Tootfinder

Three Generalizations of Erd\H{o}s Szekeres: $k$-Modal Subsequences
Charles Gong
https://arxiv.org/abs/2508.20360 https://arxiv.org/pdf/2508.20360

Three Generalizations of Erdős Szekeres: $k$-Modal Subsequences
Erdős and Szekeres showed that given a permutation $p$ of $[n]$, and the sequence defined by \newline $(p(1), p(2), \ldots, p(n))$, there exists either a decreasing or increasing subsequence, not necessarily contiguous, of length at least $\sqrt{n}$. Fan Chung considered subsequences that can have at most one change of direction, i.e. an increasing and then decreasing subsequence, or a decreasing and then increasing subsequence. She called these unimodal subsequences, and showed there exists a…

"..that old web, the small web, the indie web, whatever you want to call it, it still exists, it will still exist! People haven't stopped making websites, people haven't stopped blogging earnestly (i.e. not just for ad views), they (we) are still out there! Posting away on our little web sites, not really caring that we don't get a lot of traffic.."
Great piece by @…

the web as a space to be explored · roytang.net

Toroidal graph manifolds with small homology are not SU(2)-abelian
Giacomo Bascape
https://arxiv.org/abs/2506.21729 https://arxiv.org…

Toroidal graph manifolds with small homology are not SU(2)-abelian
We show that if $Y$ is a toroidal closed graph manifold rational homology $3$-sphere with $|H_1(Y;\mathbb{Z})| \le 5$, then there exists an irreducible representation $\fund{Y} \to SU(2)$. This answers positively to a conjecture by Baldwin and Sivek in the case of graph manifolds.

Equivalence via surjections
Tom Leinster
https://arxiv.org/abs/2508.20555 https://arxiv.org/pdf/2508.20555

Equivalence via surjections
Many types of categorical structure obey the following principle: the natural notion of equivalence is generated, as an equivalence relation, by identifying $A$ with $B$ when there exists a strictly structure-preserving map $A \to B$ that is genuinely (not just essentially) surjective in each dimension and faithful in the top dimension. We prove this principle for four types of structure: categories, monoidal categories, bicategories and double categories. The last of these theorems suggests th…

from my link log —
Three cases against IF NOT EXISTS / IF EXISTS in PostgreSQL DDL.
https://postgres.ai/blog/20211103-three-cases-against-if-not-exists-and-if-exists-in-postgresql-ddl
saved 2021-11-12

Three Cases Against IF NOT EXISTS / IF EXISTS in Postgres DDL | Postgres AI

What is this about?

Many DDL statements in PostgreSQL support modified IF EXISTS / IF NOT EXISTS. For example:

 test=# create table if not exists mytable(); CREATE TABLE test=# drop table if exists mytable; DROP TABLE 

I recommend using `IF EXISTS` / `IF NOT EXISTS`…

Swan modules and homotopy types after a single stabilisation
Tommy Hofmann, John Nicholson
https://arxiv.org/abs/2507.21975 https://arxiv.org/pdf/2507.2197…

Swan modules and homotopy types after a single stabilisation
We study Swan modules, which are a special class of projective modules over integral group rings, and their consequences for the homotopy classification of CW-complexes. We show that there exists a non-free stably free Swan module, thus resolving Problem A4 in the 1979 Problem List of C. T. C. Wall. As an application we show that, in all dimensions $n \equiv 3$ mod $4$, there exist finite $n$-complexes which are homotopy equivalent after stabilising with multiple copies of $S^n$, but not after …

A Late-Time Rise in Planet Occurrence Reproduces the Galactic Height Trend in Planet Occurrence
Christopher Lam, Sarah Ballard, Sheila Sagear, Kathryne J. Daniel
https://arxiv.org/abs/2507.21250

A Late-Time Rise in Planet Occurrence Reproduces the Galactic Height Trend in Planet Occurrence
While stellar metallicity has long been known to correlate with planetary properties, the galactic metallicity gradient alone does not account for the trend. It is therefore possible that there exists some time-dependent component to planet occurrence in the Milky Way over Gyr timescales, driven by something other than the metal enrichment of the ISM. In this paper, we investigate the observable effect of a time-dependent planet occurrence rate upon a Kepler-like sample of stars. Using a novel …

Smith normal forms of bivariate polynomial matrices
Dong Lu, Dingkang Wang, Fanghui Xiao, Xiaopeng Zheng
https://arxiv.org/abs/2507.20889 https://arxiv.org…

Smith normal forms of bivariate polynomial matrices
In 1978, Frost and Storey asserted that a bivariate polynomial matrix is equivalent to its Smith normal form if and only if the reduced minors of all orders generate the unit ideal. In this paper, we first demonstrate by constructing an example that for any given positive integer s with s >= 2, there exists a square bivariate polynomial matrix M with the degree of det(M) in y equal to s, for which the condition that reduced minors of all orders generate the unit ideal is not a sufficient condit…

Oof. #OpenStreetMap minutely replication is currently broken: https://community.openstreetmap.org/t/131884
For me this means that recent edits I made are not queryable via O…

Is OSM partially down? New data isn't able to be queried on the map, and new data isn't being rendered
I’m finding that I can pull data into JOSM and iD that I know exists (due to recently pushed edits), but a query on the map doesn’t list them (not to mention that they also aren’t being rendered; however, when something’s awaiting rendering, I always, at least by my experience, can still query it). For example, this query should list building=toilets, but it doesn’t. If I edit that location in iD I can see the aforementioned feature, and I can also pull it into JOSM, but it isn’t b…

Strict Comparisons of Infinite Utility Streams
Michael Greinecker, Michael Nielsen
https://arxiv.org/abs/2507.20567 https://arxiv.org/pdf/2507.20567…

Strict Comparisons of Infinite Utility Streams
There exists a preference relation on infinite utility streams that does not discriminate between different periods, satisfies the Pareto criterion, and so that almost all pairs of utility streams are strictly comparable. Such a preference relation provides a counterexample to a claim in [Zame, William R. ``Can intergenerational equity be operationalized?'' Theoretical Economics 2.2 (2007): 187-202.]

