We show that the monoid of all injective and extensive partial transformations of a chain with three elements admits no finite basis of its identities. This completes solving of the finite basis problem for the monoids in the basic frame of partial t...
We construct a four-dimensional diffeomorphism exhibiting a homoclinic tangency of the largest codimension, which admits a historic wandering domain of positive Lebesgue measure. Every orbit in this wandering domain exhibits historic behavior, in the...
Jan 16, 2011 · And you want a gun that will do it from sufficiently far away that Mister Grizz won't take exception to being killed and live long enough to close in and kill the shooter before he finally admits …
We show that a RFRS Poincaré-duality group $G$ admits a virtual epimorphism to the integers whose kernel is itself a Poincaré-duality group over every field if and only if the $L^2$-homology of $G$ vanishes and so do the positive-characteristic var...
We build the first example of a hyperbolic 6-manifold that admits a perfect circle-valued Morse function, which can be considered as the analogue of a fibration over the circle for manifolds with non-vanishing Euler characteristic. As a consequence,...
In \cite{Park:2014tia} we proposed a way of quantizing gravity with the Hamiltonian and Lagrangian analyses in the ADM setup. One of the key observations was that the physical configuration space of the 4D Einstein-Hilbert action admits a three-dimen...
We show that the stabilization of any countable ergodic p.m.p. equivalence relation which is not Schmidt, i.e. admits no central sequences in its full group, always gives rise to a stable equivalence relation with a unique stable decomposition, provi...
The Acceptance Probability Estimation Problem (APEP) is to additively approximate the acceptance probability of a Boolean circuit. This problem admits a probabilistic approximation scheme. A central question is whether we can design a pseudodetermini...
A real random variable admits median(s) and quantiles. These values minimize convex functions on $\mathbb R$. We show by "Convex Analysis" arguments that the function to be minimized is very natural. The relationship with some notions about functions...
From DeepSeek ------ Based on the transcript you provided, here is a detailed summary of the key points from Alexander Mercouris's video dated October 27, 2025. ### ? Military Situation on the ...
In this paper we provide a positive answer to a conjecture due to A. J. Di Scala, A. Loi, H. Hishi (see [3, Conjecture 1]) claiming that a simply-connected homogeneous Kähler manifold M endowed with an integral Kähler form $μω$, admits a holomorp...
We prove a universal embedding theorem for flag manifolds: every flag manifold admits a holomorphic isometric embedding into an irreducible classical flag manifold. This result generalizes the classical celebrated embedding theorems of Takeuchi [30]...
A natural geometric framework of noncommutative spacetime is symplectic geometry rather than Riemannian geometry. The Darboux theorem in symplectic geometry then admits a novel form of the equivalence principle such that the electromagnetism in non...
An irreducible 3--manifold with torus boundary either is a Seifert fibered space or admits at most three lens space fillings according to the Cyclic Surgery Theorem. We examine the sharpness of this theorem by classifying the non-hyperbolic manifolds...
Feb 24, 2026 · Meta Alignment Director admits OpenClaw AI agents ran wild, deleting emails and forcing her to flee to a Mac mini to defuse the "bomb".
It was recently proved that every claw-free cubic graph admits a (1, 1, 2, 2)-packing coloring--that is, its vertex set can be partitioned into two 1-packings and two 2-packings. This result was established by Brešar, Kuenzel, and Rall [Discrete Mat...
Jan 16, 2011 · And you want a gun that will do it from sufficiently far away that Mister Grizz won't take exception to being killed and live long enough to close in and kill the shooter before he finally admits …
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Under the assumption that a defining graph of a Coxeter group admits only subsequent elementary twists in $\mathbb{Z}_2$ or dihedral groups and is of type $\mathrm{FC}$, we prove Bernhard Mühlherr's Twist Conjecture...
Every compact Kähler manifold with negative first Chern class admits a unique metric $g$ such that $\text{Ric}(g) = -g$. Understanding how families of these metrics degenerate gives insight into their geometry and is important for understanding the...