Tootfinder

With great relief we observed that Lisa has condescended to use her fancy new water fountain. She actually seems quite keen on it after ignoring it for the first few hours after installation. #CatsOfMastodon

Structural results on idealistic equivalence relations
Filippo Calderoni, Luca Motto Ros
https://arxiv.org/abs/2506.08217 https://arx…

Structural results on idealistic equivalence relations
We address some fundamental problems concerning the structure of idealistic equivalence relations. In particular, we show that, under analytic determinacy, there are continuum many idealistic analytic equivalence relations that are not classwise Borel isomorphic to an orbit equivalence relation. Moreover, we also discuss alternative formulations of the E1 conjecture, and present an elementary counterexample to one of its earliest variants proposed by Hjorth and Kechris in 1997.

Isomorphism of \'etale fundamental groups lifts to isomorphism of stratified fundamental group
Indranil Biswas, Manish Kumar, A. J. Parameswaran
https://arxiv.org/abs/2506.03829

Isomorphism of étale fundamental groups lifts to isomorphism of stratified fundamental group
It is shown that if a finite generically smooth morphism $f\,:\,Y\,\longrightarrow\, X$ of smooth projective varieties induces an isomorphism of the étale fundamental groups, then the induced map of the stratified fundamental groups $π_1^{str}(f)\, :\, π_1^{str}(Y,\, y)\,\longrightarrow\, π_1^{str}(X,\, f(y))$ is also an isomorphism.

This https://arxiv.org/abs/2502.20338 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

KeBaB: $k$-mer based breaking for finding long MEMs
Long maximal exact matches (MEMs) are used in many genomics applications such as read classification and sequence alignment. Li's ropebwt3 finds long MEMs quickly because it can often ignore much of its input. In this paper we show that a fast and space efficient $k$-mer filtration step using a Bloom filter speeds up MEM-finders such as ropebwt3 even further by letting them ignore even more. We also show experimentally that our approach can accelerate metagenomic classification without signific…

Refining Yoneda Lemma under Finiteness Constrains and Applications
Antonio Ceres, Cristina Costoya, Antonio Viruel
https://arxiv.org/abs/2506.01501 https:/…

Refining Yoneda Lemma under Finiteness Constrains and Applications
Classical Yoneda Lemma asserts that the isomorphism type of an object $a$ in a category $C$ is determined by the natural type of the set-valued functor $Hom_C(a,-)$. Here we show that if finiteness hypothesis are assumed to hold in $C$, then the isomorphism type of an object $a$ in $C$ is determined by the integer-valued function $|Hom_C(a,-)|$ on objects in $C$. We present applications of this result to the isomorphism problem in Group, Graph, and Ring Theory.

This https://arxiv.org/abs/2505.21177 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry
Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs …

LensCraft: Your Professional Virtual Cinematographer
Zahra Dehghanian, Morteza Abolghasemi, Hossein Azizinaghsh, Amir Vahedi, Hamid Beigy, Hamid R. Rabiee
https://arxiv.org/abs/2506.00988

LensCraft: Your Professional Virtual Cinematographer
Digital creators, from indie filmmakers to animation studios, face a persistent bottleneck: translating their creative vision into precise camera movements. Despite significant progress in computer vision and artificial intelligence, current automated filming systems struggle with a fundamental trade-off between mechanical execution and creative intent. Crucially, almost all previous works simplify the subject to a single point-ignoring its orientation and true volume-severely limiting spatial …

Unfolding Boxes with Local Constraints
Long Qian, Eric Wang, Bernardo Subercaseaux, Marijn J. H. Heule
https://arxiv.org/abs/2506.01079 https://

Unfolding Boxes with Local Constraints
We consider the problem of finding and enumerating polyominos that can be folded into multiple non-isomorphic boxes. While several computational approaches have been proposed, including SAT, randomized algorithms, and decision diagrams, none has been able to perform at scale. We argue that existing SAT encodings are hindered by the presence of global constraints (e.g., graph connectivity or acyclicity), which are generally hard to encode effectively and hard for solvers to reason about. In this…

SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry
Peijie Wang, Chao Yang, Zhong-Zhi Li, Fei Yin, Dekang Ran, Mi Tian, Zhilong Ji, Jinfeng Bai, Cheng-Lin Liu
https://arxiv.org/abs/2505.21177

SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry
Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs …