Tootfinder

Asymptotic expansion for groupoids and Roe type algebras
Xulong Lu, Qin Wang, Jiawen Zhang
https://arxiv.org/abs/2506.16772 https://a…

Asymptotic expansion for groupoids and Roe type algebras
In this paper, we introduce a notion of expansion for groupoids, which recovers the classical notion of expander graphs by a family of pair groupoids and expanding actions in measure by transformation groupoids. We also consider an asymptotic version for expansion and establish structural theorems, showing that asymptotic expansion can be approximated by domains of expansions. On the other hand, we introduce dynamical propagation and quasi-locality for operators on groupoids and the associated …

A Quaternionic Integration Similar to the Complex One
Michael Parfenov
https://arxiv.org/abs/2506.16239 https://arxiv.org/pdf/2506.16…

A Quaternionic Integration Similar to the Complex One
The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the notion of a number complex plane, the theory of the quaternionic integration similar to the complex one is built. The complex Taylor Theorem, Cauchy's Theorem, Cauchy's Integral Formula, Laurent's series, Laurent's theorem, and Cauchy's Residue Theorem are dir…

Observer Time from Causality in Perturbative Quantum Gravity
Allic Sivaramakrishnan
https://arxiv.org/abs/2506.16109 https://arxiv.or…

Observer Time from Causality in Perturbative Quantum Gravity
It is unclear whether an observable notion of time exists in quantum gravity even in principle because spacetime itself fluctuates. We propose a form of observable time in perturbative quantum gravity. First, we define an elapsed proper time in curved space using intersections of worldlines and future light cones. Here, time arises from causality via the dependence on light cones. We then propose that performing the gravitational path integral describes quantum gravity corrections to this notio…

Centre driven Controlled Evolution of Wireless Virtual Networks based on Broadcast Tokens
Vignesh Babu, Atishay Jain, Kannan Karthik
https://arxiv.org/abs/2506.16615

Centre driven Controlled Evolution of Wireless Virtual Networks based on Broadcast Tokens
In a wireless sensor network, the virtual connectivity between nodes is a function of the keys shared between various nodes. Pre-embedding these key configurations in the nodes would make the network inflexible. On the other hand, permitting subsets of nodes to engage in a common key synthesis phase to create secure distributed connections amongst themselves, would decouple and conceal the information flow from the controlling centre. An intermediate solution is the notion of a centre driven ke…

Pr\"{u}fer codes on vertex-colored rooted trees
R. W. R. Darling, Grant Fickes
https://arxiv.org/abs/2506.15796 https://arxiv.or…

Prüfer codes on vertex-colored rooted trees
Prüfer codes provide an encoding scheme for representing a vertex-labeled tree on $n$ vertices with a string of length $n-2$. Indeed, two labeled trees are isomorphic if and only if their Prüfer codes are identical, and this supplies a proof of Cayley's Theorem. Motivated by a graph decomposition of freight networks into a corpus of vertex-colored rooted trees, we extend the notion of Prüfer codes to that setting, i.e., trees without a unique labeling, by defining a canonical label for a ver…

Leibniz $2$-algebras, linear $2$-racks and the Zamolodchikov Tetrahedron equation
Nanyan Xu, Yunhe Sheng
https://arxiv.org/abs/2506.16714 https://

Leibniz $2$-algebras, linear $2$-racks and the Zamolodchikov Tetrahedron equation
In this paper, first we show that a central Leibniz 2-algebra naturally gives rise to a solution of the Zamolodchikov Tetrahedron equation. Then we introduce the notion of linear 2-racks and show that a linear 2-rack also gives rise to a solution of the Zamolodchikov Tetrahedron equation. We show that a central Leibniz 2-algebra gives rise to a linear 2-rack if the underlying 2-vector space is splittable. Finally we discuss the relation between linear 2-racks and 2-racks, and show that a linear…

Crowned Lie groups and nets of real subspaces
Daniel Beltita, Karl-Hermann Neeb
https://arxiv.org/abs/2506.16422 https://arxiv.org/pd…

Crowned Lie groups and nets of real subspaces
We introduce the notion of a complex crown domain for a connected Lie group $G$, and we use analytic extensions of orbit maps of antiunitary representations to these domains to construct nets of real subspaces on $G$ that are isotone, covariant and satisfy the Reeh--Schlieder and Bisognano--Wichmann conditions from Algebraic Quantum Field Theory. This provides a unifying perspective on various constructions of such nets.The representation theoretic properties of different crowns are discussed i…

heise | Digitaler Garten: Mit Notion einfach Wissen sammeln
Der "digitale Garten" bietet Platz für persönliches Wissen, das nachhaltig wächst. Wer bequem loslegen möchte, nutzt einfach Notion. Wir zeigen, wie es geht.
…

Deformations of quasi-Hamiltonian spaces
Jean-Philippe Burelle, Mohamed Moussadek Maiza, Maxence Mayrand
https://arxiv.org/abs/2505.16689 https://

Deformations of quasi-Hamiltonian spaces
We introduce a notion of deformations of quasi-Hamiltonian $G$-spaces to Hamiltonian $G$-spaces and provide several examples. In particular, we show that the double $G \times G$ of a Lie group, viewed as a quasi-Hamiltonian $G \times G$-space, deforms smoothly to the cotangent bundle $T^*G$. Likewise, any conjugacy class of $G$ sufficiently close to the identity deforms to a coadjoint orbit. We further show that the moduli space of flat $G$-connections on a compact oriented surface with boundar…

The binary product in the 2-category of triangular bialgebras and twisted morphisms
Alessandro Ardizzoni, Andrea Sciandra
https://arxiv.org/abs/2506.16469 …

The binary product in the 2-category of triangular bialgebras and twisted morphisms
It is well known that the tensor product of two bialgebras constitutes the binary product in the category of cocommutative bialgebras and morphisms of bialgebras between them. In this paper, we extend this result to triangular bialgebras and twisted morphisms of triangular bialgebras. This is pursued by adopting the framework of 2-categories and the proper notion of binary product, as well as by employing a description of twists on the tensor product bialgebra, specifically developed for this p…

Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets
Gianmichele Di Matteo, Tobias Lamm
https://arxiv.org/abs/2506.17151

Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets
Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain dimension $n$, we show a uniform $C^{1,α}$-regularity result for a sequence of such maps in the limit $p \searrow n$, assuming a uniform $n$-energy bound on its elements. The method of the proof follows the exact same lines as in \cite{strz3} but we need to chec…

On the evolution of the mass density profile of dense molecular clouds
S. Donkov, I. Zh. Stefanov, T. V. Veltchev, R. S. Klessen
https://arxiv.org/abs/2506.16854

On the evolution of the mass density profile of dense molecular clouds
We aim to obtain the equations which govern the evolution of the mass density profile of a dense irrotational molecular cloud (MC). Our study is based on the notion of "ensemble of MCs", introduced in our previous work. The MCs are modeled by use of the "ensemble abstract representative member": a spherically symmetric, isotropic and isothermal MC which accretes radially matter from its surroundings. Applying the equations of hydrodynamics to a self-gravitating isothermal spherical gas cloud, w…

Heterotopic energy for Sobolev mappings
Antoine Detaille, Jean Van Schaftingen
https://arxiv.org/abs/2506.16204 https://arxiv.org/pdf…

Heterotopic energy for Sobolev mappings
We study the notion of heterotopic energy defined as the limit of Sobolev energies of Sobolev mappings in a given homotopy class approximating almost everywhere a given Sobolev mapping. We show that the heterotopic energy is finite if and only if the mappings in the corresponding homotopy classes are homotopic on a codimension one skeleton of a triangulation of the domain. When this is the case, the heterotopic energy of a mapping is the sum of its Sobolev energy and its disparity energy, defin…

A data-based notion of quantiles on Hadamard spaces
Ha-Young Shin, Hee-Seok Oh
https://arxiv.org/abs/2506.12534 https://arxiv.org/pdf…

A data-based notion of quantiles on Hadamard spaces
This paper defines an alternative notion, described as data-based, of geometric quantiles on Hadamard spaces, in contrast to the existing methodology, described as parameter-based. In addition to having the same desirable properties as parameter-based quantiles, these data-based quantiles are shown to have several theoretical advantages related to large-sample properties like strong consistency and asymptotic normality, breakdown points, extreme quantiles and the gradient of the loss function. …

Mutation of $n$-cotorsion pairs in extriangulated categories
Huimin Chang, Yu Liu, Panyue Zhou
https://arxiv.org/abs/2506.16188 https://

Mutation of $n$-cotorsion pairs in extriangulated categories
In this article, we introduce the notion of $n$-cotorsion pairs in extriangulated categories, which extends both the cotorsion pairs established by Nakaoka and Palu and the $n$-cotorsion pairs in triangulated categories developed by Chang and Zhou. We further prove that any mutation of an $n$-cotorsion pair remains an $n$-cotorsion pair. As applications, we provide a geometric characterization of $n$-cotorsion pairs in $n$-cluster categories of type $A_{\infty}$, and we realize mutations of $n$…

Gavin Newsom and His Cruel Notion of 'Cruel' (Victor Davis Hanson/American Greatness)
https://amgreatness.com/2025/06/09/gavin-newsom-and-his-cruel-notion-of-cruel/
http://www.memeorandum.com/250609/p58#a250609p58

Seahawks HC scoffs at notion Darnold won't start https://www.espn.com/nfl/story/_/id/45445004/seahawks-mike-macdonald-scoffs-notion-sam-darnold-start

Reporting like this without immediately undermining the notion of "anatomical sex" is very bad. The idea that "anatomical" or "biological" sex are meaningful terms (they are not, just ask any organization that has tried to use them as a sorting criterion) is explicitly anti-trans.
#quebec

Treefera, which uses satellite imagery, drone imagery, and AI to provide real-time insights into supply chains, raised a $30M Series B led by Notion Capital (Cate Lawrence/Tech.eu)
https://tech.eu/2025/06/03/treefera-secure…

Treefera secures $20M Series B for AI-driven supply chain resilience solutions
Supply chain resilience startup Treeferachas secured $20 million in its Series B funding round, led by Notion Capital with participation from other investors.  In the face of growing economic uncertainty, a stringent regulatory landscape, and increasing environmental risk, Treefera’s platform utilises satellite imagery, drone imagery, and adaptive AI in order to provide real-time, tailored insights into supply chains.  This is especially significant within the first mile of supply chains,…

From Partial to Monadic: Combinatory Algebra with Effects
Liron Cohen (BGU), Ariel Grunfeld (BGU), Dominik Kirst (PICUBE), \'Etienne Miquey (I2M)
https://arxiv.org/abs/2506.09453

From Partial to Monadic: Combinatory Algebra with Effects
Partial Combinatory Algebras (PCAs) provide a foundational model of the untyped $λ$-calculus and serve as the basis for many notions of computability, such as realizability theory. However, PCAs support a very limited notion of computation by only incorporating non-termination as a computational effect. To provide a framework that better internalizes a wide range of computational effects, this paper puts forward the notion of Monadic Combinatory Algebras (MCAs). MCAs generalize the notion of P…

I did not expect Martin Fowler to be so anti-CQRS. Anyone have other writeups that have a more balanced perspective?
#Programming r…

bliki: CQRS
CQRS (Command Query Responsibility Segregation) is the notion that you can use a different model to update information than the model you use to read information

A categorical formulation of the Deligne-Terasoma approach to double shuffle theory
Benjamin Enriquez, Khalef Yaddaden
https://arxiv.org/abs/2506.15348 htt…

A categorical formulation of the Deligne-Terasoma approach to double shuffle theory
In this paper, we introduce the notion of a bimodule with a factorization structure (BFS) and show that such a structure gives rise to an algebra morphism. We then prove that this framework offers an interpretation of the geometric construction underlying both the Betti and de Rham harmonic coproducts of the double shuffle theory developed in \cite{DeT, EF1, EF2, EF3}.

