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• Identity_is_UniqueProved

  Sep 2026

• Equality_of_Ordered_PairsProved

  Sep 2026

• Pythagorass_TheoremProved

  Sep 2026

• Composition_of_Relations_is_AssociativeProved

  Sep 2026

• Division_TheoremProved

  Sep 2026

• De_Moivres_FormulaProved

  Sep 2026

• Odd_Number_TheoremProved

  Sep 2026

• Square_Root_of_Prime_is_IrrationalProved

  Sep 2026

• Rational_Numbers_are_Countably_InfiniteProved

  Sep 2026

• Fundamental_Theorem_of_ArithmeticProved

  Sep 2026

• Cardinality_of_Set_of_SubsetsProved

  Sep 2026

• Euclids_TheoremProved

  Sep 2026

• Lagranges_Theorem_Group_TheoryProved

  Sep 2026

• Reflection symmetry of $\zeta$: $\zeta(\bar{s}) = \overline{\zeta(s)}$Proved

  Sep 2026

• First-order Euler–Maclaurin summation formula on an interval $[a,b]$Proved

  Sep 2026

• $-\zeta'/\zeta$ has a simple pole of residue $1$ at $s=1$: boundedness of the differenceProved

  Sep 2026

• Big-$O$ form of the simple pole of $-\zeta'/\zeta$ at $s=1$Proved

  Sep 2026

• Euler–Maclaurin formula for the truncated zeta representation $\zeta_0(N, s)$Proved

  Sep 2026

• $\zeta$ has a simple pole of residue $1$ at $s=1$: boundedness of $\zeta(s) - (s-1)^{-1}$Proved

  Sep 2026

• A point interior to a rectangle does not lie on the rectangle's borderProved

  Sep 2026

• mme_subrankCapacityPoly_ge_of_witnessesProved

  Sep 2026

• Reciprocal of a complex power: $1/x^s = x^{-s}$Proved

  Sep 2026

• mme_omega_ltProved

  Sep 2026

• mme_omega_strassen_ltProved

  Sep 2026

• Triangle inequality for a sum of six termsProved

  Sep 2026

• mme_CW_laser_per_N_witnessProved

  Sep 2026

• Local boundedness of $\frac{f'}{f} + \frac{1}{s-p}$ on a punctured neighborhood of a simple poleProved

  Sep 2026

• mme_CW_border_rank_le_charNonZeroProved

  Sep 2026

• Logarithmic derivative near a simple pole (open-set version): $\frac{f'}{f} + \frac{1}{s-p} = O(1)$Proved

  Sep 2026

• Differentiation under the integral sign for the Euler–Maclaurin tail integral of $\zeta_0$Proved

  Sep 2026

• Uniform boundedness of $\int_3^T \frac{(\log x)^n}{x^2}\, dx$ over all $T > 3$Proved

  Sep 2026

• Derivative after subtracting a simple pole: $\bigl(f - \tfrac{A}{z - p}\bigr)'(x) = f'(x) + \tfrac{A}{(x-p)^2}$Proved

  Sep 2026

• Logarithmic derivative near a simple pole: $\frac{f'}{f} + \frac{1}{s - p} = O(1)$ as $s \to p$Proved

  Sep 2026

• Derivative in the real direction along a horizontal line: $\dfrac{d}{d\sigma} f(\sigma + it) = f'(\sigma + it)$Proved

  Sep 2026

• Conjugation symmetry of $\zeta'$: $\zeta'(\overline{s}) = \overline{\zeta'(s)}$Proved

  Sep 2026

• mme_CW_block_kronPow_MM_correctedProved

  Sep 2026

• Derivative commutes with the coercion $\mathbb{R} \hookrightarrow \mathbb{C}$: $\dfrac{d}{dy}\,\bigl(f(y) : \mathbb{C}\bigr) = f'(y)$Proved

  Sep 2026

• Dropping the vanishing $i = 0$ term: $\sum_{i=0}^{N} i^{-1} = \sum_{i=1}^{N} i^{-1}$Proved

  Sep 2026

• The sum $\sum_{i=0}^{N} i^{-1}$ equals the harmonic number $H_N$Proved

  Sep 2026

• Integrability of the logarithm-weighted sawtooth integrand $(\lfloor x \rfloor + \tfrac12 - x)\, x^{-(s+1)}\, (-\log x)$ on $(N, \infty)$Proved

  Sep 2026

• Integrability of the Euler–Maclaurin sawtooth integrand $(\lfloor x \rfloor + \tfrac12 - x)\, x^{-(s+1)}$ on $(N, \infty)$Proved

