Tootfinder

GP3: A 3D Geometry-Aware Policy with Multi-View Images for Robotic Manipulation
Quanhao Qian, Guoyang Zhao, Gongjie Zhang, Jiuniu Wang, Ran Xu, Junlong Gao, Deli Zhao
https://arxiv.org/abs/2509.15733

GP3: A 3D Geometry-Aware Policy with Multi-View Images for Robotic Manipulation
Effective robotic manipulation relies on a precise understanding of 3D scene geometry, and one of the most straightforward ways to acquire such geometry is through multi-view observations. Motivated by this, we present GP3 -- a 3D geometry-aware robotic manipulation policy that leverages multi-view input. GP3 employs a spatial encoder to infer dense spatial features from RGB observations, which enable the estimation of depth and camera parameters, leading to a compact yet expressive 3D scene re…

DriveSplat: Decoupled Driving Scene Reconstruction with Geometry-enhanced Partitioned Neural Gaussians
Cong Wang, Xianda Guo, Wenbo Xu, Wei Tian, Ruiqi Song, Chenming Zhang, Lingxi Li, Long Chen
https://arxiv.org/abs/2508.15376

DriveSplat: Decoupled Driving Scene Reconstruction with Geometry-enhanced Partitioned Neural Gaussians
In the realm of driving scenarios, the presence of rapidly moving vehicles, pedestrians in motion, and large-scale static backgrounds poses significant challenges for 3D scene reconstruction. Recent methods based on 3D Gaussian Splatting address the motion blur problem by decoupling dynamic and static components within the scene. However, these decoupling strategies overlook background optimization with adequate geometry relationships and rely solely on fitting each training view by adding Gaus…

LeanGeo: Formalizing Competitional Geometry problems in Lean
Chendong Song, Zihan Wang, Frederick Pu, Haiming Wang, Xiaohan Lin, Junqi Liu, Jia Li, Zhengying Liu
https://arxiv.org/abs/2508.14644

LeanGeo: Formalizing Competitional Geometry problems in Lean
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 …

Geometry on curves which go around a Whitney umbrella
Masayuki Hara
https://arxiv.org/abs/2508.15293 https://arxiv.org/pdf/2508.15293

Geometry on curves which go around a Whitney umbrella
We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors of the curve. Then we obtain several functions which represents geometry on Whitney umbrella. Looking at the top terms of them with respect to the radius, we study geometry on Whitney umbrella.

A Timeless Game: A Game-Theoretic Model of Mass-Geometry Relations
Milad Ghadimi
https://arxiv.org/abs/2509.15229 https://arxiv.org/pdf/2509.15229

A Timeless Game: A Game-Theoretic Model of Mass-Geometry Relations
We develop a minimal, timeless game-theoretic representation of the mass-geometry relation. An "Object" (mass) and "Space" (geometry) choose strategies in a static normal-form game; utilities encode stability as mutual consistency rather than dynamical payoffs. In a 2x2 toy model, the equilibria correspond to "light-flat" and "heavy-curved" configurations; a continuous variant clarifies when only trivial interior equilibria appear versus a continuum along a matching ray. Philosophically, the po…

Hierarchical Retrieval: The Geometry and a Pretrain-Finetune Recipe
Chong You, Rajesh Jayaram, Ananda Theertha Suresh, Robin Nittka, Felix Yu, Sanjiv Kumar
https://arxiv.org/abs/2509.16411

Hierarchical Retrieval: The Geometry and a Pretrain-Finetune Recipe
Dual encoder (DE) models, where a pair of matching query and document are embedded into similar vector representations, are widely used in information retrieval due to their simplicity and scalability. However, the Euclidean geometry of the embedding space limits the expressive power of DEs, which may compromise their quality. This paper investigates such limitations in the context of hierarchical retrieval (HR), where the document set has a hierarchical structure and the matching documents for…

Multi-spacecraft Measurements of the Evolving Geometry of the Solar Alfv\'en Surface Over Half a Solar Cycle
Samuel T. Badman, Michael L. Stevens, Stuart D. Bale, Yeimy J. Rivera, Kristopher G. Klein, Tatiana Niembro, Rohit Chhiber, Ali Rahmati, Phyllis L. Whittlesey, Roberto Livi, Davin E. Larson, Christopher J. Owen, Kristoff W. Paulson, Timothy S. Horbury, Jean Morris, Helen O'Brien, Jean-Baptiste Dakeyo, Jaye L. Verniero, Mihailo Martinovic, Marc Pulupa, Federico Fraschetti…

Multi-spacecraft Measurements of the Evolving Geometry of the Solar Alfvén Surface Over Half a Solar Cycle
The geometry of a star's Alfvén surface determines stellar angular momentum loss, separates a causally distinct 'corona' and stellar wind, and potentially affects exoplanetary habitability. The solar Alfvén surface is the only such structure that is directly measurable and since 2021, has been routinely measured in situ by NASA's Parker Solar Probe (Parker). We use these unique measurements in concert with Solar Orbiter and L1 in situ data spanning the first half of the Solar Cycle 25 in time…

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family
Jacek Karwowski, Frank Nielsen
https://arxiv.org/abs/2508.14369

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family
The extended Gaussian family is the closure of the Gaussian family obtained by completing the Gaussian family with the counterpart elements induced by degenerate covariance or degenerate precision matrices, or a mix of both degeneracies. The parameter space of the extended Gaussian family forms a symmetric positive semi-definite matrix bicone, i.e. two partial symmetric positive semi-definite matrix cones joined at their bases. In this paper, we study the Hilbert geometry of such an open bounde…

Laguerre geometry for optimization of gridshell with specified force distribution
Kohei Kabaki, Kentaro Hayakawa, Makoto Ohsaki
https://arxiv.org/abs/2508.15179 https://

Laguerre geometry for optimization of gridshell with specified force distribution
For the design of gridshells consisting of continuous beams in two directions and quadrilateral faces to cover a large space of architecture, it is important to arrange each row and column of beams along a planar curve and ensure planar faces for constructability and cross-sectional compatibility at joints. It is also important that the gridshell is in equilibrium mainly with axial forces against the design loads; i.e., bending deformation should be avoided. In this study, we first find a conti…

PhysHDR: When Lighting Meets Materials and Scene Geometry in HDR Reconstruction
Hrishav Bakul Barua, Kalin Stefanov, Ganesh Krishnasamy, KokSheik Wong, Abhinav Dhall
https://arxiv.org/abs/2509.16869

PhysHDR: When Lighting Meets Materials and Scene Geometry in HDR Reconstruction
Low Dynamic Range (LDR) to High Dynamic Range (HDR) image translation is a fundamental task in many computational vision problems. Numerous data-driven methods have been proposed to address this problem; however, they lack explicit modeling of illumination, lighting, and scene geometry in images. This limits the quality of the reconstructed HDR images. Since lighting and shadows interact differently with different materials, (e.g., specular surfaces such as glass and metal, and lambertian or di…

Improving Cram\'er-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
https://arxiv.org/abs/2509.17886 https://arxiv.org…

Improving Cramér-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
This work presents a geometric refinement of the classical Cramér-Rao bound (CRB) by incorporating curvature-aware corrections based on the second fundamental form associated with the statistical model manifold. That is, our formulation shows that relying on the extrinsic geometry of the square root embedding of the manifold in the ambient Hilbert space comprising square integrable functions with respect to a fixed base measure offers a rigorous (and intuitive) way to improve upon the CRB and …

The layering of the Martian atmosphere observed in forward scattering geometry: #Mars camera CaSSIS aboard ESA's ExoMars Trace Gas Orbiter reveals the glowing atmosphere of Mars in unprecedented detail.

Recursively subdividing/tessellating a hexagon with Catmull-Clark (made with unreleased thi.ng/geom-mesh pkg, anim is from March 2017)...
#TilingTuesday #Geometry #Subdivision

Fractal failures of Ratner rigidity in higher rank geometry
Subhadip Dey, Hee Oh
https://arxiv.org/abs/2509.17915 https://arxiv.org/pdf/2509.17915

Fractal failures of Ratner rigidity in higher rank geometry
Ratner's theorem shows that in a locally symmetric space of noncompact type and finite volume, every immersed totally geodesic subspace of noncompact type is topologically rigid: its closure is an immersed submanifold. We construct the first explicit higher-rank, infinite-volume examples in which this rigidity fails, via floating geodesic planes. Specifically, we exhibit a Zariski-dense Hitchin surface group $Γ<\mathrm{SL}_3(\mathbb{R})$ such that $Γ\backslash \mathrm{SL}_3(\mathbb{R})/ \ma…

The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution
A. A. Ara\'ujo Filho, N. Heidari, Iarley P. Lobo, Yuxuan Shi, Francisco S. N. Lobo
https://arxiv.org/abs/2509.17867

The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution
This paper investigates a new black hole solution within the framework of bumblebee gravity, incorporating non-commutative corrections parameterized by $Θ$ and implemented through the Moyal twist $\partial_r \wedge \partial_θ$. Notably, the event horizon remains unaffected by $Θ$, while the surface gravity becomes ill-defined, in agreement with the behavior previously reported for the non-commutative Schwarzschild black hole [1]. The propagation of light is examined by analyzing null geodesi…

Kalman Filtering-Assisted Node Deployment for Distributed OTFS-ISAC: A Geometry-Aware Design for the Joint Sensing and Communication
Jyotsna Rani, Kuntal Deka, Ganesh Prasad, Zilong Liu
https://arxiv.org/abs/2509.16700

Kalman Filtering-Assisted Node Deployment for Distributed OTFS-ISAC: A Geometry-Aware Design for the Joint Sensing and Communication
Integrated sensing and communication (ISAC) is a key enabler for next-generation wireless networks, offering spectrum efficiency and reduced hardware complexity. While monostatic ISAC has been well studied, its limited spatial diversity reduces reliability in high-mobility scenarios. Distributed ISAC alleviates this via cooperative nodes, but conventional OFDM-based designs remain vulnerable to Doppler shifts and multipath fading. Orthogonal time frequency space (OTFS) modulation has recently e…

MAGENTA: Magnitude and Geometry-ENhanced Training Approach for Robust Long-Tailed Sound Event Localization and Detection
Jun-Wei Yeow, Ee-Leng Tan, Santi Peksi, Woon-Seng Gan
https://arxiv.org/abs/2509.15599

MAGENTA: Magnitude and Geometry-ENhanced Training Approach for Robust Long-Tailed Sound Event Localization and Detection
Deep learning-based Sound Event Localization and Detection (SELD) systems degrade significantly on real-world, long-tailed datasets. Standard regression losses bias learning toward frequent classes, causing rare events to be systematically under-recognized. To address this challenge, we introduce MAGENTA (Magnitude And Geometry-ENhanced Training Approach), a unified loss function that counteracts this bias within a physically interpretable vector space. MAGENTA geometrically decomposes the regr…

Darboux's Theorem in $p$-adic symplectic geometry
Luis Crespo, \'Alvaro Pelayo
https://arxiv.org/abs/2508.15443 https://arxiv.org/pdf/2508.15443

Darboux's Theorem in $p$-adic symplectic geometry
Let $p$ be a prime number. We derive an analog of Moser's Path Method for $p$-adic analytic manifolds and use it to prove a $p$-adic analog of Darboux's Theorem. Hence, in the $p$-adic category there are also no local symplectic invariants other than the dimension, as it happens in the real case: locally near any point, a $2n$-dimensional $p$-adic analytic symplectic manifold is symplectomorphic to $((\mathbb{Q}_p)^{2n},\sum_{i=1}^n\mathrm{d} x_1\wedge\mathrm{d} y_i)$. We also prove a $p$-adic …

On the geometry and uniqueness of asymptotically locally hyperbolic static vacuum black holes
Brian Harvie, Ye-Kai Wang
https://arxiv.org/abs/2509.18026 https://

On the geometry and uniqueness of asymptotically locally hyperbolic static vacuum black holes
We establish an inequality relating the surface gravity and topology of a horizon in a $3$-dimensional asymptotically locally hyperbolic static space with the geometry at infinity. Equality is achieved only by the Kottler black holes, and this rigidity leads to several new static black hole uniqueness theorems for a negative cosmological constant. First, the ADS-Schwarzschild black hole with critical surface gravity $κ=\sqrt{-Λ}$ is unique. Second, the toroidal Kottler black holes are unique …

Replaced article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Point Counting on Igusa Varieties for function fields
Paul Hamacher, Wansu Kim

The #MobilityDB team just announced v1.3.0-alpha featuring
New temporal types:
🆕 tgeometry & tgeography that can represent the temporal evolution of any geometry type (polygon, multipoint, etc.)
🆕 temporal circular buffer (tcbuffer)
🆕 temporal pose (tpose) type, storing the evolution of a pose
(point position orientation)
and more ...

Release MobilityDB v1.3.0-alpha · MobilityDB/MobilityDB
This is the alpha release for MobilityDB 1.3. Major changes w.r.t. 1.2 New temporal types: New temporal geometry tgeometry and temporal geography tgeography types, which can represent the temporal...

GaussianArt: Unified Modeling of Geometry and Motion for Articulated Objects
Licheng Shen, Saining Zhang, Honghan Li, Peilin Yang, Zihao Huang, Zongzheng Zhang, Hao Zhao
https://arxiv.org/abs/2508.14891

GaussianArt: Unified Modeling of Geometry and Motion for Articulated Objects
Reconstructing articulated objects is essential for building digital twins of interactive environments. However, prior methods typically decouple geometry and motion by first reconstructing object shape in distinct states and then estimating articulation through post-hoc alignment. This separation complicates the reconstruction pipeline and restricts scalability, especially for objects with complex, multi-part articulation. We introduce a unified representation that jointly models geometry and …

The formal theory of tangentads
Marcello Lanfranchi
https://arxiv.org/abs/2509.15524 https://arxiv.org/pdf/2509.15524…

The formal theory of tangentads
Tangent categories offer a categorical context for differential geometry, by categorifying geometric notions like the tangent bundle functor, vector fields, Euclidean spaces, vector bundles, connections, etc. In the last decade, the theory has been extended in new directions, providing concepts such as tangent monads, tangent fibrations, tangent restriction categories, reverse tangent categories and many more. It is natural to wonder how these new flavours interact with the geometric construc…

Learning Protein-Ligand Binding in Hyperbolic Space
Jianhui Wang, Wenyu Zhu, Bowen Gao, Xin Hong, Ya-Qin Zhang, Wei-Ying Ma, Yanyan Lan
https://arxiv.org/abs/2508.15480 https://…

Learning Protein-Ligand Binding in Hyperbolic Space
Protein-ligand binding prediction is central to virtual screening and affinity ranking, two fundamental tasks in drug discovery. While recent retrieval-based methods embed ligands and protein pockets into Euclidean space for similarity-based search, the geometry of Euclidean embeddings often fails to capture the hierarchical structure and fine-grained affinity variations intrinsic to molecular interactions. In this work, we propose HypSeek, a hyperbolic representation learning framework that em…

Critical trajectories in kinetic geometry
Helge Dietert, Cl\'ement Mouhot, Lukas Niebel, Rico Zacher
https://arxiv.org/abs/2508.14868 https://arxiv.org…

Critical trajectories in kinetic geometry
We construct critical trajectories in kinetic geometry, i.e. curves in $\mathbb{R}^{1+2n}$ that are: tangential to the vector fields $\partial_t+v\cdot \nabla_x$ and $\nabla_v$, connecting any two given points, respecting the underlying kinetic scaling, and with the property, that the singularity of the $v$-tangent vector near the starting point equates the degeneracy of the dependency of the curve velocity in terms of the endpoint velocity. The construction is based on Newton's laws of motio…

Geometry-Driven Lattice of Photonic Spin-Meron Tubes in Free Space
Anand Hegde, Komal Gupta, Yanan Dai, Chen-Bin Huang
https://arxiv.org/abs/2508.14450 https://

Geometry-Driven Lattice of Photonic Spin-Meron Tubes in Free Space
We theoretically demonstrate the first photonic spin-meron tube lattice in free space using spin-angular momentum vectors. Square-block diffraction creates $C_{4}$-symmetric beams with $π/2$ phase steps. Non-paraxial spin-orbit coupling then forms finite-length meron tubes ($N_{\mathrm{sk}} \approx \pm 1/2$, $> 25,λ$). Extending the formalism, we show that $C_{3}$ geometry of a triangular block yields a spin-skyrmion tube. Stratton-Chu theory and full-vectorial finite-difference time-domain c…

TextCrafter: Optimization-Calibrated Noise for Defending Against Text Embedding Inversion
Duoxun Tang, Xinhang Jiang, Jiajun Niu
https://arxiv.org/abs/2509.17302 https://…

TextCrafter: Optimization-Calibrated Noise for Defending Against Text Embedding Inversion
Text embedding inversion attacks reconstruct original sentences from latent representations, posing severe privacy threats in collaborative inference and edge computing. We propose TextCrafter, an optimization-based adversarial perturbation mechanism that combines RL learned, geometry aware noise injection orthogonal to user embeddings with cluster priors and PII signal guidance to suppress inversion while preserving task utility. Unlike prior defenses either non learnable or agnostic to pertur…

been faffing around with 3d geometry in build123d recently, and failing to get the cad kernel to produce geometric objects that do what i want
so i sat down to do some algebra
it’s annoying that the usual material about conic sections explains how ellipses and parabolas and hyperbolas work … but not how to derive them given a cone and a plane
so i worked it out for my particular problem, and happily things cancelled out very nicely, making the result nice and simple
(…

Topology and Spectral Entanglement in Cavity-Mediated Photon Scattering
Eric R. Bittner, Andrei Piryatinski
https://arxiv.org/abs/2509.15465 https://arxiv.…

Topology and Spectral Entanglement in Cavity-Mediated Photon Scattering
We develop a diagrammatic theory of cavity-mediated photon-photon interactions in a topological insulator using the SSH model. The fourth-order vertex $Γ^{(4)}(ω_1,ω_2)$ governs spectral entanglement and Kerr nonlinearity, leading to a nonlinear topological phase diagram. We also compute the electronic self-energy from vacuum photon exchange and identify symmetry-imposed limits on band renormalization. These results link band geometry to the emergence of light-matter correlations.

From a story in today’s Wall Street Journal about Woody Allen and his new novel:

Though he’s already at work on a second novel, he rarely reads fiction—“I feel like I’m wasting time.”
More often he reads philosophy and books by physicists.
“I keep thinking I’m going to learn something of deep value that’s going to make me feel better in life,” he says.
“It never does.”

Two Number Theory Items (and Woody Allen)
James Douglas Boyd has recently spent a lot of time interacting with Mochizuki and others at RIMS working in anabelian geometry. Material from interviews he conducted are available here (Mochizuki …

Intrinsic Linear Response from Zeeman Quantum Geometry in 2D Unconventional Magnets
Neelanjan Chakraborti, Sudeep Kumar Ghosh, Snehasish Nandy
https://arxiv.org/abs/2508.14745 h…

Intrinsic Linear Response from Zeeman Quantum Geometry in 2D Unconventional Magnets
Unconventional magnets with zero net magnetization yet momentum-dependent spin splitting constitute a newly identified class of materials that provide a rich platform for quantum-geometry-driven transport phenomena. Exploiting the interplay between momentum translation and spin rotation, we uncover a distinct linear transport response governed by a generalized quantum geometric tensor, the Zeeman quantum geometric tensor (ZQGT). We show that the ZQGT drives a linear intrinsic gyrotropic magneti…

Spectral Curves with Complex Multiplication in Hermitian Matrix Models
Ali Nassar
https://arxiv.org/abs/2509.16997 https://arxiv.org/pdf/2509.16997

Spectral Curves with Complex Multiplication in Hermitian Matrix Models
We show that elliptic curves with complex multiplication (CM) naturally emerge in the spectral geometry of Hermitian one-matrix models in the two-cut phase. Focusing on a symmetric quartic potential, we derive the corresponding genus-one spectral curve and compute its modular $j$-invariant in closed form as a function of the quartic coupling $g$. We identify specific values of $g$ for which the elliptic curve exhibits $CM$, i.e., its endomorphism ring is larger than $\mathbb{Z}$. This establish…

Deep Learning as the Disciplined Construction of Tame Objects
Gilles Bareilles, Allen Gehret, Johannes Aspman, Jana Lep\v{s}ov\'a, Jakub Mare\v{c}ek
https://arxiv.org/abs/2509.18025

Deep Learning as the Disciplined Construction of Tame Objects
One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization theory, and deep learning theory and practice. To do so, we gradually introduce the concepts and tools used to build convergence guarantees for stochastic gradient descent in a general nonsmooth nonconvex, but tame, setting. This illustrates some ways in which tam…

Crosslisted article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Functional Liftings of Restricted Geometric Inequalities
Andreas Malliaris, James Melbourne, Cyril Roberto, Michael Roysdon

Evaluation Codes in Bottleneck Metrics
Mahir Bilen Can, Dillon Montero, Ferruh \"Ozbudak
https://arxiv.org/abs/2509.17682 https://arxiv.org/pdf/2509.1…

Evaluation Codes in Bottleneck Metrics
Analogs of Reed-Solomon codes are introduced within the framework of bottleneck poset metrics. These codes are proven to be maximum distance separable. Furthermore, the results are extended to the setting of Algebraic Geometry codes.

The GJMS operators in geometry, analysis, and physics
Jeffrey S. Case, A. Rod Gover
https://arxiv.org/abs/2509.16047 https://arxiv.org/pdf/2509.16047

The GJMS operators in geometry, analysis, and physics
The GJMS operators, introduced by Graham, Jenne, Mason, and Sparling, are a family of conformally invariant linear differential operators with leading term a power of the Laplacian. These operators and their method of construction have had a major impact in geometry, analysis, and physics. We describe the GJMS operators and their construction, and briefly survey their importance and impact.

Obstruction sequences to homotopy equivalences
Coline Emprin
https://arxiv.org/abs/2509.17895 https://arxiv.org/pdf/2509.17895

Obstruction sequences to homotopy equivalences
We develop an obstruction theory for the existence of gauge equivalences in complete differential graded Lie algebras. Specifically, this theory provides a characterization of homotopy equivalences between differential graded algebras governed by operads or properads, potentially colored in a groupoid. We apply this framework to establish new homotopy equivalence results in both algebraic topology and algebraic geometry, with a particular focus on the study of minimal models for highly connecte…

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Computational Resolution of Hadamard Product Factorization for $4 \times 4$ Matrices
Igor Rivin

VideoFrom3D: 3D Scene Video Generation via Complementary Image and Video Diffusion Models
Geonung Kim, Janghyeok Han, Sunghyun Cho
https://arxiv.org/abs/2509.17985 https://

VideoFrom3D: 3D Scene Video Generation via Complementary Image and Video Diffusion Models
In this paper, we propose VideoFrom3D, a novel framework for synthesizing high-quality 3D scene videos from coarse geometry, a camera trajectory, and a reference image. Our approach streamlines the 3D graphic design workflow, enabling flexible design exploration and rapid production of deliverables. A straightforward approach to synthesizing a video from coarse geometry might condition a video diffusion model on geometric structure. However, existing video diffusion models struggle to generate …

Replaced article(s) found for cs.CG. https://arxiv.org/list/cs.CG/new
[1/1]:
- Implicit Toolpath Generation for Functionally Graded Additive Manufacturing via Gradient-Informed...
Charles Wade, Devon Beck, Robert MacCurdy

A Framework for Optimal Ankle Design of Humanoid Robots
Guglielmo Cervettini, Roberto Mauceri, Alex Coppola, Fabio Bergonti, Luca Fiorio, Marco Maggiali, Daniele Pucci
https://arxiv.org/abs/2509.16469 …

A Framework for Optimal Ankle Design of Humanoid Robots
The design of the humanoid ankle is critical for safe and efficient ground interaction. Key factors such as mechanical compliance and motor mass distribution have driven the adoption of parallel mechanism architectures. However, selecting the optimal configuration depends on both actuator availability and task requirements. We propose a unified methodology for the design and evaluation of parallel ankle mechanisms. A multi-objective optimization synthesizes the mechanism geometry, the resulting…

GOGS: High-Fidelity Geometry and Relighting for Glossy Objects via Gaussian Surfels
Xingyuan Yang, Min Wei
https://arxiv.org/abs/2508.14563 https://arxiv.o…

GOGS: High-Fidelity Geometry and Relighting for Glossy Objects via Gaussian Surfels
Inverse rendering of glossy objects from RGB imagery remains fundamentally limited by inherent ambiguity. Although NeRF-based methods achieve high-fidelity reconstruction via dense-ray sampling, their computational cost is prohibitive. Recent 3D Gaussian Splatting achieves high reconstruction efficiency but exhibits limitations under specular reflections. Multi-view inconsistencies introduce high-frequency surface noise and structural artifacts, while simplified rendering equations obscure mate…

Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms
Eric D'Hoker, Michael Gutperle, Christoph F. Uhlemann
https://arxiv.org/abs/2508.14959

Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms
We construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra $F(4)$. The geometry is a product of complexified maximally symmetric spaces $\mathcal M_{6 {\mathbb C}}$ and $\mathcal M_{2 {\mathbb C}}$ warped over a complexified surface $Σ_{\mathbb C}$. We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter compris…

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Universal families of twisted cotangent bundles
Peter Crooks
https://

Four ways (of many) recursively subdividing/tessellating a pentagon (made with #TilingTuesday

Replaced article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Towards the dual motivic Steenrod algebra in positive characteristic
Martin Frankland, Markus Spitzweck

Support-Projected Petz Monotone Geometry of Two-Qubit Families: Three-Channel Identity and Non-Reduction of Curvatures
Gunhee Cho, Jeongwoo Jae
https://arxiv.org/abs/2509.14578 …

Support-Projected Petz Monotone Geometry of Two-Qubit Families: Three-Channel Identity and Non-Reduction of Curvatures
We investigate the information geometry of pure two-qubit variational families by pulling back arbitrary Petz monotone quantum metrics to circuit-defined submanifolds and making them intrinsic via support projection onto the active numerical range of the quantum Fisher information tensor. This framework strictly generalizes the symmetric logarithmic derivative (SLD/Bures) case and includes, as special examples, the Wigner-Yanase and Bogoliubov-Kubo-Mori metrics among many others. Our first main…

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Characterization of higher rank via affine maps
David Lenze
https://

Cosmological viability of anisotropic inflation in Thurston spacetimes
Devika J. S., Tanay Gupta, Sukanta Panda
https://arxiv.org/abs/2509.16553 https://ar…

Cosmological viability of anisotropic inflation in Thurston spacetimes
The introduction of anisotropy into large scale geometry of the universe has led to the development of Thurston spacetimes possessing an inherent anisotropic curvature in them. Studies related to these anisotropic spacetimes have revealed how they could explain the evolutionary dynamics and light propagation in the universe. Here, we consider these spacetimes under the inflationary epoch to examine whether we could address the possibility of anisotropic inflation in the universe. Researches hav…

Crosslisted article(s) found for cs.CG. https://arxiv.org/list/cs.CG/new
[1/1]:
- Topological potentials guiding protein self-assembly
Ivan Spirandelli, Dmitriy Morozov, Arnur Nigmetov, Myfanwy E. Evans

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Entropy approximations of algebraic matroids over finite fields
Guillermo Matera

