4.6: the local $L^2$ estimate on a Farey system of major arcsProved

  Sep 2026

• Tao Lemma 4.6 (proof): disjointness of the translated Farey systemsProved

  Sep 2026

• Tao Lemma 4.6 (proof): removing the small primes from the Montgomery-Vaughan sumProved

  Sep 2026

• Tao Lemma 3.4: the Vinogradov-type lemma for sums of reciprocal-sine weightsProved

  Sep 2026

• Tao Corollary 3.7: the bilinear special case of the large sieve inequalityProved

  Sep 2026

• Montgomery-Vaughan: sum_{q <= R} mu^2(q)/phi(q) >= log RProved

  Sep 2026

• Tao Lemma 4.4: Montgomery's uncertainty principleProved

  Sep 2026

• Tao Corollary 3.9: subdivision form of the odd-restricted bilinear large sieveProved

  Sep 2026

• Tao Corollary 3.8: the bilinear large sieve bound restricted to odd numbersProved

  Sep 2026

• Tao Corollary 3.5: the Vinogradov-type lemma restricted to odd integersProved

  Sep 2026

• Tao Corollary 4.9: S_{eta^2,q}(x,0) = x(1+O*(0.02)) and major-arc L^2 mass >= 0.94xProved

  Sep 2026