The paper determines sharp winner’s-bias constants for independent non-identically distributed noise and pairwise nonnegatively correlated noise, with the stated theorems formally verified in Lean 4.
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An algorithm produces quadratic twists with rational points and fixed root number, yielding explicit multiquadratic rank-growth bounds conditional on the Parity Conjecture.
The weak Viterbo conjecture is established for convex bodies in four dimensions invariant under the natural quaternion-group action, including a characterization of equality cases.
For bordered Riemann surfaces with free boundary symmetry, the paper constructs equivariant proper minimal immersions into Euclidean space and complete bounded immersions into the unit ball.
A new refined MNOP conjecture for Quot schemes and Hilbert schemes of points is formulated and proved modulo n!
Saxl’s conjecture
Let be a staircase partition. Then … with multiplicity for all partitions of .
Seymour’s second-neighborhood conjecture
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Furstenberg–Kesten conjecture on bigeodesics in two-dimensional first-passage percolation
Let be i.i.d. edge weights on the nearest-neighbor edges of , with a continuous distribution. A bigeodesic is a doubly infinite path whose finite segments are…
Bi-Lipschitz embeddings: Hilbert spaces vs. finite-dimensional Euclidean spaces
Let be a metric space. Say it is doubling if there is a finite constant such that every ball , for and , can be covered by at most balls of ra…
Common-root conjecture for truncated binomials
For integers and , let and denote the truncated binomial polynomials used in the paper. Common-root conjecture. The polynomials …
Projection-body volume for four-dimensional polytopes with at most six facets
A finite free-entropy gap for two self-adjoint variables
Removing the moment assumption from a stipulated planar no-bigeodesics theorem
Spectral chart selection and average trace-class distortion
The sharp minimum multiplicity in a staircase tensor square