Poset saturation of unions of chains
Shengjin Ji, Bal\'azs Patk\'os, Erfei Yue
https://arxiv.org/abs/2505.23128 https://arxiv…

Poset saturation of unions of chains
A family $\mathcal{G}$ of sets is a(n induced) copy of a poset $P=(P,\leqslant)$ if there exists a bijection $b:P\rightarrow \mathcal{G}$ such that $p\leqslant q$ holds if and only if $b(p)\subseteq b(q)$. The induced saturation number sat$^*(n,P)$ is the minimum size of a family $\mathcal{F}\subseteq 2^{[n]}$ that does not contain any copy of $P$, but for any $G\in 2^{[n]}\setminus \mathcal{F}$, the family $\mathcal{F}\cup \{G\}$ contains a copy of $P$. We consider sat$^*(n,P)$ for posets $P$ …

Fresh from intimidating ABC and CBS with meritless lawsuits,
Donald Trumpis suing Rupert Murdoch and the Wall Street Journal reporters who broke the story of a lewd birthday message for Jeffrey Epstein.
But, unlike with the frivolous allegations against the big broadcasters,
there’s clearly a fact of the matter here:
an authentic letter either exists or it does not;
-- and there is plenty to be revealed in the process of finding out.
Trump’s time-proven …

On two maximally entangled couples
Felix Huber, Jens Siewert
https://arxiv.org/abs/2506.21282 https://arxiv.org/pdf/2506.21282…

On two maximally entangled couples
In a seminal article, Higuchi and Sudbery showed that a pure four-qubit state can not be maximally entangled across every bipartition. Such states are now known as absolutely maximally entangled (AME) states. Here we give a series of old and new proofs of the fact that no four-qubit AME state exists. These are based on invariant theory, methods from coding theory, and basic properties from linear algebra such as the Pauli commutation relations.

General Strong Bound on the Uncrossed Number which is Tight for the Edge Crossing Number
Gaspard Charvy, Tom\'a\v{s} Masa\v{r}\'ik
https://arxiv.org/abs/2507.20937 https…

General Strong Bound on the Uncrossed Number which is Tight for the Edge Crossing Number
We investigate a very recent concept for visualizing various aspects of a graph in the plane using a collection of drawings introduced by Hliněný and Masařík [GD 2023]. Formally, given a graph $G$, we aim to find an uncrossed collection containing drawings of $G$ in the plane such that each edge of $G$ is not crossed in at least one drawing in the collection. The uncrossed number of $G$ ($unc(G)$) is the smallest integer $k$ such that an uncrossed collection for $G$ of size $k$ exists. The …

Listening to part 4, Beer brings up an interesting point. Ashby's Law of Requisite Variety proposes that, for all humans, there exists a maximum complexity that can be understood.
Beer suggests that we may not even be able to understand our own modern lives (this is from 1977). I wonder if we might think of conspiracy theories as a mechanism to decrease variety within models that have internal contradictions.

Disentangling tensor product structures
Antoine Soulas
https://arxiv.org/abs/2506.21173 https://arxiv.org/pdf/2506.21173

Disentangling tensor product structures
As a contribution to the field of quantum mereology, we study how a change of tensor productstructure in a finite-dimensional Hilbert space affects its entanglement properties. In particular, we askwhether, given a time-evolving state, there exists a tensor product structure in which no entanglementis generated. We give a concrete, constructive example of disentangling tensor product structure in thecase of a C-NOT gate evolution between two qbits, before showing that this cannot be achieved fo…

“zpool import -FX” is not my favorite command. But when the hosting system panics and leaves the virtual devices backing a FreeBSD VM’s zfs filesystem in an inconsistent state, I'm sure glad it exists.
(I do have hourly zfs snapshots mirrored to a different system that I could restore from if necessary, which comforts me in situations like this. But it's nice not to have to roll back by even a few minutes, other than for the few affected files identified by “zpool scrub” checks…

We’re on a terrible path that we aren’t even aware exists: collapsing the marine food chain.
The End Permian event did that. It was ugly. Lots of fungal spores in the fossil record, not a lot of bones. Barely anything survived.
We’re having issues with phytoplankton in the #GreatLakes too. Invasive mussels have done huge damage to how the food chain (Esp. in

Phytoplankton, key to ocean life, falling 2% per year in North Atlantic
Two main types of phytoplankton have been decreasing in biomass in the North Atlantic by two per cent each year for the past 60 years, a new study …

Asymptotic stability of solutions to semilinear evolution equations in Banach spaces
Francesco Cellarosi, Anirban Dutta, Giusy Mazzone
https://arxiv.org/abs/2506.21437

Asymptotic stability of solutions to semilinear evolution equations in Banach spaces
We prove a new linearization principle for the nonlinear stability of solutions to semilinear evolution equations of parabolic type. We assume that the set of equilibria forms a finite dimensional manifold of normally stable and normally hyperbolic equilibria. In addition, we assume that the linearized operator is the generator of an analytic semigroup (not necessarily stable). We show that if a mild solution to our evolution equation exists globally in time and remains ``close'' to the manifol…

Stabbing Faces By a Convex Curve
David Eppstein
https://arxiv.org/abs/2508.17549 https://arxiv.org/pdf/2508.17549…

Stabbing Faces By a Convex Curve
We prove that, for every plane graph $G$ and every smooth convex curve $C$ not on a single line, there exists a straight-line drawing of $G$ for which every face is crossed by $C$.

