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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

• Tao, Proposition 7.2 — major arc sums (positive scale, zeros with multiplicity)Open

  Sep 2026

• Theorem A, cumulative, unconditional: $\liminf_{T\to\infty} N_0^*(T)/N(T) \ge 2/3$Proved

  Aug 2026

• Theorem A, cumulative, unconditional: $\liminf_{T\to\infty} N_0^*(T)/N(T) \ge 2/3$Proved

  Aug 2026

• Cumulative Theorem A from three hypothesesProved

  Aug 2026

• Cumulative Theorem A from three hypothesesProved

  Aug 2026

• Theorem A from three hypotheses (explicit formula, Riemann–von Mangoldt, $\Gamma$-facts)Proved

  Aug 2026

• Theorem A from three hypotheses (explicit formula, Riemann–von Mangoldt, $\Gamma$-facts)Proved

  Aug 2026

• Theorem A with Weil's explicit formula as the only assumptionProved

  Aug 2026

• Theorem A with Weil's explicit formula as the only assumptionProved

  Aug 2026

• Cumulative Theorem A modulo the thm:traces hypothesisProved

  Aug 2026

• Cumulative Theorem A modulo the thm:traces hypothesisProved

  Aug 2026

• Theorem A (dyadic $2/3$ form) modulo the thm:traces hypothesisProved

  Aug 2026

• Theorem A (dyadic $2/3$ form) modulo the thm:traces hypothesisProved

  Aug 2026

• $\lambda \to 1^-$ wrapper for Theorem AProved

  Aug 2026

• $\lambda \to 1^-$ wrapper for Theorem AProved

  Aug 2026

• Theorem A at fixed $\lambda \in (0,1)$ modulo the thm:traces hypothesisProved

  Aug 2026

• Theorem A at fixed $\lambda \in (0,1)$ modulo the thm:traces hypothesisProved

  Aug 2026

• The four side conditions of the assembly hold eventuallyProved

  Aug 2026

• The four side conditions of the assembly hold eventuallyProved

  Aug 2026

• The block-decomposition package holds for all large $T$Proved

  Aug 2026

• The block-decomposition package holds for all large $T$Proved

  Aug 2026

• Dyadic-to-cumulative wrapper for zero-count lower boundsProved

  Aug 2026

• Dyadic-to-cumulative wrapper for zero-count lower boundsProved

  Aug 2026

• Block inputs hold for all sufficiently large $T$Proved

  Aug 2026

• Block inputs hold for all sufficiently large $T$Proved

  Aug 2026

• prop:block and [eq:Ncount] packaged as block inputs at height $T$Proved

  Aug 2026

• prop:block and [eq:Ncount] packaged as block inputs at height $T$Proved

  Aug 2026

• Finite Poisson bound: $\sum_{0 \le k < d} |\hat\varphi(\gamma_\rho - \tau_k)|^2 \le aL^2$ for on-line zerosProved

  Aug 2026

• Finite Poisson bound: $\sum_{0 \le k < d} |\hat\varphi(\gamma_\rho - \tau_k)|^2 \le aL^2$ for on-line zerosProved

  Aug 2026

• Sum over a subtype filter equals sum over Finset.filterProved

  Aug 2026

• Sum over a subtype filter equals sum over Finset.filterProved

  Aug 2026

• The off-line zeros of the window come in pairs: $\#\mathrm{offLine} = 2p$Proved

  Aug 2026

• The off-line zeros of the window come in pairs: $\#\mathrm{offLine} = 2p$Proved

  Aug 2026

• prop:block (ii): $\operatorname{tr} P \le N_{\mathrm{on}}(I')$Proved

  Aug 2026

• prop:block (ii): $\operatorname{tr} P \le N_{\mathrm{on}}(I')$Proved

  Aug 2026

• Trace of the on-line part: $\operatorname{tr}\bigl(\sum m_z u_z u_z^{\mathsf T}\bigr) = \sum m_z \|u_z\|^2$Proved

  Aug 2026

• Trace of the on-line part: $\operatorname{tr}\bigl(\sum m_z u_z u_z^{\mathsf T}\bigr) = \sum m_z \|u_z\|^2$Proved

  Aug 2026

• prop:block (ii): $n_+(Q) \le p$Proved

  Aug 2026

• prop:block (ii): $n_+(Q) \le p$Proved

  Aug 2026

• Positive index is invariant under positive scaling: $n_+(rA) = n_+(A)$Proved

  Aug 2026

• Positive index is invariant under positive scaling: $n_+(rA) = n_+(A)$Proved

  Aug 2026

• prop:block (i): $n_+(A) \le s_1 + s_2 + p$Proved

  Aug 2026

• prop:block (i): $n_+(A) \le s_1 + s_2 + p$Proved

  Aug 2026

• Splitting a sum over $\mathcal{Z}(I')$ into on-line points and off-line pairsProved

  Aug 2026

• Splitting a sum over $\mathcal{Z}(I')$ into on-line points and off-line pairsProved

  Aug 2026

• The H-EF bridge: zero-side and prime-side matrices agreeProved

  Aug 2026

• The H-EF bridge: zero-side and prime-side matrices agreeProved

  Aug 2026

• The Weil explicit formula for $\zeta$, literature form [eq:EFstd]Proved

  Aug 2026

• The Weil explicit formula for $\zeta$, literature form [eq:EFstd]Proved

  Aug 2026

• Prime side of the explicit formula on the line $\operatorname{Re} s = c > 1$Proved

  Aug 2026