principia math

The sharp universal Gaussian EOT coupling bound Statement Let A,B be positive-definite covariance matrices on R^d. Let piepsilon be their Gaussian entropic optimal-transport coupli…

Lemma. Let $\overline d$ be an upper density on $G$. Suppose $q$ is a finitely additive probability measure on all subsets of $G$ such that

MathDB 363496: a four-element counterexample Result Conjecture 3.13 of arXiv:2406.07166v2 is false. The counterexample uses three very simple pseudoultrametric-preserving maps. For…

Lemma. If a Borel set $E\subset\mathbb R^N$ has nonempty interior, then $\dim_F(E)=N$.

MathDB 365102: the logarithmic-growth barycenter conjecture is false Result The literal Conjecture 1 of arXiv:2410.02715v2 is false. A smooth counterexample is … This potential sat…

Signed edge coloring of two cliques joined by one edge Theorem Let $G_n$ be the graph obtained from two vertex-disjoint copies of $K_n$ by adding one edge between them. For every s…

A weighted-gauge counterexample to the residue-class decomposition Statement Let $m$ be normalized Lebesgue measure on the unit circle $\mathbb T$. For a continuous, normalized,…

MathDB 351036 -- correction, proof, and divisor formula Corrected statement For positive integers n,a,d, define the geometric sum … The source context requires k to divide phi(n),…

MathDB 347688: a five-dimensional representation of $X_{2,9}$ Result The answer is yes: … The representation is defined by integral affine inequalities and has integral witnesses f…

Exact deficit and the asymptotic size of the cone Statement For $k\ge 2$, put … Section 4 of Bovdi and Leung's construction gives a maximal commutative algebraic system … The autho…