Odd relaxation in three-dimensional Fermi liquids
Seth Musser, Sankar Das Sarma, Johannes Hofmann
https://arxiv.org/abs/2508.18342 https://arxiv.org/pdf/25…

Odd relaxation in three-dimensional Fermi liquids
Recent theoretical works predict a hierarchy of long-lived, non-hydrodynamic modes in two-dimensional Fermi liquids arising from the feature -- supposedly unique to two dimensions -- that relaxation by head-on scattering is not efficient in the presence of Pauli blocking. This leads to a parity-based separation of scattering rates, with odd-parity modes relaxing much more slowly than even-parity ones. In this work, we establish that a similar effect exists in isotropic three-dimensional Fermi l…

Static Spherical Vacuum Solution to Bumblebee Gravity with Time-like VEVs
Hao Li, Jie Zhu
https://arxiv.org/abs/2506.17957 https://ar…

Static Spherical Vacuum Solution to Bumblebee Gravity with Time-like VEVs
The static spherical vacuum solution in a bumblebee gravity model where the bumblebee field \(B_μ\) has a time-like vacuum expectation value \(b_μ\) is studied. We show that in general curved spacetime solutions are not allowed and only the Minkowski spacetime exists. However, it is surprising that a non-trivial solution can be obtained so long as a unique condition for the vacuum expectation \(b^2\equiv -b^μb_μ=2/κ\), where \(κ=8πG\) is satisfied. We argue that naturally this solution i…

PasteTrace: A Single Source Plagiarism Detection Tool For Introductory Programming Courses
Jesse McDonald, Scott Robertson, Anthony Peruma
https://arxiv.org/abs/2506.17355

PasteTrace: A Single Source Plagiarism Detection Tool For Introductory Programming Courses
Introductory Computer Science classes are important for laying the foundation for advanced programming courses. However, students without prior programming experience may find these courses challenging, leading to difficulties in understanding concepts and engaging in academic dishonesty such as plagiarism. While there exists plagiarism detection techniques and tools, not all of them are suitable for academic settings, especially in introductory programming courses. This paper introduces PasteT…

War is an unconscionable horror. The illusions of "international law" and "rules of war" have lead us to believe that war can be clean, managed, and "civilized."
But wars are fought by humans and humans are messy. Humans are not well suited to following orderly rules. Humans respond to their environment. Humans in extraordinary situations can be extraordinarily vindictive and brutal. Sufficiently traumatized humans can act without a conscience, spreading trauma like an infection. If humans respond to their situation, then there can be no "civilized" war because war is itself an situation outside of the society. It is a place that promotes antisocial behavior and punishes pro-social behavior. War cannot be expected to follow "international law" because it is what fills the void created by the failure of "international law" (so long as we rely on nations).
To call for war is to inflict atrocities on civilians. It is to kill the parents and children who serve, and to destroy the combatants who survive. It is to infect both sides with a trauma that will spread if untreated, when soldiers come home or when they become mercenaries in other wars.
And yet... there are times when the brutality, the incompetence, the evil becomes so unbearable that no other option exists, when taking up arms is simply bringing symmetry to an existing asymmetric conflict. There are times when the worst possible thing is inescapable, though it can never be justified.
In this new era of war, in the scramble of conflict under the collapsing of the (poorly named) "Pax Americana," I hope that we, the people, can understand that war is not a tool to fulfill an objective. It is not part of a larger strategy. It is not an extension of deplomacy.
War is a failure.
While it may be the only way to deal with the irrational - the genocidal, the slaver, the dictator - it is still a failure. It is a failure to build a world in which these people can't control armies and economies, can't turn populations in to cults and bend nations to their will.
And we will continue to have such wars until we unite against those who would use as as pawns, who would control our lives and lead us to our deaths. We will have these wars until we unite, as one world, against those rulers. This is what I mean, and what a lot of other people mean, when we say, "No War, but Class War."

Iced tea - that is, cold tea, not some sweet schlock in a can or powder containing who knows what mixed with water - is why summer exists.

A non-computable c.e. closed subset of $[0,1]$
Serikzhan Badaev, Nikolay Bazhenov, Sergey Goncharov, Birzhan Kalmurzayev, Alexander Melnikov
https://arxiv.org/abs/2508.06187 htt…

A non-computable c.e. closed subset of $[0,1]$
We prove that there exists a $Σ^0_1$ closed subset of $[0,1]$ that is not homeomorphic to any computably compact space. We show that the index set of c.e. subspaces of $[0,1]$ that admit a computably compact presentation is not arithmetical, as witnessed by subsets of $[0,1]$. The index set result is new for computable Polish spaces in general, not only for those realised as c.e. closed subsets of $[0,1]$.

To add a single example here (feel free to chime in with your own):
Problem: editing code is sometimes tedious because external APIs require boilerplate.
Solutions:
- Use LLM-generated code. Downsides: energy use, code theft, potential for legal liability, makes mistakes, etc. Upsides: popular among some peers, seems easy to use.
- Pick a better library (not always possible).
- Build internal functions to centralize boilerplate code, then use those (benefits: you get a better understanding of the external API, and a more-unit-testable internal code surface; probably less amortized effort).
- Develop a non-LLM system that actually reasons about code at something like the formal semantics level and suggests boilerplate fill-ins based on rules, while foregrounding which rules it's applying so you can see the logic behind the suggestions (needs research).
Obviously LLM use in coding goes beyond this single issue, but there are similar analyses for each potential use of LLMs in coding. I'm all cases there are:
1. Existing practical solutions that require more effort (or in many cases just seem to but are less-effort when amortized).
2. Near-term researchable solutions that directly address the problem and which would be much more desirable in the long term.
Thus in addition to disastrous LLM effects on the climate, on data laborers, and on the digital commons, they tend to suck us into cheap-seeming but ultimately costly design practices while also crowding out better long-term solutions. Next time someone suggests how useful LLMs are for some task, try asking yourself (or them) what an ideal solution for that task would look like, and whether LLM use moves us closer to or father from a world in which that solution exists.