Designing Intent: A Multimodal Framework for Human-Robot Cooperation in Industrial Workspaces
Francesco Chiossi, Julian Rasch, Robin Welsch, Albrecht Schmidt, Florian Michahelles
https://arxiv.org/abs/2506.15293

Designing Intent: A Multimodal Framework for Human-Robot Cooperation in Industrial Workspaces
As robots enter collaborative workspaces, ensuring mutual understanding between human workers and robotic systems becomes a prerequisite for trust, safety, and efficiency. In this position paper, we draw on the cooperation scenario of the AIMotive project in which a human and a cobot jointly perform assembly tasks to argue for a structured approach to intent communication. Building on the Situation Awareness-based Agent Transparency (SAT) framework and the notion of task abstraction levels, we …

On the Physical Untenability of the Standard Notion of Quantum State
Christian de Ronde
https://arxiv.org/abs/2505.23989 https://arxi…

On the Physical Untenability of the Standard Notion of Quantum State
The notion of quantum state plays a fundamental role within the Standard account of Quantum Mechanics (SQM) as established by Dirac and von Neumann during 1930s and up to the present. In this work we expose the deep inconsistencies that exist within the multiple definitions of the notion of quantum state that are provided within this axiomatic formulation. As we will argue, these different inconsistent definitions continue to be -- even today -- uncritically confused within the mainstream physi…

Torsion Theories in a Non-pointed Context
Andrea Cappelletti, Andrea Montoli
https://arxiv.org/abs/2506.13349 https://arxiv.org/pdf/2…

Torsion Theories in a Non-pointed Context
We study a non-pointed version of the notion of torsion theory in the framework of categories equipped with a posetal monocoreflective subcategory such that the coreflector inverts monomorphisms. We explore the connections of such torsion theories with factorization systems and categorical Galois structures. We describe several examples of these torsion theories, in the dual of elementary toposes, in varieties of universal algebras used as models for non-classical logic, and in coslices of the …

"Fields" in classical and quantum field theories
Alberto Ibort, Arnau Mas, Luca Schiavone
https://arxiv.org/abs/2506.15327 https://

"Fields" in classical and quantum field theories
The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning of physical states, etc. Among them the notion of ``field'' itself is notoriously difficult to address. These notes aim to analyze such notion from the perspective offered by the groupoid description of quantum mechanics inspired by Schwinger's picture of quantum mechanics. Then, a natural interpre…

Nope. Get out of here Notion. Moving my stuff to @… #AI #AISlop

Tractable Graph Structures in EFX Orientation
V\'aclav Bla\v{z}ej, Sushmita Gupta, M. S. Ramanujan, Peter Strulo
https://arxiv.org/abs/2506.15379 https…

Tractable Graph Structures in EFX Orientation
Since its introduction, envy-freeness up to any good (EFX) has become a fundamental solution concept in fair division of indivisible goods. Its existence remains elusive -- even for four agents with additive utility functions, it is unknown whether an EFX allocation always exists. Unsurprisingly, restricted settings to delineate tractable and intractable cases have been explored. Christadolou, Fiat et al.[EC'23] introduced the notion of EFX-orientation, where the agents form the vertices of a g…

How hunter-gatherers slept: sleep and rest in the prehistoric era https://lithub.com/how-exactly-did-hunter-gatherers-sleep-on-rest-and-relaxation-in-the-prehistoric-era

How Exactly Did Hunter-Gatherers Sleep? On Rest and Relaxation in the Prehistoric Era
“…human vanity cherishes the absurd notion that our species is the final goal of evolution.” Richard Dawkins, The Blind Watchmaker (1986) * Sleep was a mystery to our distant ance…

K3 surfaces over small number fields and Kummer constructions in families
Stefan Schr\"oer
https://arxiv.org/abs/2506.14732 https://

K3 surfaces over small number fields and Kummer constructions in families
We construct K3 surfaces over number fields that have good reduction everywhere. These do not exists over the rational numbers, by results of Abrashkin and Fontaine. Our surfaces exist for three quadratic number fields, and an infinite family of $S_3$-number fields. To this end we develop a theory of Kummer constructions in families, based on Romagny's notion of the effective models, here applied to sign involutions. This includes quotients of non-normal surfaces by infinitesimal group schemes …

The G-Gromov-Hausdorff Distance and Equivariant Topology
Sunhyuk Lim, Facundo Memoli
https://arxiv.org/abs/2506.15414 https://arxiv.o…

The G-Gromov-Hausdorff Distance and Equivariant Topology
For an arbitrary finite group G, we consider a suitable notion of Gromov Hausdorff distance between compact G-metric spaces and derive lower bounds based on equivariant topology methods. As applications, we prove equivariant rigidity and finiteness theorems, and obtain sharp bounds on the Gromov Hausdorff distance between spheres.

⇢ The notion of “intelligence” in AI has always been very narrow, and I’d argue that even that of “general intelligence” remains a very narrow one, and like previous ideas of intelligence, it’s largely socially constructed, i.e., closely tied to a particular set of skills valued by a particular group of people.
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⇢ The notion of “intelligence” in AI has always been very narrow, and I’d argue that even that of “general intelligence” remains a very narrow one, and like previous ideas of intelligence, it’s largely socially constructed, i.e., closely tied to a particular set of skills valued by a particular group of people.
□

Beyond Universality: Cultural Diversity in Music and Its Implications for Sound Design and Sonification
Rub\'en Garc\'ia-Benito
https://arxiv.org/abs/2506.14877

Beyond Universality: Cultural Diversity in Music and Its Implications for Sound Design and Sonification
The Audio Mostly (AM) conference has long been a platform for exploring the intersection of sound, technology, and culture. Despite growing interest in sonic cultures, discussions on the role of cultural diversity in sound design and sonification remain limited. This paper investigates the implicit biases and gaps within the discourse on music and sound aesthetics, challenging the notion of music as a 'universal language'. Through a historical and cross-cultural analysis of musicology and ethno…

Percolation in the marked stationary Random Connection Model for higher-dimensional simplicial complexes
Dominik Pabst
https://arxiv.org/abs/2506.15038 htt…

Percolation in the marked stationary Random Connection Model for higher-dimensional simplicial complexes
We introduce a novel percolation model that generalizes the classical Random Connection Model (RCM) to a random simplicial complex, allowing for a more refined understanding of connectivity and emergence of large-scale structures in random topological spaces. Regarding percolation with respect to the notion of up-connectivity, we establish the existence of a sharp phase transition for the appearance of a giant component, akin to the well-known threshold behavior in random graphs. This sharp pha…

This is of historical interest on so many levels.
When the notion of AI first appeared, chess was considered the epitome of intelligence (before that it was calculating)—which, of course, it isn’t. Now AI is all about pattern recognition, which certainly covers more of what we associate with human intelligence, but go figure, it’s not *just* pattern recognition either. ⇢

Hermitian Cubic norm structures and groups of relative rank one
Michiel Smet
https://arxiv.org/abs/2506.14509 https://arxiv.org/pdf/2…

Hermitian Cubic norm structures and groups of relative rank one
Hermitian cubic norm structures were recently introduced in order to study the class of skew-dimension one structurable algebras (which are typically only defined over fields of characteristic different from $2$ and $3$) over arbitrary rings and fields. Here, we generalize the quartic norm for these algebras and show that elements for which the quartic norm is invertible are conjugate invertible. This leads to the notion of a division hermitian cubic norm structure, defined as one in which the …