Recovering Parametric Scenes from Very Few Time-of-Flight Pixels
Carter Sifferman, Yiquan Li, Yiming Li, Fangzhou Mu, Michael Gleicher, Mohit Gupta, Yin Li
https://arxiv.org/abs/2509.16132

Recovering Parametric Scenes from Very Few Time-of-Flight Pixels
We aim to recover the geometry of 3D parametric scenes using very few depth measurements from low-cost, commercially available time-of-flight sensors. These sensors offer very low spatial resolution (i.e., a single pixel), but image a wide field-of-view per pixel and capture detailed time-of-flight data in the form of time-resolved photon counts. This time-of-flight data encodes rich scene information and thus enables recovery of simple scenes from sparse measurements. We investigate the feasib…

Crosslisted article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Atoms meet symbols
Leonardo F. Cavenaghi, Ludmil Katzarkov, Maxim Kontsevich

Sparse, Geometry- and Material-Aware Bases for Multilevel Elastodynamic Simulation
Ty Trusty, David I. W. Levin, Danny M. Kaufman
https://arxiv.org/abs/2508.13386 https://

Sparse, Geometry- and Material-Aware Bases for Multilevel Elastodynamic Simulation
We present a multi-level elastodynamics timestep solver for accelerating incremental potential contact (IPC) simulations. Our method retains the robustness of gold standard IPC in the face of intricate geometry, complex heterogeneous material distributions and high resolution input data without sacrificing visual fidelity (per-timestep relative displacement error of $\approx1\%$). The success of our method is enabled by a novel, sparse, geometry- and material-aware basis construction method whi…

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
Stefano Antonini, Luca V. Iliesiu, Pratik Rath, Patrick Tran
https://arxiv.org/abs/2509.15295

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the…

Crosslisted article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- Infinite Euclidean Distance Discriminants
Felix Rydell, Emil Horobet
https…

Replaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Non-maximal Anosov representations from surface groups to $\mathrm{SO}_0(2,3)$
Junming Zhang

Replaced article(s) found for cs.CG. https://arxiv.org/list/cs.CG/new
[1/1]:
- k-Planar and Fan-Crossing Drawings and Transductions of Planar Graphs
Petr Hlin\v{e}n\'y, Jan Jedelsk\'y

Constraints on the Sen black hole mass and charge from quasi-periodic oscillations
Kuantay Boshkayev, Marco Muccino
https://arxiv.org/abs/2508.15682 https://

Constraints on the Sen black hole mass and charge from quasi-periodic oscillations
We analyze quasi-periodic oscillation data from selected X-ray binary systems hosting black holes. To model the spacetime geometry, we resort the static Sen solution -- originally derived in the framework of heterotic string theory -- which reduces to the Schwarzschild spacetime for vanishing electric charge. By fitting the observed frequencies within the relativistic precession model, we constrain the mass and charge parameters of the Sen black hole and discuss their astrophysical implications…

Replaced article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Birational conjugacies between endomorphisms on the projective plane
Serge Cantat, Junyi Xie

RangeSAM: Leveraging Visual Foundation Models for Range-View repesented LiDAR segmentation
Paul Julius K\"uhn, Duc Anh Nguyen, Arjan Kuijper, Holger Graf, Dieter Fellner, Saptarshi Neil Sinha
https://arxiv.org/abs/2509.15886

RangeSAM: Leveraging Visual Foundation Models for Range-View repesented LiDAR segmentation
Point cloud segmentation is central to autonomous driving and 3D scene understanding. While voxel- and point-based methods dominate recent research due to their compatibility with deep architectures and ability to capture fine-grained geometry, they often incur high computational cost, irregular memory access, and limited real-time efficiency. In contrast, range-view methods, though relatively underexplored - can leverage mature 2D semantic segmentation techniques for fast and accurate predicti…

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Legendrian non-squeezing via microsheaves
Eric Kilgore
https://

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/2]:
- $E_2L_\infty$-algebras, Generalized Geometry, and Tensor Hierarchies
Leron Borsten, Hyungrok Kim, Christian Saemann

Crosslisted article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expa...
Louie Bernhardt

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Vanishing of Schubert coefficients in probabilistic polynomial time
Igor Pak, Colleen Robichaux

Replaced article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- A Combination Theorem for Trees of Metric Bundles
Rakesh Halder
https://

Replaced article(s) found for cs.CG. https://arxiv.org/list/cs.CG/new
[1/1]:
- Minimizing an Uncrossed Collection of Drawings
Petr Hlin\v{e}n\'y, Tom\'a\v{s} Masa\v{r}\'ik

The non-orientable spacetime of the eternal black hole
Ovidiu Racorean
https://arxiv.org/abs/2508.15005 https://arxiv.org/pdf/2508.15005

The non-orientable spacetime of the eternal black hole
We derive the metric of the BTZ black hole for the special case of interchanging the characteristics of space and time coordinates. We maximally extend the geometry of this interior solution and show that the line element is similar to its exterior solution counterpart. Thus, we assign the thermofield double state dual to this interior geometric construction. As a result, we have two independent thermofield double states corresponding to the BTZ metric: one dual to the exterior solution and one…

MExECON: Multi-view Extended Explicit Clothed humans Optimized via Normal integration
Fulden Ece U\u{g}ur, Rafael Redondo, Albert Barreiro, Stefan Hristov, Roger Mar\'i
https://arxiv.org/abs/2508.15500

MExECON: Multi-view Extended Explicit Clothed humans Optimized via Normal integration
This work presents MExECON, a novel pipeline for 3D reconstruction of clothed human avatars from sparse multi-view RGB images. Building on the single-view method ECON, MExECON extends its capabilities to leverage multiple viewpoints, improving geometry and body pose estimation. At the core of the pipeline is the proposed Joint Multi-view Body Optimization (JMBO) algorithm, which fits a single SMPL-X body model jointly across all input views, enforcing multi-view consistency. The optimized body …

Replaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Singularities of Ricci flow and diffeomorphisms
Tobias Holck Colding, William P. Minicozzi II

Higher-form symmetries as higher automorphism bundles
Alonso Perez-Lona
https://arxiv.org/abs/2509.15301 https://arxiv.org/pdf/2509.15301

Higher-form symmetries as higher automorphism bundles
The notion of global higher-form symmetries has received much attention, but leaves room for a more systematic mathematical formulation. In this article, we highlight the concept of higher automorphism bundles from the field of higher categorical differential geometry and higher gauge theory, and we demonstrate that this neatly reproduces and clarifies many examples and phenomena discussed in the literature. We rigorously construct the higher-form symmetries of pure gauge theory of a general st…

Crosslisted article(s) found for cs.CG. https://arxiv.org/list/cs.CG/new
[1/1]:
- Distance Approximating Minors for Planar and Minor-Free Graphs
Hsien-Chih Chang, Jonathan Conroy

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Estimating Reeb chords using microlocal sheaf theory
Wenyuan Li
https://

Crosslisted article(s) found for math.MG. https://arxiv.org/list/math.MG/new
[1/1]:
- On Markowitz's pseudodistance for conformal manifolds
Adam Chalumeau (IRMA, uni.lu)

SceneGen: Single-Image 3D Scene Generation in One Feedforward Pass
Yanxu Meng, Haoning Wu, Ya Zhang, Weidi Xie
https://arxiv.org/abs/2508.15769 https://arx…

SceneGen: Single-Image 3D Scene Generation in One Feedforward Pass
3D content generation has recently attracted significant research interest due to its applications in VR/AR and embodied AI. In this work, we address the challenging task of synthesizing multiple 3D assets within a single scene image. Concretely, our contributions are fourfold: (i) we present SceneGen, a novel framework that takes a scene image and corresponding object masks as input, simultaneously producing multiple 3D assets with geometry and texture. Notably, SceneGen operates with no need …

Crosslisted article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Atoms meet symbols
Leonardo F. Cavenaghi, Ludmil Katzarkov, Maxim Kontsevich

Static AdS Black Holes Surrounded by Strings and Quintessence-like Field within Rastall Gravity Framework
Allan. R. P. Moreira, Faizuddin Ahmed, Abdelmalek Bouzenada
https://arxiv.org/abs/2509.15274

Static AdS Black Holes Surrounded by Strings and Quintessence-like Field within Rastall Gravity Framework
In this work, we tested the physical properties of Rastall black holes in the presence of string clouds and quintessence. The modified spacetime geometry arising from the Rastall framework is first established, providing the basis for analyzing the geodesic structure. We study null geodesics in detail, testing photon trajectories, the conditions for photon spheres, BH shadows, the associated effective radial force, and the topological features of photon rings. Also, the analysis is further test…

Crosslisted article(s) found for cs.CG. https://arxiv.org/list/cs.CG/new
[1/1]:
- Lifting Cocycles: From Heuristic to Theory
Sigurd Gaukstad, Mathias Karsrud Nordal, Marius Thaule

Crosslisted article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Quantum cohomology of variations of GIT quotients and flips
Zhaoxing Gu, Song Yu, Tony Yue YU

[2025-08-22 Fri (UTC), 8 new articles found for math.AG Algebraic Geometry]
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Replaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Geography of pinched four-manifolds
Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes

Arbitrarily long-lived quasinormal modes of proper-time flow black holes
Milena Skvortsova
https://arxiv.org/abs/2509.18061 https://arxiv.org/pdf/2509.1806…

Arbitrarily long-lived quasinormal modes of proper-time flow black holes
We investigate the quasinormal modes (QNMs) of a massive scalar field in the background of a regular black hole arising from the proper-time flow in asymptotically safe gravity. This quantum-corrected geometry, characterized by a deformation parameter q, smoothly interpolates between a near-extremal regular black hole and the Schwarzschild solution. Employing both the WKB approximation with Padé resummation and time-domain integration, we compute the complex frequencies for various values of t…

[2025-09-22 Mon (UTC), 13 new articles found for math.AG Algebraic Geometry]
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Crosslisted article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- A special concavity property for positive Hessian quotient operators
Pengfei Guan, Marcin Sroka

[2025-09-23 Tue (UTC), 16 new articles found for math.AG Algebraic Geometry]
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Charged particle dynamics in singular spacetimes: hydrogenic mapping and curvature-corrected thermodynamics
Abdullah Guvendi, Semra Gurtas Dogan, Omar Mustafa, Hassan Hassanabadi
https://arxiv.org/abs/2509.16289

Charged particle dynamics in singular spacetimes: hydrogenic mapping and curvature-corrected thermodynamics
We analyze the dynamics of charged test particles in a singular, horizonless spacetime arising as the massless limit of a charged wormhole in the Einstein--Maxwell--Scalar framework. The geometry, sustained solely by an electric charge \(Q\), features an infinite sequence of curvature singularity shells, with the outermost at \(r_\ast = \frac{2|Q|}π\) acting as a hard boundary for nonradial motion, while radial trajectories can access it depending on the particle's charge-to-mass rat…

[2025-08-22 Fri (UTC), 2 new articles found for cs.CG Computational Geometry]
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Atoms meet symbols
Leonardo F. Cavenaghi, Ludmil Katzarkov, Maxim Kontsevich
https://arxiv.org/abs/2509.15831 https://arxiv.org/pdf/2509.15831