Gawd the Thunderbird people have really scrod the pooch when it comes to vectoring incoming (or marked) gunk to a spam folder.
Thunderbird (141.0 on MacOS) now insists on using a "Junk" folder, whether that exists or not. And even if one tries to override that T-bird puts it back to "Junk".
I guess the new slogan at Thunderbird is "If it worked, break it".
Thunderbird is certainly trying to circle the drain, as is Firefox.
Oh, and I woul…

Failure of flatness over finite-dimensional Hopf subalgebras
Serge Skryabin
https://arxiv.org/abs/2506.16292 https://arxiv.org/pdf/25…

Failure of flatness over finite-dimensional Hopf subalgebras
It is proved in this paper that for any finite-dimensional nonsemisimple Hopf algebra $A$ there exists a Hopf algebra $H$ containing $A$ as a Hopf subalgebra such that $H$ is not flat over $A$. On the other hand, there is a class of infinite-dimensional Hopf algebras with the property that all Hopf algebras without exception are faithfully flat modules over Hopf subalgebras from this class.

Data Verbalisation: What is Text Doing in a Data Visualisation?
Paul Murrell
https://arxiv.org/abs/2506.15129 https://arxiv.org/pdf/2…

Data Verbalisation: What is Text Doing in a Data Visualisation?
This article discusses the role that text elements play in a data visualisation. We argue that there is a need for a simple, coherent explanation of text elements similar to the understanding that already exists for non-text elements like bars, points, and lines. We explore examples of how text is used within a data visualisation and use existing knowledge and assessment techniques to evaluate when text is effective and when it is not. The result is a framework that aims to be easy to understan…

Classical analog of the T. D. Lee model for renormalization
K. Xu, C. P. Sun
https://arxiv.org/abs/2506.15161 https://arxiv.org/pdf/2…

Classical analog of the T. D. Lee model for renormalization
While divergence and renormalization of physical quantities are frequently encountered in quantum field theory (QFT), they are not necessarily quantum-specific characteristics. We show in this paper that there exists a classical counterpart of the Lee model which is the model of coupled harmonic oscillators (CHO). It is demonstrated that the frequency divergence in this classical model precisely replicates the phenomenon of mass divergence in the Lee model, as does the corresponding renormaliza…

@… @… it’s the next sentence that intrigues me now.
If we don’t need to remove the content, just not use an algorithm to show it to children in a “feed”, then the content still exists, is still indexable etc.
Non…

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 …

Minimal sofic shift on a group that is not finitely-generated
Ville Salo
https://arxiv.org/abs/2507.06599 https://arxiv.org/pdf/2507.…

Minimal sofic shift on a group that is not finitely-generated
We prove that there exists a group which is not finitely generated, but admits a minimal sofic shift. This answers a question of Doucha, Melleray and Tsankov. The group is of the form $(F_4 \times F_2) \rtimes F_{\infty}$. The construction itself is based on simulation theory and properties of Thompson's~$V$.

people are nostalgic for forums but i'm not very
github sends me to the forum
forum has a post from 2019 with a hotlink to some storage service
the storage service is dead
this is exactly how using forums was like in their heyday, except that rapidshare no longer exists
edit: i think it was temporarily down or something

Fair Division Among Couples and Small Groups
Paul G\"olz, Hannane Yaghoubizade
https://arxiv.org/abs/2508.13432 https://arxiv.org/pdf/2508.13432

Fair Division Among Couples and Small Groups
We study the fair allocation of indivisible goods across groups of agents, where each agent fully enjoys all goods allocated to their group. We focus on groups of two (couples) and other groups of small size. For two couples, an EF1 allocation -- one in which all agents find their group's bundle no worse than the other group's, up to one good -- always exists and can be found efficiently. For three or more couples, EF1 allocations need not exist. Turning to proportionality, we show that, when…

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/

Optimal and Suboptimal Decoders under Finite-Alphabet Interference: A Mismatched Decoding Perspective
Sibo Zhang, Bruno Clerckx
https://arxiv.org/abs/2506.12646

Optimal and Suboptimal Decoders under Finite-Alphabet Interference: A Mismatched Decoding Perspective
Interference widely exists in communication systems and is often not optimally treated at the receivers due to limited knowledge and/or computational burden. Evolutions of receivers have been proposed to balance complexity and spectral efficiency, for example, for 6G, while commonly used performance metrics, such as capacity and mutual information, fail to capture the suboptimal treatment of interference, leading to potentially inaccurate performance evaluations. Mismatched decoding is an infor…

The It{\^o}-F\"ollmer formula -- nonstandard cases
W. M. Bednorz, R. M. {\L}ochowski, P. L. Zondi, F. J. Mhlanga, D. Hove
https://arxiv.org/abs/2508.14617 https://

The It{ô}-Föllmer formula -- nonstandard cases
The purpose of this note is to prove the It{ô}-Föllmer formula for the càdlàg paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partitions. By this we mean, for example, that we do not require the jumps of the quadratic variation to occur exactly at the times when the path itself jumps or that the quadratic variation exists at all time instances. Moreover, we deal with more general partitions than partitions with vanishing mesh used by Föllmer, als…

It is worth reading this week’s European Commission's recommendations on network tariffs. Like the German NRA, they warn that a simple exemption from network tariffs as exists in Germany for large batteries is not a solution.
From: @…

Clean Energy Wire (@CLEW@mastodon.energy)
Attached: 1 image Network operators call for slowing Germany's grid battery boom Requests for large-scale batteries far exceed realistic demand, available grid capacity, operator says https://www.cleanenergywire.org/news/german-network-operators-call-slowing-grid-battery-boom

A counter example for the Homogeneity Conjecture
Ming Xu, Shaoqiang Deng
https://arxiv.org/abs/2506.09471 https://arxiv.org/pdf/2506.…

A counter example for the Homogeneity Conjecture
We construct a counter example to show that the Homogeneity Conjecture, first proposed by J.A. Wolf in 1962, is not true. To be precise, we prove that on the Lie group Sp(2), there exists a left invariant Riemannian metric and a cyclic subgroup Γ of order (2n+1), such that the left translation of each element of Γ on Sp(2) is a Clifford-Wolf translation, but the Riemannian quotient Γ\Sp(2) is not homogeneous.

Liquid Crystal-Based RIS Loss-Trade-Off Analysis
Bowu Wang, Mohamadreza Delbari, Robin Neuder, Alejandro Jim\'enez-S\'aez, Vahid Jamali
https://arxiv.org/abs/2508.11489 …

Liquid Crystal-Based RIS Loss-Trade-Off Analysis
Liquid crystal (LC) technology has emerged as a promising solution for large reconfigurable intelligent surfaces (RISs) at millimeter wave (mmWave) bands, offering advantages such as low power consumption, scalability, and continuously tunable phase shifts. For LC-RIS based on the delay-line architecture, i.e., with dedicated phase shifters, there exists a trade-off between the maximum achievable phase-shift range and the corresponding insertion loss, which has not been studied for LC-RIS-assis…

The Implementability of Liberalism
H\'ector Hermida-Rivera
https://arxiv.org/abs/2506.16059 https://arxiv.org/pdf/2506.16059

The Implementability of Liberalism
This note shows that under the unrestricted domain, there exists a choice liberal and Nash implementable social choice rule if and only if there are at least three players and the outcome set is at least twice as large as the player set. A social choice rule is choice liberal if and only if for every player, there exists at least one pair of outcomes such that if this player strictly prefers one over the other, the one he prefers is socially desirable and the other one is not. A social choice r…

Classifying Emergence in Robot Swarms: An Observer-Dependent Approach
Ricardo Vega, Cameron Nowzari
https://arxiv.org/abs/2507.07315 https://

Classifying Emergence in Robot Swarms: An Observer-Dependent Approach
Emergence and swarms are widely discussed topics, yet no consensus exists on their formal definitions. This lack of agreement makes it difficult not only for new researchers to grasp these concepts, but also for experts who may use the same terms to mean different things. Many attempts have been made to objectively define 'swarm' or 'emergence,' with recent work highlighting the role of the external observer. Still, several researchers argue that once an observer's vantage point (e.g., scope, r…

Recursive characterisation of skew morphisms of finite cyclic groups
Martin Bachrat\'y, Michal Hagara
https://arxiv.org/abs/2506.11626 https://

Recursive characterisation of skew morphisms of finite cyclic groups
A skew morphism of a finite group $G$ is an element $φ$ of $\mathrm{Sym}(G)$ preserving the identity element of $G$ and having the property that for each $a\in G$ there exists a non-negative integer $i_a$ such that $φ(ab)=φ(a)φ^{i_a}(b)$ for all $b\in G$. In this paper we show that if a skew morphism $φ$ of $\mathbb{Z}_n$ is not an automorphism of $\mathbb{Z}_n$, then it is uniquely determined by a triple $(h,α,β)$ where $h$ is an element of $\mathbb{Z}_n$, $α$ is a skew morphism of $\m…

A kind editor had pity upon me:
#poetry

Upon a Single Fact
Upon a single fact is life supported: I-AM exists and works and speaks, before All time began, when space and earth were sorted, His plan completed, the Fartherest Edge and Core. The human mind cannot fully know The only limitless God whose spiritual Being Is Air to breathe and Wind that chooses to blow Wherever he desires, and no man seeing. This central truth: the eternal One not only Speaks but writes as well: his plan revealed, The unknown explained, the deepest secret unsealed- He lays the…

Sad but funny😆
From: @…
https://social.coop/@afewbugs/114929620840207383

Bordered contact invariants and half Giroux torsion
Hyunki Min, Konstantinos Varvarezos
https://arxiv.org/abs/2506.14050 https://arxi…

Bordered contact invariants and half Giroux torsion
We show that there exist infinitely many closed contact 3-manifolds containing half Giroux torsion along a separating torus whose contact invariants do not vanish. This provides counterexamples to Ghiggini's conjecture and suggests that separating half Giroux torsion may not obstruct symplectic fillability. The main tools are the bordered contact invariants recently developed by the authors and the innermost contact structures on knot complements. We also show that there exists a closed contact…

On existence of a variational regularization parameter under Morozov's discrepancy principle
Liang Ding, Long Li, Weimin Han, Wei Wang
https://arxiv.org/abs/2506.11397

On existence of a variational regularization parameter under Morozov's discrepancy principle
Morozov's discrepancy principle is commonly adopted in Tikhonov regularization for choosing the regularization parameter. Nevertheless, for a general non-linear inverse problem, the discrepancy $\|F(x_α^δ)-y^δ\|_Y$ does not depend continuously on $α$ and it is questionable whether there exists a regularization parameter $α$ such that $τ_1δ\leq \|F(x_α^δ)-y^δ\|_Y\leq τ_2 δ$ $(1\le τ_1<τ_2)$. In this paper, we prove the existence of $α$ under Morozov's discrepan…