A Spintronic Battery with Reversible Modulation of Spin Polarization through Li Charge/Discharge: A First Principles Computational Modelling Case Study for an Antiperovskite System
Sk Mujaffer Hossain, Vinila Bedekara, Priyanka Yadavb, Ram Janay Chudhary, Satishchandra Ogale
https://arxiv.org/abs/2506.14401

A Spintronic Battery with Reversible Modulation of Spin Polarization through Li Charge/Discharge: A First Principles Computational Modelling Case Study for an Antiperovskite System
A key notion defining the progress of the emergent fields of modern electronics, renewable energy, and smart systems is charge storage, which is primarily embodied in various battery chemistries and systems. In addition to the charge property, the electron also has the spin property, which is exploited in the field of spintronics to access novel magnetically controlled device actions that are not accessible to conventional electronics. An interesting question is whether the two can be fruitfull…

dbpedia_all: DBpedia network (v3.6)
A network among all entries in DBpedia, a project that extracts structured information from Wikipedia. Nodes represent entities in DBpedia and an edge connects two entities based on DBpedia's notion of their relatedness. The data is extracted from the version 3.6 of the database.
This network has 3966924 nodes and 13820853 edges.
Tags: Informational, Relatedness, Unweighted, Multigraph

Gradient-Normalized Smoothness for Optimization with Approximate Hessians
Andrei Semenov, Martin Jaggi, Nikita Doikov
https://arxiv.org/abs/2506.13710 http…

Gradient-Normalized Smoothness for Optimization with Approximate Hessians
In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The key innovation of our analysis is a novel notion called Gradient-Normalized Smoothness, which characterizes the maximum radius of a ball around the current point that yields a good relative approximation of the gradient field. Our theory establishes a natural …

CIRO7.2: A Material Network with Circularity of -7.2 and Reinforcement-Learning-Controlled Robotic Disassembler
Federico Zocco, Monica Malvezzi
https://arxiv.org/abs/2506.11748

CIRO7.2: A Material Network with Circularity of -7.2 and Reinforcement-Learning-Controlled Robotic Disassembler
The competition over natural reserves of minerals is expected to increase in part because of the linear-economy paradigm based on take-make-dispose. Simultaneously, the linear economy considers end-of-use products as waste rather than as a resource, which results in large volumes of waste whose management remains an unsolved problem. Since a transition to a circular economy can mitigate these open issues, in this paper we begin by enhancing the notion of circularity based on compartmental dynam…

On the notion of elementary particles on curved space-times
Alberto Ibort, Arnau Mas, Luca Schiavone
https://arxiv.org/abs/2506.14296 https://

On the notion of elementary particles on curved space-times
Wigner's program that identified elementary particles with unitary irreducible representations of Poincaré group, is extended, inspired by the modern categorical/groupoidal picture of Quantum Mechanics, to general Lorentzian space-times.

The invariant subspace problem and Rosenblum operators I
Junsheng Fang, Bingzhe Hou, Chunlan Jiang, Yuanhang Zhang
https://arxiv.org/abs/2506.15270 https:/…

The invariant subspace problem and Rosenblum operators I
Let $T\in B(\mathcal{H})$ be an invertible operator. From the 1940's, Gelfand, Hille and Wermer investigated the invariant subspaces of $T$ by analyzing the growth of $\|T^n\|$, where $n\in \mathbb{Z}$. In this paper, we study the invariant subspaces of $T$ by estimating the growth of $\|T^n+λT^{-n}\|$, where $n\in \mathbb{N}$ and $λ$ is a nonzero complex constant. The key ingredient of our approach is introducing the notion of shift representation operators, which is base…

Having an absolutely awful time with the notion that the most recent pivot/s to video are hedging the bet that people won’t be able to fucking read anymore

Affine Deformations of Divisible Convex Cones and Affine Spacetimes
Antoine Ablondi
https://arxiv.org/abs/2506.12172 https://arxiv.or…

Affine Deformations of Divisible Convex Cones and Affine Spacetimes
Given a subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})\ltimes\mathbb{R}^{d+1}$ obtained by adding a translation part to a torsion-free discrete subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})$ dividing a convex domain in the sense of Benoist, we construct two maximal convex domains on which the affine action of that subgroup is free and properly continuous. We also introduce a notion of "affine spacetime" structure, with which quotients of those domains are naturally endowed. In that setting, we show th…

Brick-splitting Torsion Pairs and Trim Lattices
Sota Asai, Osamu Iyama, Kaveh Mousavand, Charles Paquette
https://arxiv.org/abs/2506.13602 https://

Brick-splitting Torsion Pairs and Trim Lattices
We introduce the notion of brick-splitting torsion pairs as a modern analogue and generalization of the classical notion of splitting torsion pairs. A torsion pair is called brick-splitting if any given brick is either torsion or torsion-free with respect to that torsion pair. After giving some properties of these pairs, we fully characterize them in terms of some lattice-theoretical properties, including left modularity. This leads to the notion of brick-directed algebras, which are those for …

Maximal prepositive cones on quaternion algebras with involution
Andrew Leader
https://arxiv.org/abs/2506.13426 https://arxiv.org/pdf…

Maximal prepositive cones on quaternion algebras with involution
We give a description of prepositive cones -- a notion of ordering on algebras with involution introduced by Astier and Unger -- in the specific context of quaternion algebras with involution. Our main result establishes that, for a broad class of quaternion algebras with involution, every prepositive cone is maximal.

Initial ideal of a general rational or elliptic curve on quadrics
Francesca Cioffi, Davide Franco, Giovanna Ilardi
https://arxiv.org/abs/2506.12428 https:/…

Initial ideal of a general rational or elliptic curve on quadrics
Over an algebraically closed field of characteristic zero, we prove that the generic initial ideal with respect to the degree reverse lexicographic term order of a general rational or elliptic curve on quadrics is almost revlex. Following constructive arguments, our proof combines features of a pencil of quadrics, interpolation methods and the notion of double generic initial ideal.

Baffles me that Italy has adopted the US(?) notion of Outlet Malls with free buses to and fro, all to go sit in a place that is…basically what city center looks like. In the US, only malls look like this. So that they can imitate an…Italian city! #Italy25

Nonstandard methods for ultrafilter relation extensions
Leonardo Raffaello Maximilian Gasparro, Lorenzo Luperi Baglini
https://arxiv.org/abs/2506.04692 htt…

Nonstandard methods for ultrafilter relation extensions
We study two types of ultrafilter relation extensions with nonstandard methods and provide characterisations of these extensions in terms of generators of ultrafilters. These characterisations are then used to determine whether various relation properties are preserved by these extensions. Lastly, we study the notion of self-divisible ultrafilter and, with the mentioned characterizations, generalize this notion for a class of relations.

