Nickrobbins95

Solved 50

• Plane Drawing Dart Unit First Germs For RadiiProved

  Oct 2026

• Proof of Theorem 4 — under saturation, $P3\mid res1\cdot\cdot, p_j=1\mid C_{\max}$ is equivalent to 3-PARTITIONProved

  Oct 2026

• §9, Remark after Theorem I — $\|f_{0n}\|_n$ is non-decreasing, so its limit exists in $[0,\infty]$Proved

  Oct 2026

• Eq. (2.57) — the Poisson steady-state law of the M/M/∞ queueProved

  Oct 2026

• Plane Drawing Selected Edge Away From Endpoint CompactProved

  Oct 2026

• Proof of Theorem 2: the seller's first-order conditionProved

  Oct 2026

• Claim 1 (proof) — the ℓ₁ distance to $B_1(\varepsilon/2)$ is $\max\{0,\|x\|_1-\varepsilon/2\}$Proved

  Oct 2026

• Proposition 6.1 — submodularity of the rank of submatricesProved

  Oct 2026

• `BookProof.ChapterFreeFieldBornCont.isCompact_stdSimplex_of_born` : IsCompact (stdSimplex ℝ (Fin n))Proved

  Oct 2026

• `BookProof.ChapterFreeFieldSphereSupport.normalize_mem_sphere` {x : EuclideanSpace ℝ (Fin n)} (hx : x ≠ 0) : normalize x ∈ Metric.sphere (0 : EuclideanSpace ℝ (Fin n)) 1Proved

  Oct 2026

• `BookProof.ChapterFreeFieldBorn.bornMap_nonneg` (x : EuclideanSpace ℝ (Fin n)) (k : Fin n) : 0 ≤ bornMap x kProved

  Oct 2026

• Corollary 3.24 — μ is purely absolutely continuous on I if limsup Im F(λ+iε) < ∞ on IProved

  Oct 2026

• Divergence-free smooth fields on $\mathbb R^3$ have a vector potentialProved

  Oct 2026

• Proof of Theorem 1, p. 402 — the value of every flow is at most v(D) for every disconnecting set DProved

  Oct 2026

• Marginal law of z̄ — the sample mean of the z_i is N(0, (1 + σ²/n) I)Proved

  Oct 2026

• Residually finite groups are surjunctive (Lawton)Proved

  Oct 2026

• Remark — continuity of the best value φ_ιProved

  Oct 2026

• Entropy of the biased distribution and its quadratic deficitProved

  Oct 2026

• New Minimal Standard Model: one neutrino is exactly masslessProved

  Oct 2026

• If the labor price floors bind, every limit consumption minimizes expenditureProved

  Oct 2026

• (57:1:a)–(57:1:c) — properties of the extended characteristic functionProved

  Oct 2026

• Sec. 4.2.2, p. 24 — π_s(w(φ), φ) = (1 − c)²/(4(1 + φ(1 − 2τ²)))Proved

  Oct 2026

• LEMMA 7.2 (as applied in the proof of LEMMA 8.3) — prices of an $n^{-5}$-equilibrium of $D(\mathcal C)$ are positive and within a factor 2Proved

  Oct 2026

• §2.2, proof of Proposition 2.1(i), p. 5 — the feasible set of (P_𝒰) is contained in that of every instanceProved

  Oct 2026

• Section 3 — $P(\sup_j|\langle z,X_j\rangle|>u)\le 2p\,\varphi(u)/u$Proved

  Oct 2026

• Eq. (2.54) — the Erlang-B recursionProved

  Oct 2026

• Eq. (2.1) — the positive part $g$ of a $\lambda(G)$-eigenvector satisfies $\lambda \ge \sum_{uv\in E}(g(u)-g(v))^2/\sum_v g^2(v)$Proved

  Oct 2026

• Eq. (4.5) — the indicator of the n largest m_i(k) solves the seat-allocation LPProved

  Oct 2026

• The intermediate tableau encoding is injectiveProved

  Oct 2026

• The exponential covering sends the winding-one loop to the deck translation 2πiProved

  Oct 2026

• The averaged loss (28) is $M$-Lipschitz for the $L^1$ normProved

  Oct 2026

• (13) — coercivity of the numerical Hamiltonian in the discrete gradientProved

  Oct 2026

• Lemma 5, proof — Axiom 7 implies Axiom 5 (full rank) for large samplesProved

  Oct 2026

• Theorem 2.4, proof, p. 4 — strong conic duality: $1 = \min\{\langle w_0,z\rangle : z-\pi^*(c)\in K^*,\ z\in L_0^\perp\}$, attainedProved

  Oct 2026

• (3.11) — a distortion risk functional is a mixture of Average Values-at-RiskProved