Epstein shit and adjacent, Rural America, Poverty, Abuse
Everyone who's not a pedophile thinks pedophiles are bad, but there's this special obsessed hatred you'll find among poor rural Americans. The whole QAnon/Epstein obsession may not really make sense to folks raised in cities. Like, why do these people think *so much* about pedophiles? Why do they think that everyone in power is a pedophile? Why would the Pizzagate thing make sense to anyone? What is this unhinged shit? A lot of folks (who aren't anarchists) might be inclined to ask "why can't these people just let the cops take care of it?"
I was watching Legal Eagle's run down on the Trump Epstein thing earlier today and I woke up thinking about something I don't know if I've ever talked about. Now that I'm not in the US, I'm not at any risk of talking about it. I don't know how much I would have been before, but that's not something I'm gonna dig into right now. So let me tell you a story that might explain a few things.
I'm like 16, maybe 17. I have my license, so this girl I was dating/not dating/just friends with/whatever would regularly convince me to drive her and her friends around. I think she's like 15 at the time. Her friends are younger than her.
She tells me that there's a party we can go to where they have beer. She was told to invite her friends, so I can come too. We're going to pick her friends up (we regularly fill the VW Golf well beyond the legal limit and drive places) and head to the party.
So I take these girls, at least is 13 years old, down to this party. I'm already a bit sketched out bringing a 13 year old to a party. We drive out for a while. It's in the country. We drive down a long dark road. Three are some barrel fires and a shack. This is all a bit strange, but not too abnormal for this area. We're a little ways outside of a place called Mill City (in Oregon).
We park and walk towards the shack. This dude who looks like a rat comes up and offers us beer. He laughs and talks to the girl who invited me, "What's he doing here? You're supposed to bring your girl friends." She's like, "He's our ride." I don't remember if he offered me a beer or not.
We go over to this shed and everyone starts smoking, except me because I didn't smoke until I turned 18. The other girls start talking about the rat face dude, who's wandered over by the fire with some other guys. They're mainly teasing one of the 13 year old girls about having sex with him a bunch of times. They say he's like, 32 or something. The other girls joke about him only having sex with 13 year olds because he's too ugly to have sex with anyone closer to his own age.
Somewhere along the line it comes out that he's a cop. I never forgot that, it's absolutely seared in to my memory. I can picture his face perfectly still, decades later, and them talking about how he's a deputy, he was in his 30's, and he was having sex with a 13 year old girl. I was the only boy there, but there were a few older men. This was a chunk of the good ol' boys club of the town. I think there were a couple of cops besides the one deputy, and a judge or the mayor or some kind of big local VIP.
I kept trying to get my friend to leave, but she wanted to stay. Turns out under age drinking with cops seems like a great deal if you're a kid because you know you won't get busted. I left alone, creeped the fuck out.
I was told later that I wasn't invited and that I couldn't talk about it, I've always been good at compartmentalization, so I never did.
Decades later it occurred to me what was actually happening. I'm pretty sure that cop was giving meth he'd seized as evidence to these kids. This wasn't some one-off thing. It was regular. Who knows how many decades it went on after I left, or how many decades it had been going on before I found out. I knew this type of thing had happened at least a few times before because that's how that 13 year old girl and that 32 year old cop had hooked up in the first place.
Hearing about Epstein's MO, targeting these teenage girls from fucked up backgrounds, it's right there for me. I wouldn't be surprised if they were involved in sex trafficking of minors or some shit like that... but who would you call if you found out? Half the sheriff's department was there and the other half would cover for them.
You live in the city and shit like that doesn't happen, or at least you don't think it happens. But rural poor folks have this intuition about power and abuse. It's right there and you know it.
Trump is such a familiar character for me, because he's exactly that small town mayor or sheriff. He'll will talk about being tough on crime and hunting down pedophiles, while hanging out at a party that exists so people can fuck 8th graders.
The problem with the whole thing is that rural folks will never break the cognitive dissonance between "kill the peods" and "back the blue." They'll never go kill those cops. No, the pedos must be somewhere else. It must be the elites. It must be outsiders. It can't be the cops and good ol' boys everyone respects. It can't be the mayor who rigs the election to win every time. It can't be the "good upstanding" sheriff. Nah, it's the Clintons.
To be fair, it's probably also the Clitnons, a bunch of other politicians, billionaires, etc. Epstein was exactly who everyone thought he was, and he didn't get away with it for so long without a whole lot of really powerful help.
There are still powerful people who got away with involvement with #Epstein. #Trump is one of them, but I don't really believe that he's the only one.
#USPol #ACAB

Counterexample to the conjectured coarse grid theorem
Sandra Albrechtsen, James Davies
https://arxiv.org/abs/2508.15342 https://arxiv.org/pdf/2508.15342

Counterexample to the conjectured coarse grid theorem
We show that for every $M,A,n \in \mathbb{N}$ there exists a graph $G$ that does not contain the $(154\times 154)$-grid as a $3$-fat minor and is not $(M,A)$-quasi-isometric to a graph with no $K_n$ minor. This refutes the conjectured coarse grid theorem by Georgakopoulos and Papasoglu and the weak fat minor conjecture of Davies, Hickingbotham, Illingworth, and McCarty. Our construction is a slight modification of the recent counterexample to the weak coarse Menger conjecture from Nguyen, Sco…

A Practical Introduction to Regression-based Causal Inference in Meteorology (II): Unmeasured confounders
Caren Marzban, Yikun Zhang, Nicholas Bond, Michael Richman
https://arxiv.org/abs/2506.18652

A Practical Introduction to Regression-based Causal Inference in Meteorology (II): Unmeasured confounders
One obstacle to ``elevating" correlation to causation is the phenomenon of confounding, i.e., when a correlation between two variables exists because both variables are in fact caused by a third variable. The situation where the confounders are measured is examined in an earlier, accompanying article. Here, it is shown that even when the confounding variables are not measured, it is still possible to estimate the causal effect via a regression-based method that uses the notion of Instrumental V…

The Algebraic Structure of Morphosyntax
Isabella Senturia, Matilde Marcolli
https://arxiv.org/abs/2507.00244 https://arxiv.org/pdf/25…

The Algebraic Structure of Morphosyntax
Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, morphology has compositional properties responsible for word formation, organized into a magma of morphological trees. However, unlike syntax, we do not have movement within morphology. A coproduct decomposition exists, but it requires extending the set of morphological trees beyond those which are generated solely by …

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.
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The Myhill isomorphism theorem does not generalize much
C\'ecilia Pradic
https://arxiv.org/abs/2507.05028 https://arxiv.org/pdf/2…