So the idea that Musk’s time in Washington is over is an obvious farce. To promulgate this notion is to be either ignorant or nefarious. The destruction that Musk set in motion remains running in the background as an ambient menace to our safety and livelihoods. Musk’s legacy is still being written.
Alex Shepard - The New Republic #USA

Elon Musk’s Reign of Terror Is Only Just Beginning
His “departure” from the government is anything but.

Combinatorial $n$-od covers of graphs
Logan C. Hoehn, Hugo Adrian Maldonado-Garcia
https://arxiv.org/abs/2506.11979 https://arxiv.org…

Combinatorial $n$-od covers of graphs
We introduce the notion of a combinatorial $n$-od cover, for $n \geq 3$, which is a tool that may be used to show that certain continua embedded in the plane are not simple $n$-od-like. Using this tool, we generalize a classic example of Ingram, and give a construction, for each $n \geq 3$, of an indecomposable plane continuum which is simple $(n+1)$-od-like but not simple $n$-od-like, and such that each non-degenerate proper subcontinuum is an arc. These examples may be compared with related c…

The double of a simplicial complex
Kathryn Lesh, Bridget Schreiner, Nathalie Wahl
https://arxiv.org/abs/2506.10436 https://arxiv.org/…

The double of a simplicial complex
We introduce the notion of doubling and r-tupling for simplicial complexes, a notion reminiscent to that of matching complexes in graph theory. We prove a connectivity result for such complexes and relate r-tupling to stabilizing r times faster in homological stability.

Here the addendum. Brown writes:
“There exists no coherent notion of what AI is or could be.”
There is in fact a perfectly coherent definition of AI — one that does not refute Brown’s point, but rather proves it.
2/

On the validity of the Radon-Nikodym Theorem
Paolo Roselli, Michel Willem
https://arxiv.org/abs/2506.12023 https://arxiv.org/pdf/2506…

On the validity of the Radon-Nikodym Theorem
This paper presents a new general formulation of the Radon-Nikodym theorem in the setting of abstract measure theory. We introduce the notion of weak localizability for a measure and show that this property is both necessary and sufficient for the validity of a Radon-Nikodym-type representation under a natural compatibility relation between measures. The proof relies solely on elementary tools, such as Markov's inequality and the monotone convergence theorem. In addition to establishing the mai…

from my link log —
A formulae-as-type notion of control: classical logic and call/cc in Scheme.
https://dl.acm.org/doi/10.1145/96709.96714
saved 2025-05-06

Fire from The Atlantic.
#USPol #Tariffs

Cartesian Forest Matching
Bastien Auvray, Julien David, Richard Groult, Thierry Lecroq
https://arxiv.org/abs/2506.02704 https://arxiv…

Cartesian Forest Matching
In this paper, we introduce the notion of Cartesian Forest, which generalizes Cartesian Trees, in order to deal with partially ordered sequences. We show that algorithms that solve both exact and approximate Cartesian Tree Matching can be adapted to solve Cartesian Forest Matching in average linear time. We adapt the notion of Cartesian Tree Signature to Cartesian Forests and show how filters can be used to experimentally improve the algorithm for the exact matching. We also show a one to one c…

Towards fault-tolerant quantum computation with universal continuous-variable gates
Sheron Blair, Francesco Arzani, Giulia Ferrini, Alessandro Ferraro
https://arxiv.org/abs/2506.13643

Towards fault-tolerant quantum computation with universal continuous-variable gates
Continuous-variable (CV) systems have shown remarkable potential for quantum computation, particularly excelling in scalability and error correction through bosonic encoding. Within this framework, the foundational notion of computational universality was introduced in [Phys. Rev. Lett. 82, 1784 (1999)], and has proven especially successful since it allows for the identification of finite sets of universal CV gates independent of the encoding scheme. However, achieving the critical objective of…

Localization sequences for logarithmic topological cyclic homology
John Rognes, Steffen Sagave, Christian Schlichtkrull
https://arxiv.org/abs/2506.08492 ht…

Localization sequences for logarithmic topological cyclic homology
We introduce the notion of an E_k-ring with prelogarithmic structure, define logarithmic topological Hochschild homology and logarithmic topological cyclic homology in this context, and establish localization sequences for these theories. Our approach is based on Thom R-algebras. It extends and strengthens our earlier work on the subject in several regards. Our examples include the fraction field of topological K-theory, the existence of which was suggested by calculations by Ausoni and the fir…

Level structures on parahoric torsors and complete integrability
Georgios Kydonakis, Lutian Zhao
https://arxiv.org/abs/2506.12302 https://

Level structures on parahoric torsors and complete integrability
For a smooth complex algebraic curve $X$ and a reduced effective divisor $D$ on $X$, we introduce a notion of $D$-level structure on parahoric $\mathcal{G}_{\boldsymbol θ}$-torsors over $X$, for any connected complex reductive Lie group $G$. A moduli space of parahoric $\mathcal{G}_{\boldsymbol θ}$-torsors equipped with a $D$-level structure is constructed and we identify a canonical moment map with respect to the action of a level group on this moduli space. This action extends to a Poisson …

Quand un 'oui' ne dit pas tout : penser au-delŠ du consentement": https://blog.rmendes.net/2025/05/31/quand-un-oui-ne-dit.html

This is of historical interest on so many levels.
When the notion of AI first appeared, chess was considered the epitome of intelligence (before that it was calculating)—which, of course, it isn’t. Now AI is all about pattern recognition, which certainly covers more of what we associate with human intelligence, but go figure, it’s not *just* pattern recognition either. ⇢

This is of historical interest on so many levels.
When the notion of AI first appeared, chess was considered the epitome of intelligence (before that it was calculating)—which, of course, it isn’t. Now AI is all about pattern recognition, which certainly covers more of what we associate with human intelligence, but go figure, it’s not *just* pattern recognition either. ⇢

Partial Redundancy in Saturation
M\'arton Hajdu, Laura Kov\'acs, Andrei Voronkov
https://arxiv.org/abs/2505.22213 https://arx…

