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Non-reciprocal couplings can make added dissipation raise the barrier that protects an attractor against rare escape — a protective reversal impossible at equilibrium. We ask, and bound, how strong this effect can be per unit of entropy production. For a linear stochastic system x=Lx+ε ξ, ⟨ξξ⊤⟩=Q, with Hurwitz L=−A+N (A=A⊤≻0, N=−N⊤), the barrier’s sensitivity to a dissipation increment M≽0 is the linear form ⟨M,K⟩ of a response operator K built from the stationary Gramian, and a reversal occurs iff λmaxK>0. Under isotropic noise Q=I we conjecture the universal bound supNλmaxK+/Si≤1/128 a13, a1=λminA, and prove it — sharp constant included — in the following cases: the value 1/128a13 and the saturating 7:1 geometry in the small-coupling limit in every dimension (an explicit copositivity certificate; unconditional for d≤4, otherwise conditional on a rank-two reduction we verify numerically), and the full two-mode case for all couplings. An exact Schur complement lowers the governing matrix inequality by one dimension, and we show the isotropy hypothesis is load-bearing — for general Q the ratio is unbounded, so Q=I is not a normalisation. A free-coordinate reduction recasts the general statement as a matrix inequality on a compact box and reduces d=3 to a matrix sum-of-squares certificate (whose existence the Hol–Scherer theorem guarantees where the matrix is strictly positive). The residual — d≥3 at all couplings — remains open; it is numerically unbroken over >107 configurations up to d=12. Ensemble simulations reproduce every prediction from trajectory data on circuit, optical, mechanical, and quantum realisations.

Coding agents are rapidly becoming a major application of agentic LLMs, but serving them efficiently remains challenging. Progress on this challenge requires understanding real workload patterns, yet the data needed for such analysis is largely absent. Existing public traces and benchmarks do not capture real, day-to-day coding-agent usage across multiple agents and model families for serving-system analysis. To help fill this gap, we collect and release a trace of roughly 4,300 coding-agent sessions, containing about 350,000 LLM steps and 430,000 tool calls from our own day-to-day use of Claude Code and Codex. Our analysis shows that coding-agent workloads feature long autonomous loops, long contexts with short outputs, diverse and heavily-tailed tool calls, and high but imperfect prefix cache hit rates. These findings point to concrete opportunities for optimizing serving, including lower-overhead tool calling, append-length-aware prefill, semantic-aware tool-latency prediction, and improved KV-cache management around human-paced gaps. We release the dataset, trace collection pipeline, and analysis code at https://github.com/uw-syfi/TraceLab.git the project website is https://tracelab.cs.washington.edu.

For $r \geq 2$ and graphs $H_1, \ldots, H_r, G$, we say that $G$ is $(H_1, \ldots, H_r)$ vertex-Ramsey, or $(H_1, \ldots, H_r)_v$-Ramsey, if whenever we colour the vertices of $G$ with colours from the set $[r]=\{1,2, \ldots, r\}$ there exists $j \in [r]$ such that some copy of $H_j$ in $G$ is monochromatic in colour $j$. Given any fixed collection of graphs $H_1, \ldots, H_r$, Luczak, Ruciński and Voigt and Kreuter determined in the 1990s the threshold edge probability $p$ at which the binomial random graph $G(n,p)$ becomes $(H_1, \ldots, H_r)_v$-Ramsey. More recently, Das, Morris and Treglown investigated the vertex-Ramsey property in the randomly perturbed setting. When $r=2$ they determined the number of random edges one must add to a dense graph to ensure that with probability $1-o(1)$ the resulting graph is $(H_1, H_2)_v$-Ramsey whenever one of $H_1$ or $H_2$ is a clique. They posed the problem of extending their results to all pairs of graphs $(H_1, H_2)$. In this paper we resolve a more general form of their problem and determine for any $r\geq 2$ and $r$-tuple of graphs $(H_1, \ldots, H_r)$ the number of random edges one must add to a dense graph to ensure that with probability $1-o(1)$ the resulting graph is $(H_1, \ldots, H_r)_v$-Ramsey.

In this short note we establish the Schur--Zassenhaus Theorem and Sylow's Third Theorem for finite skew braces. More precisely, we prove that every Hall ideal of a finite skew brace admits a sub-skew brace complement, and more generally that every left ideal whose order is coprime to that of the Hall ideal can be embedded in such a complement. Using similar ideas we show that every left ideal of prime-power order is contained in a Sylow sub-skew brace. Finally, we prove that the number of Sylow $p$-sub-skew braces is congruent to $1$ modulo $p$, and provide examples showing that the corresponding containment property fails for arbitrary sub-skew braces.

We use the Banerjee--Mandal--Sahoo dipole-current Ward identity for the one-loop logarithmic soft-photon theorem as input and determine its finite-energy action on Mellin-difference hard currents. The commutator with such hard currents has a scheme-independent hard-hard residue that survives every one-particle redefinition. With the meromorphic continuation stated explicitly below, a two-particle Plancherel transform identifies this residue with an analytic two-particle primary module, and the coefficient map is a hard-current one-cocycle. The cocycle defines a minimal filtered abelian extension. It has a canonical two-particle primitive and integrates to an affine action. For scalar hard legs, the fixed-leg operator agrees coefficient by coefficient with the symmetry-governed long-range logarithmic tower of Choi, Kadhe, and Puhm. Applied to a tree-level scalar-QED photon-exchange block, the finite-energy analysis determines the logarithmic two-particle coefficient functional from the ordinary hard amplitude and the Banerjee--Mandal--Sahoo ordered-pair soft kernel. This gives a finite-energy relation between the Banerjee--Mandal--Sahoo dipole-current Ward identity and the exponentiated long-range celestial OPE.