The Myhill isomorphism theorem does not generalize much
The Myhill isomorphism is a variant of the Cantor-Bernstein theorem. It states that, from two injections that reduces two subsets of $\mathbb{N}$ to each other, there exists a bijection $\mathbb{N} \to \mathbb{N}$ that preserves them. This theorem can be proven constructively. We investigate to which extent the theorem can be extended to other infinite sets other than $\mathbb{N}$. We show that, assuming Markov's principle, the theorem can be extended to the conatural numbers $\mathbb{N}_{\inft…

"Nothing exists in isolation. Not a single thing." -- more @ #activism

Everything is Connected (In a Giant Tangled Knot)
welcome to the existential hairball 🐈

Y'all were wondering which way the army would break. This is as clear an answer as you're going to get.
This isn't a mistake. It's a message.
Edit: cut out "During drills they were perfectly in time" because I don't have receipts to show. Linking to a longer video in a threads post that shows a bit more intense of a juxtaposition between themselves and the division in front of them. This thread makes the same claim about drills, but I also don't see video.
https://www.threads.com/@davidmorehouse/post/DK7ExrKs5iw?xmt=AQF0w52awa66lUQeIuolzDaz8uSFcMmJLHALm9RZc4P75w
Edit: to clarify a bit, this is one division. The division in front of them in the longer video is in step. This isn't "the whole army is going to refuse" but this may be, "some units are fed up enough to make it clear they don't want to play, which is saying a lot."
Any division that exists needs to be cultivated. The way you cultivate that is absolutely not by lumping them all together. Some of the military voted for Trump, some don't care, some hate him. All of them are being treated like shit right now. All of them swore an oath to defend the constitution. Some of them probably know what that means.
I'm absolutely not a fan of the military, but I will take every opportunity I can to humanize these folks. Look for every opportunity you can to remind them that they are welcome on our side whenever they're ready to actually fulfill their oath, and we will appreciate every subtle bit of resistance they give to those who are violating it in the meantime.

This https://arxiv.org/abs/2407.08881 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces
Consider $N \geq 1$, $k \geq 2$, and $χ$ a Dirichlet character modulo $N$ such that $χ(-1) = (-1)^k$. For any bound $B$, one can show that $\dim S_k(Γ_0(N),χ) \le B$ for only finitely many triples $(N,k,χ)$. It turns out that this property does not extend to the newspace; there exists an infinite family of triples $(N,k,χ)$ for which $\dim S_k^{\text{new}}(Γ_0(N),χ) = 0$. However, we classify this case entirely. We also show that excluding the infinite family for which $\dim S_k^{\text{…

Labelling Data with Unknown References
Adrian de Wynter
https://arxiv.org/abs/2506.03083 https://arxiv.org/pdf/2506.03083

Labelling Data with Unknown References
An evaluator is trustworthy when there exists some agreed-upon way to measure its performance as a labeller. The two ways to establish trustworthiness are either by testing it, or by assuming the evaluator `knows' somehow the way to label the corpus. However, if labelled references (e.g., a development set) are unavailable, neither of these approaches work: the former requires the data, and the latter is an assumption, not evidence. To address this, we introduce an algorithm (the `No-Data Algor…

Germ expansion for SL(2) in arbitrary characteristics
Jean-Pierre Labesse
https://arxiv.org/abs/2507.05003 https://arxiv.org/pdf/2507…

Germ expansion for SL(2) in arbitrary characteristics
Let $F$ be a local field of characteristic $p$ and $G$ be a connected reductive group over $F$. Recall that Shalika's germ expansion of orbital integrals of regular semi-simple elements near the identity, when it exists, is a sum indexed by the set of unipotent conjugacy classes in $G(F)$. Observe that if $G=SL(2)$ this set is always compact; it is finite if $p\ne2$ while it is uncountable if $p= 2$. As a consequence, Shalika's germ expansion for elliptic elements does not make sense if $p=2$. …

Abelian motives and Shimura varieties in nonzero characteristic
James S. Milne
https://arxiv.org/abs/2508.09972 https://arxiv.org/pdf/2508.09972

Abelian motives and Shimura varieties in nonzero characteristic
Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are believed to be beyond reach, and may not even be correct as stated. I argue in this article that there exists a theory of motives, accessible to proof, weaker than Grothendieck's, but with many of the same consequences.

Finiteness and infiniteness of gradings of Noetherian rings
Cheng Meng
https://arxiv.org/abs/2508.01628 https://arxiv.org/pdf/2508.01628

Finiteness and infiniteness of gradings of Noetherian rings
In this paper we show that for a torsion-free abelian group $G$, $\operatorname{rank}_\mathbb{Z}G<\infty$ if and only if there exists a Noetherian $G$-graded ring $R$ such that the set $\{R_g \neq 0\}$ generates the group $G$. For every $G$ of finite rank, we construct a $G$-graded ring $R$ such that $R_g \neq 0$ for all $g \in G$. We prove such rings give examples of PIDs which are not ED. We also use the relations between the graded division ring and the group cohomology to prove some vanishi…

Strictly Expansive Matrices
Darrin Speegle
https://arxiv.org/abs/2506.07538 https://arxiv.org/pdf/2506.07538

Strictly Expansive Matrices
If $A$ is an integer valued, strictly expansive matrix, then there exists an orthonormal $A$-wavelet whose Fourier transform is compactly supported and smooth. We show that strongly connected diagonally dominant integer matrices are strictly expansive, and that integer matrices with determinant two are not strictly expansive with respect to particularly nice sets.