Partial Redundancy in Saturation
Redundancy elimination is one of the crucial ingredients of efficient saturation-based proof search. We improve redundancy elimination by introducing a new notion of redundancy, based on partial clauses and redundancy formulas, which is more powerful than the standard notion: there are both clauses and inferences that are redundant when we use our notions and not redundant when we use standard notions. In a way, our notion blurs the distinction between redundancy at the level of inferences and …

This https://arxiv.org/abs/2409.11231 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Positively closed $Sh(B)$-valued models
We study positively closed and strongly positively closed topos-valued models of coherent theories. Positively closed is a global notion (it is defined in terms of all possible outgoing homomorphisms), while strongly positively closed is a local notion (it only concerns the definable sets inside the model). For $\mathbf{Set}$-valued models of coherent theories they coincide. We prove that if $\mathcal{E}=Sh(X)$ for an extremally disconnected Stone space (or equivalently $\mathcal{E}=Sh(B,τ_{…

I wish someone else would make a compelling Notion alternative because I'm tired of it being so damn buggy all the time

This https://arxiv.org/abs/2411.18970 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems
Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used frameworks such as Plug-and-Play (PnP) algorithms. In this work, we introduce Fixed-points of Restoration (FiRe) priors as a new framework for expanding the notion of priors in PnP to general restoration models beyond traditional denoising models. The key ins…

Surface Nematic Quasi-Uniformity
Andrea Pedrini, Epifanio G. Virga
https://arxiv.org/abs/2506.10795 https://arxiv.org/pdf/2506.10795

Surface Nematic Quasi-Uniformity
Line fields on surfaces are a means to describe the nematic order that may pattern them. The least distorted nematic fields are called uniform, but they can only exist on surfaces with negative constant Gaussian curvature. To identify the least distorted nematic fields on a generic surface, we relax the notion of uniformity into that of quasi-uniformity and prove that all such fields are parallel transported (in Levi-Civita's sense) by the geodesics of the surface. Both global and local constru…

Multiple mixing and fractional cohomological equation
Zhenqi Jenny Wang
https://arxiv.org/abs/2506.08392 https://arxiv.org/pdf/2506.0…

Multiple mixing and fractional cohomological equation
We introduce the notion of the (multiple) fractional cohomological equation and, by studying its solutions, develop a novel framework to obtain the decay of matrix coefficients for partially hyperbolic algebraic actions. In particular, we show that mere partial Hölder regularity of \(L^2\) vectors is sufficient for exponential decay of matrix coefficients. As an application, under the assumption of ergodicity, we obtain explicit and sharp exponential mixing rates of all orders for a large cl…

Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space
Minh Ha Quang, Frank Nielsen
https://arxiv.org/abs/2506.10494 https://

Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space
This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures equivalent to a fixed one, we present a closed form expression for this divergence that directly generalizes the finite-dimensional version. Using the notion of Log-Determinant divergences between positive definite unitized trace class operators, we then define a…

The building blocks of asymptotically flat spacetimes
Shadi Ali Ahmad
https://arxiv.org/abs/2506.11190 https://arxiv.org/pdf/2506.111…

The building blocks of asymptotically flat spacetimes
The classification of all possible induced representations arising from theories admitting a Poincaré symmetry has molded our very conception of particles in flat space. In this note, we argue that if one takes the same viewpoint on the asymptotic symmetry group instead of the global one, the familiar relativistic classification is enhanced to provide a new notion of excitations in asymptotically flat spacetimes. These excitations blur the line between the quantum description of a particle and…

This https://arxiv.org/abs/2312.09214 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Shifted coisotropic structures for differentiable stacks
We introduce a notion of coisotropics on 1-shifted symplectic Lie groupoids (i.e. quasi-symplectic groupoids) using twisted Dirac structures and show that it satisfies properties analogous to the corresponding derived-algebraic notion in shifted Poisson geometry. In particular, intersections of 1-coisotropics are 0-shifted Poisson. We also show that 1-shifted coisotropic structures transfer through Morita equivalences, giving a well-defined notion for differentiable stacks. Most results are for…

On Levi operators between normed and vector lattices
Eduard Emelyanov
https://arxiv.org/abs/2506.12578 https://arxiv.org/pdf/2506.125…

On Levi operators between normed and vector lattices
The notion of Levi operator is an operator abstraction of the Levy property of a norm. Various aspects of Levi operators have been studied recently by several authors. The present paper is devoted to Levi operators from a normed lattice to a vector lattice. It is proved that every finite rank operator is a Levi operator. An example is given showing that the sum of a positive rank one operator and a positive compact Levi operator need not to be a Levi operator. We prove that every quasi Levi ope…

A valuative approach to the anticanonical minimal model program
Sung Rak Choi, Sungwook Jang, Donghyeon Kim, Dae-Won Lee
https://arxiv.org/abs/2506.13637 h…

A valuative approach to the anticanonical minimal model program
In this paper, we show that the log canonical threshold of a potentially klt triple can be computed by a quasi-monomial valuation. The notion of potential triples provides a larger and more flexible framework to work with than that of generalized pairs. Our main result can be considered as an extension to the result of Xu on klt pairs. As an application of the main result, we show that we can run the MMP on any potentially klt triples and $-(K_X+Δ)$-MMP on the potentially klt pairs.

Peak algebra in noncommuting variables
Farid Aliniaeifard, Shu Xiao Li
https://arxiv.org/abs/2506.12868 https://arxiv.org/pdf/2506.12…

Peak algebra in noncommuting variables
The well-known descent-to-peak map $Θ_{\mathrm{QSym}}$ for the Hopf algebra of quasisymmetric functions, $\mathrm{QSym}$, and the peak algebra $Π$ were originally defined by Stembridge in 1997. We define the labelled descent-to-peak map $Θ_{\mathrm{NCQSym}}$ and extend the notion of the peak algebra to noncommuting variables. Moreover, we define Schur $Q$-functions in noncommuting variables having properties analogous to the classical Schur $Q$-functions.

Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature
Christina Sormani, Wenchuan Tian, Wai-Ho Yeung
https://arxiv.org/abs/2506.12491

Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature
In 2014, Gromov conjectured that sequences of manifolds with nonnegative scalar curvature should have subsequences which converge in some geometric sense to limit spaces with some notion of generalized nonnegative scalar curvature. In recent joint work with Changliang Wang, the authors found a sequence of warped product Riemannian metrics on $\Sph^2\times \Sph^1$ with nonnegative scalar curvature whose metric tensors converge in the $W^{1,p}$ sense for $p<2$ to an extreme warped product limit s…

Some functor calculus on semirings
Pronay Biswas, Amartya Goswami, Sujit Kumar Sardar
https://arxiv.org/abs/2506.13378 https://arxiv.…

Some functor calculus on semirings
We develop a functorial framework for the ideal theory of commutative semirings using coherent frames and spectral spaces. Two central constructions-the radical ideal functor and the $k$-radical ideal functor-are shown to yield coherent frames, with the latter forming a dense sublocale of the former. We define a natural transformation between these functors and analyze their categorical and topological properties. Further, we introduce a notion of support that assigns to each semiring a bound…

Here the addendum. Brown writes:
“There exists no coherent notion of what AI is or could be.”
There is in fact a perfectly coherent definition of AI — one that does not refute Brown’s point, but rather proves it.
2/

Gluing topological graph C*-algebras
Atul Gothe, John Quigg, Mariusz Tobolski
https://arxiv.org/abs/2506.11592 https://arxiv.org/pdf/…

Gluing topological graph C*-algebras
We introduce regular closed subgraphs of Katsura's topological graphs and use them to generalize the notion of an adjunction space from topology. Our construction attaches a topological graph onto another via a regular factor map. In our main theorem, we prove that under suitable assumptions the C*-algebra of the adjunction graph is a pullback of the C*-algebras of the topological graphs being glued. It generalizes (and slightly improves) the pushout-to-pullback theorem proved in the context of…

Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space
Prasenjit Ghosh, Jayanta Ghosh, T. K. Samanta
https://arxiv.org/abs/2506.12049 https://…

Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space
Atomic system in fuzzy Hilbert space is introduced and the existence of the fuzzy atomic systems for a strongly fuzzy bounded linear operator is studied. The notion of a K-frame in fuzzy Hilbert space is presented and some of their characterizations are given. We will see that fuzzy frame operator of a fuzzy K-frame in fuzzy Hilbert space is invertible under some sufficient condition and validates this by giving some examples. Fuzzy K-frame property in fuzzy Hilbert space preserve by a strongly…

Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent
Souvik Bhowmick, Sekhar Ghosh, Vishvesh Kumar
https://arxiv.org/abs/2506.11832

Infinitely many solutions for nonlinear superposition operators of mixed fractional order involving critical exponent
This paper addresses elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in sublinear regimes. We establish the existence of infinitely many nontrivial weak solutions using a variational framework that combines a truncation argument with the notion of genus. A central part of our analysis is the verification of the Palais--Smale $(\mathrm{PS})_c$ condition for every $q \in (1, p_{s_\sharp}^*)$, despite the challenges posed by the la…

Bubbling of rank two bundles over surfaces
Xuemiao Chen
https://arxiv.org/abs/2506.09614 https://arxiv.org/pdf/2506.09614

Bubbling of rank two bundles over surfaces
In this paper, motivated by the singularity formation of ASD connections in gauge theory, we study an algebraic analogue of the singularity formation of families of rank two holomorphic vector bundles over surfaces. For this, we define a notion of fertile families bearing bubbles and give a characterization of it using the related discriminant. Then we study families that locally form the singularity of the type $\mathcal{O}\oplus \mathcal{I}$ where $\mathcal{I}$ is an ideal sheaf defining poin…

This https://arxiv.org/abs/2412.12921 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Equivariant and Invariant Parametrized Topological Complexity
For a $G$-equivariant fibration $p \colon E\to B$, we introduce and study the invariant analogue of Cohen, Farber and Weinberger's parametrized topological complexity, called the invariant parametrized topological complexity. This notion generalizes the invariant topological complexity introduced by Lubawski and Marzantowicz. We establish the equivariant fibrewise homotopy invariance of this notion and derive several bounds, including a cohomological lower bound and a dimensional upper bound. A…

Achieving Equitability with Subsidy
Yuanyuan Wang, Tianze Wei
https://arxiv.org/abs/2505.23251 https://arxiv.org/pdf/2505.23251

Achieving Equitability with Subsidy
We study the fair allocation problem of indivisible items with subsidies. In this paper, we mainly consider the notion of fairness - equitability (EQ), which requires that items be allocated such that all agents value the bundle they receive equally. Firstly, we study the upper bounds of the required subsidy to achieve EQ in different settings of items and provide the corresponding lower bounds. Secondly, we consider the bounded subsidy for achieving EQ and another popular notion of fairness - …

Axioms of Quantum Mechanics in light of Continuous Model Theory
Boris Zilber
#toXiv_bot_toot

This https://arxiv.org/abs/2505.00338 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

New Distributed Interactive Proofs for Planarity: A Matter of Left and Right
We provide new distributed interactive proofs (DIP) for planarity and related graph families. The notion of a \emph{distributed interactive proof} (DIP) was introduced by Kol, Oshman, and Saxena (PODC 2018). In this setting, the verifier consists of $n$ nodes connected by a communication graph $G$. The prover is a single entity that communicates with all nodes by short messages. The goal is to verify that the graph $G$ satisfies a certain property (e.g., planarity) in a small number of rounds, …

Geometric effects of hyperbolic cohomology classes on K\"ahler manifolds
Francesco Bei, Simone Diverio, Stefano Trapani
https://arxiv.org/abs/2506.09907

Geometric effects of hyperbolic cohomology classes on Kähler manifolds
We introduce the notion of Kähler topologically hyperbolic manifold, as a"topological" generalization of Kähler [Gro91] and weakly Kähler [BDET24] hyperbolic manifolds. Analogously to [BCDT24], we show the birational invariance of this property and then that Kähler topologically hyperbolic manifolds are not uniruled nor bimeromorphic to compact Kähler manifolds with trivial first real Chern class. Then, we prove spectral gap theorems for positive holomorphic Hermitian vector bundles on Kä…

Conclusive Local State Marking: More Nonlocality With No Entanglement
Samrat Sen
https://arxiv.org/abs/2506.09415 https://arxiv.org/p…

Conclusive Local State Marking: More Nonlocality With No Entanglement
Nonlocality exhibited by ensembles of composite quantum states, wherein local operations and classical communication (LOCC) yield suboptimal discrimination probabilities compared to global strategies, is one of the striking nonclassical features of quantum theory. A variant of this phenomenon arises in conclusive local state discrimination, where the correct state must be identified with zero error, albeit allowing for inconclusive outcomes. More recently, the notion of local state marking has …

