Latest Developments

A new arithmetic of linear orders proves that nA+mB≅kB+lA always implies A+B≅B+A.

The authors prove almost-everywhere classical simulation results for massively parallel quantum-query algorithms and constant-round extensions.

The preprint claims lim S_n/√n=√e, proving that Schäffer’s upper-bound constant is asymptotically optimal.

A preprint proves that the one-third powers of the defects of a finite-lower-order holomorphic curve are summable.

The authors prove the spherical volume bound under simultaneous Ricci and scalar-curvature lower bounds with a dimension-dependent Ricci constant.

A construction gives regular sublinear expanders with degree about one-half log-squared n that have no cycle covering a positive fraction of vertices.

An optimal-transport construction gives the maximum Spearman rho for every prescribed value of Spearman’s footrule.

Every free ergodic pmp action of a free group is orbit equivalent to a totally weak-mixing action.

A family of quantum states and Pauli observables makes the fractional chromatic number grow faster than any constant multiple of ε⁻².

The authors prove γ_b(G)≤2mp(G) for every graph, improving the previous general bound and yielding a polynomial-time 2-approximation.