Atoms meet symbols
This paper introduces a novel framework for constructing invariants in $G$-equivariant birational geometry by unifying two recent approaches: the \emph{theory of atoms} recently developed by Katzarkov, Kontsevich, Pantev, and Yu, and the theory of \emph{modular symbols} due to Kontsevich, Tschinkel, and Pestun. We initiate the theory of Chen-Ruan atoms. Assuming the blowup formula for the quantum Chen-Ruan cohomology, we outline how to extend the theory of atoms to global quotient orbifolds a…

[2025-09-23 Tue (UTC), 2 new articles found for cs.CG Computational Geometry]
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Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons
Shu-Cheng Chang, Yingbo Han, Chin-Tung Wu
https://arxiv.org/abs/2508.13495 https://arxiv.…

Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons
In this paper, we study the geometry and topology of complete gradient shrinking Sasaki-Ricci solitons. We first prove that they must be connected at infinity. This is a Sasaki analogue of gradient shrinking Kähler-Ricci solitons. Secondly, with the positive sectional curvature, we show that they must be compact. All results are served as a generalization of Perelman in dimension three, of Naber in dimension four, and of Munteanu-Wang in all dimensions, respectively.

Approximate Fiber Products of Schemes and Their \'Etale Homotopical Invariants
Dongfang Zhao
https://arxiv.org/abs/2509.15616 https://arxiv.org/pdf/250…

Approximate Fiber Products of Schemes and Their Étale Homotopical Invariants
The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, $ϕ: X \to S$ and $ψ: Y \to S$, coincide exactly. This condition of strict equality, however, is insufficient for describing the geometric structure of semantic spaces in modern large language models, whose foundational architecture is the Transformer. The token spaces of these models are fundamentally arithmetic, and recent work has revealed complex geometric sing…

[2025-09-22 Mon (UTC), 2 new articles found for cs.CG Computational Geometry]
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[2025-08-22 Fri (UTC), 6 new articles found for math.DG Differential Geometry]
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[2025-09-22 Mon (UTC), 8 new articles found for math.DG Differential Geometry]
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A note on non-crossing path partitions in the plane
Javier Tejel
https://arxiv.org/abs/2509.17485 https://arxiv.org/pdf/2509.17485

A note on non-crossing path partitions in the plane
In the paper ``Lower bounds on the number of crossing-free subgraphs of $K_N$'' (Computational Geometry 16 (2000), 211-221), it is shown that a double chain of $n$ points in the plane admits at least $Ω(4.642126305^n)$ polygonizations, and it is claimed that it admits at most $O(5.61^n)$ polygonizations. In this note, we provide a proof of this last result. The proof is based on counting non-crossing path partitions for points in the plane in convex position, where a non-crossing path partitio…

Quantum cohomology of variations of GIT quotients and flips
Zhaoxing Gu, Song Yu, Tony Yue YU
https://arxiv.org/abs/2508.15770 https://arxiv.org/pdf/2508.1…

Quantum cohomology of variations of GIT quotients and flips
We prove a decomposition theorem for the quantum cohomology of variations of GIT quotients. More precisely, for any reductive group $G$ and a simple $G$-VGIT wall-crossing $X_- \dashrightarrow X_+$ with a wall $S$, we show that the quantum $D$-module of $X_-$ can be decomposed into a direct sum of that of $X_+$ and copies of that of $S$. As an application, we obtain a decomposition theorem for the quantum cohomology of local models of standard flips in birational geometry.

[2025-09-23 Tue (UTC), 10 new articles found for math.DG Differential Geometry]
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Systolic Inequality and Scalar Curvature
Shunichiro Orikasa
https://arxiv.org/abs/2509.17376 https://arxiv.org/pdf/2509.17376

Systolic Inequality and Scalar Curvature
We investigate the interaction between systolic geometry and positive scalar curvature through spinorial methods. Our main theorem establishes an upper bound for the two-dimensional stable systole on certain high-dimensional manifolds with positive scalar curvature under a suitable stretch-scale condition. The proof combines techniques from geometric measure theory, reminiscent of Gromov's systolic inequality, with curvature estimates derived from the Gromov-Lawson relative index theorem. This …

A Screw Approach to the Approximation of the Local Geometry of the Configuration Space and of the set of Configurations of Certain Rank of Lower Pair Linkages
Andreas Mueller
https://arxiv.org/abs/2508.13802

A Screw Approach to the Approximation of the Local Geometry of the Configuration Space and of the set of Configurations of Certain Rank of Lower Pair Linkages
A motion of a mechanism is a curve in its configuration space (c-space). Singularities of the c-space are kinematic singularities of the mechanism. Any mobility analysis of a particular mechanism amounts to investigating the c-space geometry at a given configuration. A higher-order analysis is necessary to determine the finite mobility. To this end, past research lead to approaches using higher-order time derivatives of loop closure constraints assuming (implicitly) that all possible motions ar…

On Markowitz's pseudodistance for conformal manifolds
Adam Chalumeau (IRMA, uni.lu)
https://arxiv.org/abs/2509.15745 https://arxiv.org/pdf/2509.15745…

On Markowitz's pseudodistance for conformal manifolds
In the 1980s, M. J. Markowitz introduced a conformally invariant pseudodistance on pseudo-Riemannian manifolds, inspired by the Kobayashi metric in projective geometry. This construction relies on a distinguished class of parametrized lightlike geodesics, called projectively parametrized. We begin by reviewing the fundamental properties of this pseudodistance and provide several families of examples where it is non-degenerate and, in some cases, complete. In particular, we investigate three cla…