This https://arxiv.org/abs/2503.12700 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Schur Rank, Compatibility Degree, and Canonical Decomposition
The notion of denominator vectors can be extended to all generic basis elements of upper cluster algebras in a natural way. Under a weakened version of generic pairing assumption, we provide a representation-theoretic interpretation for this extended notion. We derive several consequences in this generality. We present a counterexample to the conjecture that distinct cluster monomials have distinct denominator vectors. Utilizing a new rank function called the Schur rank, we extend the notion of…

Swap Kripke models for deontic LFIs
Mahan Vaz, Marcelo E. Coniglio
https://arxiv.org/abs/2506.06181 https://arxiv.org/pdf/2506.06181

Swap Kripke models for deontic LFIs
We present a construction of nondeterministic semantics for some deontic logics based on the class of paraconsistent logics known as Logics of Formal Inconsistency (LFIs), for the first time combining swap structures and Kripke models through the novel notion of swap Kripe models. We start by making use of Nmatrices to characterize systems based on LFIs that do not satisfy axiom (cl), while turning to RNmatrices when the latter is considered in the underlying LFIs. This paper also presents, for…

This https://arxiv.org/abs/2410.17407 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Morita theory for dynamical von Neumann algebras
Given a locally compact quantum group $\mathbb{G}$ and two $\mathbb{G}$-$W^*$-algebras $α: A\curvearrowleft \mathbb{G}$ and $β: B\curvearrowleft \mathbb{G}$, we study the notion of equivariant $W^*$-Morita equivalence $(A, α)\sim_{\mathbb{G}} (B, β)$, which is an equivariant version of Rieffel's notion of $W^*$-Morita equivalence. We prove that important dynamical properties of $\mathbb{G}$-$W^*$-algebras, such as (inner) amenability, are preserved under equivariant Morita equivalence. For …

Study of $p^{k}$-Eulerian polynomials and $p^{k}$-Fibonacci numbers for every odd prime $p$ and $k\geq0$
M. Parvathi, A. Tamilselvi, D. Hepsi
https://arxiv.org/abs/2506.09941

Study of $p^{k}$-Eulerian polynomials and $p^{k}$-Fibonacci numbers for every odd prime $p$ and $k\geq0$
In this paper, we define the notion of descent for the paths in the $p$-Bratteli diagram. This leads to the definition of $p^{k}$-Eulerian polynomials, whose coefficients count the number of paths with a given number of descents. We provide a method for constructing the $p^{k}$-Eulerian polynomials at each vertex. Furthermore, we compute the total number of descents of all paths ending at a given vertex as the corresponding $p^{k}$-Fibonacci numbers. We show that the derivative of the $p^{k}$-E…

Metric functionals and weak convergence
Armando W. Guti\'errez, Olavi Nevanlinna
https://arxiv.org/abs/2506.04154 https://arxiv.o…

Metric functionals and weak convergence
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When restricted to bounded sequences in normed linear spaces, we prove that our notion of weak convergence agrees with the standard one.

A necessary condition for liftings of positive characteristic varieties with finite fundamental groups
Ruida Di, Runjie Hu, Siqing Zhang
https://arxiv.org/abs/2506.07914

A necessary condition for liftings of positive characteristic varieties with finite fundamental groups
In this paper, we introduce a necessary condition for the existence of characteristic zero liftings of certain smooth, proper varieties in positive characteristic, using étale homotopy theory and Wall's finiteness obstruction. For a variety with finite étale fundamental group pi, we define a notion of mod-l finite dominatedness based on the F_l-chain complex of the universal cover of its l-profinite étale homotopy type. We prove that such a variety can be lifted to characteristic zero only i…

Redefining Functionality and Construction-Defining Capacity: Functions as Principles of Syntactic and Semantic Generation
Yumiko Nishiyama
https://arxiv.org/abs/2506.04278

Redefining Functionality and Construction-Defining Capacity: Functions as Principles of Syntactic and Semantic Generation
This study redefines the notion of functionality-traditionally understood as a property of mappings or structure preservation-from a more fundamental and generative perspective. Introducing the concept of a Construction-Defining function (CDF), we formalize functionality as a dual capacity to generate both syntactic terms and semantic interpretations. We provide an explicit axiomatization of CDF based on syntactic generativity and semantic compositionality, and further construct categorical mod…

This https://arxiv.org/abs/2412.11528 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Water Cells in Compositions of 1s and 2s
Mansour and Shattuck introduced the notion of water cells for integer compositions in 2018. We focus on compositions with parts restricted to 1 and 2 and consider the array of counts for such compositions of $n$ with $k$ water cells, establishing generating functions for the columns and diagonal sums, recurrences within the array in the spirit of Pascal's lemma, and connections to other restricted compositions. Most of our proofs are combinatorial, but we also make connections to Riordan arrays.

Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements
Jose Bastidas, Sarah Brauner, Mathieu Guay-Paquet, Alejandro H. Morales, GaYee Park, Franco Saliola
https://arxiv.org/abs/2506.08883

Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements
Given a permutation, there is a well-developed literature studying the number of ways one can factor it into a product of other permutations subject to certain conditions. We initiate the analogous theory for the type A Iwahori-Hecke algebra by generalizing the notion of factorization in terms of the Jucys-Murphy elements. Some of the oldest and most foundational factorization results for the symmetric groups pertain to the long cycle. Our main results give q-deformations of these long cycle fa…

On Symbol Elimination and Uniform Interpolation in Theory Extensions
Viorica Sofronie-Stokkermans
https://arxiv.org/abs/2506.01664 https://

On Symbol Elimination and Uniform Interpolation in Theory Extensions
We define a notion of general uniform interpolant, generalizing the notions of cover and of uniform interpolant and identify situations in which symbol elimination can be used for computing general uniform interpolants. We investigate the limitations of the method we propose, and identify theory extensions for which the computation of general uniform interpolants can be reduced to symbol elimination followed by the computation of uniform quantifier-free interpolants in extensions with uninterpr…

Algebraic Geometry of Cactus, Pascal, and Pappus Matroids
Emiliano Liwski, Fatemeh Mohammadi, Lisa Vandebrouck
https://arxiv.org/abs/2506.07757 https://

Algebraic Geometry of Cactus, Pascal, and Pappus Matroids
We study rank-three matroids, known as point-line configurations, and their associated matroid varieties, defined as the Zariski closures of their realization spaces. Our focus is on determining finite generating sets of defining equations for these varieties, up to radical, and describing the irreducible components of the corresponding circuit varieties. We generalize the notion of cactus graphs to matroids, introducing a family of point-line configurations whose underlying graphs are cacti. O…