AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
Assuming the nonexistence of uncountable measurable cardinals, we construct an $\mathbb F_2$-algebra and a covering class of right modules which is not closed under colimits of countable chains. This gives a counterexample to Enochs'conjecture under $V=L$.
We construct a simple expansion of the theory of nonabelian free groups in which the group admits a global type with bounded left-translation orbit but is not definably amenable. This extends the construction of Chernikov, Hrushovski, Kruckman, Krupi\'nski, Moconja, Pillay, and Ramsey, and gives a counterexample to Pet...
Horn conjectured that whenever $K$ is a nonempty compact convex subset of a Banach space and $F,G:K\to K$ are continuous commuting maps, there exists $x\in K$ such that $F(x)=G(x)$. We give a counterexample in a separable Hilbert space. The construction uses an exactly commuting ladder of coincidence-free maps between...
For every $\rho$ in (0, 1/2), we construct an entire function F of order $\rho$ whose logarithmic derivative has zero as a deficient value. This disproves an old conjecture of W. H. J. Fuchs.
We give a counterexample to completeness descent from ideal cotorsion pairs to their objects. A radical-square-zero algebra on the two-cycle gives a finite-dimensional example. The construction is intrinsically non-weakly-idempotent-complete.
We construct a quasi-Banach function lattice $X$ on $\mathbb R$ whose quasi-norm is order continuous and invariant under every translation. Nevertheless, $X$ contains a bounded sequence with common compact support which is equicontinuous in $X$ and has no norm-convergent subsequence. This provides a counterexample to C...
By using an advanced model of AI, it is proved that there exists a commutative ring having a purely-prime ideal which is not purely-maximal. This gives a counterexample to \cite[Conjecture 5.8]{Tarizadeh}.
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