  Sep 2026

• Quotient of real powers as a power of the reciprocal ratio: $x^s / y^s = (y/x)^{-s}$Proved

  Sep 2026

• Reflection symmetry of the Riemann zeta function: $\overline{\zeta(\overline{s})} = \zeta(s)$Proved

  Sep 2026

• Third $\psi$-integral of [eq:psiints]: $\int_{\mathbb{R}} \psi(r)^2 |r|\,dr \le 8 + 8\log\!\big(c_\varrho L/(4w)\big)$Proved

  Sep 2026

• Second $\psi$-integral of [eq:psiints]: $\int_{\mathbb{R}} \psi^2 \le 8L$Proved

  Sep 2026

• First $\psi$-integral of [eq:psiints]: $\int_0^\infty \psi \le 4 + 2\log\!\big(c_\varrho L/(4w)\big)$Proved

  Sep 2026

• Elementary mass bound for the taper: $\int_{\mathbb{R}} \varphi \le L$Proved

  Sep 2026

• Plateau lower bound for $b = L^{-1}\!\int\varphi^4$: $\;1 - 2w/L \le b$Proved

  Sep 2026

• Weighted second moment of $\hat\varphi$: $\int \hat\varphi(r)^2\, r^2\,dr \le 8 + 2(c_\varrho/w)^2$Proved

  Sep 2026

• Fourier inversion for $\hat\varphi^2$: $\int \hat\varphi(r)^2 \cos(ry)\,dr = 2\pi A_\varphi(y)$Proved

  Sep 2026

Posted 50

• Theorem 9.2 — reduced costs of the CGLP columns $u_i, v_i$ in terms of the LP simplex tableauOpen

  Oct 2026

• Theorem 8.5 — strengthened L&P cuts from basic $(CGLP)_k$ solutions are exactly the mixed integer Gomory cutsProved

  Oct 2026

• Theorem 7.2 — iterating split convexification over 0-1 variables, $P_{i_1,\dots,i_t}(K) = \mathrm{conv}(K \cap \{x_{i_1},\dots,x_{i_t} \in \{0,1\}\})$Proved

  Oct 2026

• Theorem 2.3 — when the lifting may be indexed by all of $Q$Open

  Oct 2026

• Theorem 11.11 — irregular L&P cuts are equivalent to no intersection cut and, if unique optimal, are strictly betterDisproved

  Oct 2026

• Theorem 7.7 — $K_t \subseteq P_{i_1,\dots,i_t}(K)$ for any $t$ distinct 0-1 indicesProved

  Oct 2026

• Theorem 8.7 — the rank of $P$ w.r.t. L&P, simple disjunctive, strengthened L&P and MIG cuts is at most $p$Open

  Oct 2026

• Lemma 8.2 — the basic index sets $M_1,M_2$ of a $(CGLP)_k$ basis are disjoint and index a nonsingular submatrixProved

  Oct 2026

• Corollary 7.3 — iterating over every 0-1 index reaches the integer hull, $P_{1,\dots,p}(K) = \mathrm{conv}(K_0)$Proved

  Oct 2026

• Proposition 13.22 — $\Pi$ as a projection, for polymatroid rank functions $r_1,r_2$Open

  Oct 2026

• Corollary 11.25 — a weak Lopsided cut needing no monoid optimization (with $b_i \le a_{i0}$)Proved

  Oct 2026

• Corollary 13.21 — lifted description of $\mathrm{conv}(P(r_1)\cup P(r_2))$ via $\mathrm{conv}\,Z(r_1,r_2)$Open

  Oct 2026

• Corollary 2.2 — extreme points of the lifted polyhedron (corrected)Open

  Oct 2026

• Proposition 12.1 — validity for a V-polyhedral disjunctive set via vertices and rays (nonempty disjuncts)Proved

  Oct 2026

• Theorem 12.5 — V-polyhedral cuts, CGLP (12.9) cuts and generalized intersection cuts coincide (nonempty disjuncts)Proved

  Oct 2026

• Theorem 7.5 — iterating the Lovász–Schrijver operator $p$ times reaches the integer hull, $N^p(K) = \mathrm{conv}(K_0)$Proved

  Oct 2026

• Proposition 13.23 — extreme points of $\Pi$ come from extreme points of $U$ (polymatroid rank functions)Open

  Oct 2026

• Theorem 11.26 — two strengthened GMI-type cuts $\alpha^+x\ge1$, $\alpha^-x\ge1$ for a 0-1 basic variableProved

  Oct 2026

• Theorem 13.7 — the facets of the dominant of an arbitrary polytope $P\subseteq[0,1]^n$Proved