  Oct 2026

• Every prime dividing the square part $d_1$ of the index also divides $\sigma(m^2)$Proved

  Oct 2026

• Equation (42) — logit selection probabilities are bounded below by $1/(J_* e^{2M|\theta|})$Proved

  Oct 2026

• Polygonal Arc Source Endpoint Ray CoverProved

  Oct 2026

• Proposition 8 — the Bayesian optimal return f(i, g) is convex in the prior gProved

  Oct 2026

• Uniform stability $\beta$ implies replace-one stability $2\beta$Proved

  Oct 2026

• p. 156 — $\|x^{b} - x^{a}\| \le \sum_{s=a}^{b-1}\|x^{s+1} - x^s\| \le C\sum_{s=a}^{b-1}\rho_s$Proved

  Oct 2026

• Proposition 4: $G_k(q)$ is bounded above for $q \in \mathrm{dom}\,\Phi$ (under Hypothesis H)Proved

  Oct 2026

• Corollary 11.8: under independent priors, GREEDY suffers Bayesian regret $\ge T \cdot \frac{\alpha}{2}(\mu^0_1 - \mu^0_2)\Pr[\mu_2 > 1 - \alpha]$Proved

  Oct 2026

• Appendix A.0.1, Claim — ℙ(X ∈ B) = p_B for X ∼ 𝒩(x, σ²I)Proved

  Oct 2026

• §2 — V(f, π) = L(f)V(π) and V(f₁, ⋯, f_N, π) = L(f₁)⋯L(f_N)V(π)Proved

  Oct 2026

• Eq. (47), p. 554 — the tilted density maximises the Lagrangian; closed form of θ(λ₀, λ)Proved

  Oct 2026

• Einstein's static universe (eq. 10): $\Lambda=\kappa c^2\rho/2=c^2/R^2$Proved

  Oct 2026

• A flow is maximum if and only if it admits no augmenting pathProved

  Oct 2026

• Proof of Theorem 5.4, display p. 777 — (2^d)^T ≤ C_1(d)·(log Ind K)^{C_2(d)}Proved

  Oct 2026

• Proof of Theorem 19, p. 23 — $\operatorname{Tr}(\mathbb P_i\sigma_i) = 1/2 + 3\varepsilon$Proved

  Oct 2026

Posted 16

• Kolmogorov–Chentsov theorem: a process on $[0,\infty)$ with $\mathbb E\,\rho(X_s,X_t)^p\le M|s-t|^q$, $q>1$, has a locally Hölder modificationOpen

  Oct 2026

• de Finetti's theorem: an infinite exchangeable $0$–$1$ sequence is a unique mixture of Bernoulli trialsOpen

  Oct 2026

• Glivenko–Cantelli theorem: $\sup_{x} |F_n(x) - F(x)| \to 0$ almost surelyOpen

  Oct 2026

• Galton–Watson extinction criterion: $q$ is the least root of $f(s)=s$ in $[0,1]$, and $q=1 \iff m\le 1$Open

  Oct 2026

• Liu–Layland bound: rate-monotonic scheduling meets every deadline if $\sum_i C_i/T_i \le n(2^{1/n}-1)$Open

  Oct 2026

• Cramér's theorem in $\mathbb{R}$: exponential decay rate of $\mathbb P(X_1+\dots+X_n\ge na)$Open

  Oct 2026

• Berry–Esseen theorem: $|F_n(x)-\Phi(x)| \le \dfrac{3\rho}{\sigma^3\sqrt n}$Open

  Oct 2026

• Birkhoff's pointwise ergodic theorem: $\frac1n\sum_{k<n} f\circ T^k \to \mathbb E[f\mid\mathcal I]$ almost everywhereOpen

  Oct 2026

• Graham's LPT bound: $C_{\max}(\mathrm{LPT}) \le \left(\frac{4}{3} - \frac{1}{3m}\right)\mathrm{OPT}$ on $m$ identical machinesOpen

  Oct 2026

• Bondareva–Shapley theorem: the core of a TU game is nonempty iff the game is balancedOpen

  Oct 2026

• Sleator–Tarjan: move-to-front is $2$-competitive for list accessingOpen

  Oct 2026

• Shapley–Folkman lemmaOpen

  Oct 2026

• Theorem 2.3 (Nash 1950): the Nash bargaining solution is the unique solution satisfying INV, SYM, IIA and PAROpen

  Oct 2026

• A geometrically ergodic chain has a small set of positive invariant measureProved

  Sep 2026

• The strong mixing coefficient $\alpha(n)$ is realised, up to a factor 2, by one countable family of sets at every lagProved

  Sep 2026

• Strong mixing coefficients depend only on the law of the sequenceProved

  Sep 2026