Tootfinder

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Uniqueness of the asymptotic limits for Ricci-flat manifolds with linear volume growth
Zetian Yan, Xingyu Zhu
https://arxiv.org/abs/2510.00420 https://arxi…

Uniqueness of the asymptotic limits for Ricci-flat manifolds with linear volume growth
Under natural assumptions on curvature and cross section, we establish the uniqueness of asymptotic limits and the exponential convergence rate for complete noncollapsed Ricci-flat manifolds with linear volume growth, which are known to only admit cylindrical asymptotic limits. In dimension four, these assumptions hold automatically, yielding unconditional uniqueness and convergence. In particular, our results show that all asymptotically cylindrical Calabi--Yau manifolds converge exponentially…

Asymptotic Schwarzschild solutions in $f(R)$ gravity and their observable effects on the photon sphere of black holes
Miguel Aparicio Resco
https://arxiv.org/abs/2510.00702 http…

Asymptotic Schwarzschild solutions in $f(R)$ gravity and their observable effects on the photon sphere of black holes
We investigate asymptotic Schwarzschild exterior solutions in the context of modified gravity theories, specifically within the framework of $f(R)$ gravity, where the asymptotic behavior recovers the standard Schwarzschild solution of General Relativity. Unlike previous studies that rely mainly on analytical approximations, our approach combines asymptotic analysis with numerical integration of the underlying differential equations. Using these solutions, we analyze strong lensing effects to ob…

The Two Ronnies: "The Confusing Library" https://youtu.be/AYxmPHLU9oA 📘📕🙃

Representation asymptotics in the homology of pure graph braid groups
Louis Hainaut, Ben Knudsen, Nicholas Wawrykow
https://arxiv.org/abs/2510.00201 https://

Representation asymptotics in the homology of pure graph braid groups
We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explicit formulas for the asymptotic multiplicities in homology of many irreducible representations of the symmetric group, in the spirit of representation stability.

Assumption-lean Inference for Network-linked Data
Wei Li, Nilanjan Chakraborty, Robert Lunde
https://arxiv.org/abs/2510.00287 https://arxiv.org/pdf/2510.00…

Assumption-lean Inference for Network-linked Data
We consider statistical inference for network-linked regression problems, where covariates may include network summary statistics computed for each node. In settings involving network data, it is often natural to posit that latent variables govern connection probabilities in the graph. Since the presence of these latent features makes classical regression assumptions even less tenable, we propose an assumption-lean framework for linear regression with jointly exchangeable regression arrays. We …

Learning to Assemble the Soma Cube with Legal-Action Masked DQN and Safe ZYZ Regrasp on a Doosan M0609
Jaehong Oh, Seungjun Jung, Sawoong Kim
https://arxiv.org/abs/2508.21272 ht…

Learning to Assemble the Soma Cube with Legal-Action Masked DQN and Safe ZYZ Regrasp on a Doosan M0609
This paper presents the first comprehensive application of legal-action masked Deep Q-Networks with safe ZYZ regrasp strategies to an underactuated gripper-equipped 6-DOF collaborative robot for autonomous Soma cube assembly learning. Our approach represents the first systematic integration of constraint-aware reinforcement learning with singularity-safe motion planning on a Doosan M0609 collaborative robot. We address critical challenges in robotic manipulation: combinatorial action space expl…

This is the third full build iteration of my miniature #QRP unun supporting both EFHW and "random wire" antennas. At this point, it is still fiddly to build, but I'd expect an experienced #HamRadio DIY / homebrew enthusiast to find the build not terribly difficult.
There's nothing…

A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture
Yuya Murakami
https://arxiv.org/abs/2508.21710 https://

A framework for proving quantum modularity: Application to Witten's asymptotic expansion conjecture
We address two linked problems at the interface of quantum topology and number theory: deriving asymptotic expansions of the Witten--Reshetikhin--Turaev invariants for 3-manifolds and establishing quantum modularity of false theta functions. Previous progress covers Seifert homology 3-spheres for the former and rank-one cases for the latter, both of which rely on single-variable integral representations. We extend these results to negative definite plumbed 3-manifolds and to general false theta…

#photography #feet #red