  Oct 2026

• Proposition 11.22 — validity of the monoidally-strengthened disjunction (with $b_i \le a_{i0}$)Proved

  Oct 2026

• Corollary 10.4 — for $y=x^*-\bar x$, $(CGLP)_y$ has an optimal cut through a boundary point of $P_D$ on $(\bar x,x^*]$Open

  Oct 2026

• Theorem 11.9 — a basic CGLP solution supported on one nonsingular cobasis yields an intersection cutProved

  Oct 2026

• Theorem 11.2 — every facet of conv $P_I$ cutting off a vertex of $P$ is a standard intersection cutOpen

  Oct 2026

• Theorem 5.3 — the $s$-$t$ Path Decomposable Subgraph Polytope of an acyclic digraphOpen

  Oct 2026

• Theorem 7.4 — $N(K) \subseteq \mathrm{conv}(K \cap \{x_j \in \{0,1\}\})$ for every 0-1 index $j$Proved

  Oct 2026

• Corollary 13.8 — facets of the dominant of a polytope have at most $\dim(P)+1$ nonzero coefficientsOpen

  Oct 2026

• Theorem 6.1 — fractionality of intermediate points in sequential convexificationProved

  Oct 2026

• Corollary 11.3 — every vertex of corner$(J)$ not a vertex of conv $P_I$ is cut off by a standard intersection cutOpen

  Oct 2026

• Theorem 6.2 — lifting an optimal solution of the restricted CGLP to an optimal solution of the full CGLPProved

  Oct 2026

• Theorem 6.4 — strengthening a lift-and-project cut into a cut valid for the whole mixed 0-1 programProved

  Oct 2026

• Theorem 7.6 — the Sherali–Adams hierarchy reaches the integer hull, $K_p = \mathrm{conv}(K_0)$Proved

  Oct 2026

• Theorem 2.18 — facets of $\mathrm{cl\,conv}(F)$ are the extreme rays of $W_0$Proved

  Oct 2026

• Theorem 4.8 — when convexifying before or after an intersection agree (pointed case)Open

  Oct 2026

• Theorem 3.3 — the constraint boundary conditionOpen

  Oct 2026

• Theorem 7.1 — the nonlinear 3-step lift-and-project equals split convexification, $P_j(K) = \mathrm{conv}(K \cap \{x_j \in \{0,1\}\})$Proved

  Oct 2026

• Theorem 1.1 — the intersection cutOpen

  Oct 2026

• Theorem 4.10 — a parsimonious mixed 0-1 representation of any regular form obtained by basic stepsOpen

  Oct 2026

• Rank of a polyhedron w.r.t. four cut families (re-issued on the corrected Ch. 8 definitions)Definition

  Oct 2026

• Tableau of Ch. 8 and the mixed integer Gomory coefficients $\bar\pi_j$ (corrected)Definition

  Oct 2026

• Reduced costs $r_{u_i}, r_{v_i}$ of the CGLP columns in tableau form (corrected eq. (9.6))Definition

  Oct 2026

• LP in standard form, basic solutions with tableau, and standard intersection cuts with $1/\lambda^*_j$ coefficientsDefinition

  Oct 2026

• CGLP (11.6) apparatus with basic solutions; equivalence to an intersection cut over genuine LP bases (corrected)Definition

  Oct 2026

• $(CGLP)_k$ apparatus of Ch. 8, with bases and Theorem 6.4's strengthening (corrected)Definition

  Oct 2026

• Vocabulary of Chapter 5 (PMS, assignable and path-decomposable subgraph polytopes), with the corrected operator Γ*Definition

  Oct 2026

• Mixed 0-1 LP relaxation with the bound rows folded in (Chapter 6)Definition

  Oct 2026

• Mixed 0-1 LP relaxation with the bound rows folded in (Chapter 7)Definition

  Oct 2026

• Sequential convexification basics (v2: reversed disjunction as a conjunction)Definition

  Oct 2026

• Inequality defines a facet (validity + facet)Definition

  Oct 2026

• Theorem 10 — convex loss and $p = 1$: $R_{\varepsilon,1}(\hat P_N,\ell) = R(\hat P_N,\ell) + \varepsilon\,\mathrm{Lip}(\ell)$ on Borel $\mathbb{R}^m$ (mission IV goal)Proved

  Oct 2026

• Theorem 7 — strong duality $R_{\varepsilon,p}(\hat P_N,\ell) = \inf_{\gamma\ge0} \mathbb{E}_{\hat P_N}[\ell_\gamma] + \gamma\varepsilon^p$ on Borel $\mathbb{R}^m$, usc losses, $\varepsilon > 0$Proved

  Oct 2026