On the connections between $F$-contractions and Meir-Keeler contractions
Laura Manolescu, Pasc Gavruta
https://arxiv.org/abs/2507.03606 https://

On the connections between $F$-contractions and Meir-Keeler contractions
In this paper, we resolve an open problem concerning the connection between $F$-contractions (Wardowski contractions) and Meir-Keeler contractions. We prove that for a nondecreasing function $F$ that has a point of discontinuity on the right, there exists an $F-$contraction that is not a Meir-Keeler contraction. Moreover, we give a condition on nonlinear $(φ,F)$-contractions to be Meir-Keeler contractions. In the final part of the paper, we give a class of $(E,F)-$contractions (in the sense of…

Convergent transcriptomic and neuroimaging signature of Autism Spectrum Disorder
Elisa Ferrari (Scuola Normale Superiore), Alessandra Retico (INFN), Alessandro Cellerino (Scuola Normale Superiore), Davide Bacciu (University of Pisa)
https://arxiv.org/abs/2505.23776

Convergent transcriptomic and neuroimaging signature of Autism Spectrum Disorder
Autism Spectrum Disorder (ASD) is a multi-factorial neurodevelopmental disorder, whose causes are still poorly understood. Effective therapies to reduce all the heterogeneous symptoms of the disorder do not exists yet, but behavioural programs started at a very young age may improve the quality of life of the patients. For this reason, many efforts have been dedicated to the research of a reliable biomarker for early diagnosis. Machine learning approaches to distinguish ASDs from healthy contro…

This https://arxiv.org/abs/2204.08031 has been replaced.
link: https://scholar.google.com/scholar?q=a

Limit theorems of Chatterjee's rank correlation
Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is asymptotically normal as long as one variable is not a measurable function of the other, (b) the corresponding asymptotic variance is uniformly bounded by 36, and (c) a consistent variance estimator exists. Similar results also hold for Azadkia-Chatterjee's graph-base…

A topologically extendible mapping class that is not smoothly extendible
Shital Lawande, Kuldeep Saha
https://arxiv.org/abs/2505.23999 https://

A topologically extendible mapping class that is not smoothly extendible
We give an example of a smooth characteristic embedding of a torus in $\s^2 \times \s^2 \# \s^1 \times \s^3$ such that there exists no diffeomorphism of the ambient $4$-manifold that induces the Dehn twist along a meridian of the torus, but there exists a homeomorphism of the ambient $4$-manifold, isotopic to identity, that induces the Dehn twist. As an application of our methods, we provide examples of two proper smooth embeddings of an annulus in $\s^2 \times \s^2 \# \s^1 \times \s^3 \setminu…

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III
Qianqian Li, Huicheng Yin
https://arxiv.org/abs/2507.08274

Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III
For the $2$-D semilinear wave equation with scale-invariant damping $\square u+\fracμ{t}\partial_tu=|u|^p$, where $t\geq 1$, $μ>0$ and $p>1$, it is conjectured that the global small data weak solution $u$ exists when $p>p_{s}(2+μ) =\frac{μ+3+\sqrt{μ^2+14μ+17}}{2(μ+1)}$ for $0<μ\le 2$ and $p>p_f(2)=2$ for $μ\geq 2$. In our previous papers, the global small solution $u$ has been obtained for $p>p_{s}(2+μ)$ and $0<μ<2$ but $μ\not=1$. In the present paper, by the vector field …

Schramm-Loewner evolution contains a topological Sierpi\'nski carpet when $\kappa$ is close to 8
Haoyu Liu, Zijie Zhuang
https://arxiv.org/abs/2506.09609

Schramm-Loewner evolution contains a topological Sierpiński carpet when $κ$ is close to 8
We consider the Schramm-Loewner evolution (SLE$_κ$) for $κ\in (4,8)$, which is the regime where the curve is self-intersecting but not space-filling. We show that there exists $δ_0>0$ such that for $κ\in (8 - δ_0,8)$, the range of an SLE$_κ$ curve almost surely contains a topological Sierpiński carpet. Combined with a result of Ntalampekos (2021), this implies that in this parameter range, SLE$_κ$ is almost surely conformally non-removable, and the conformal welding problem for SLE$_κ$…

Jordan homomorphisms and T-ideals
Matej Bre\v{s}ar, Efim Zelmanov
https://arxiv.org/abs/2508.07191 https://arxiv.org/pdf/2508.07191

Jordan homomorphisms and T-ideals
Let $A$ and $B$ be associative algebras over a field $F$ with {\rm char}$(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $φ:A\to B$ is the sum of a homomorphism and an antihomomorphism. Our second main result concerns (not necessarily surjective) Jordan homomorphisms from $H(A,*)$ to $B$, where $*$ is an involution on $A$ and $H(A,*)=\{a\in A\,|\, a^*=a\}$. We show that there exists a ${\rm T}$-ideal $G$ having…

This https://arxiv.org/abs/2502.06200 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

On the query complexity of sampling from non-log-concave distributions
We study the problem of sampling from a $d$-dimensional distribution with density $p(x)\propto e^{-f(x)}$, which does not necessarily satisfy good isoperimetric conditions. Specifically, we show that for any $L,M$ satisfying $LM\ge d\ge 5$, $ε\in \left(0,\frac{1}{32}\right)$, and any algorithm with query accesses to the value of $f(x)$ and $\nabla f(x)$, there exists an $L$-log-smooth distribution with second moment at most $M$ such that the algorithm requires $\left(\frac{LM}{dε}\right)^{�…

Finiteness properties of stabilisers of oligomorphic actions
Francesco Fournier-Facio, Peter H. Kropholler, Robert Alonzo Lyman, Matthew C. B. Zaremsky
https://arxiv.org/abs/2506.02319

Finiteness properties of stabilisers of oligomorphic actions
An action of a group on a set is oligomorphic if it has finitely many orbits of $n$-element subsets for all $n$. We prove that for a large class of groups (including all groups of finite virtual cohomological dimension and all countable linear groups), for any oligomorphic action of such a group on an infinite set there exists a finite subset whose stabiliser is not of type $\mathrm{FP}_\infty$. This leads to obstructions on finiteness properties for permutational wreath products and twisted Br…

Infinite induced-saturated graphs
Marthe Bonamy, Carla Groenland, Tom Johnston, Natasha Morrison, Alex Scott
https://arxiv.org/abs/2506.08810 https://

Infinite induced-saturated graphs
A graph $G$ is $H$-induced-saturated if $G$ is $H$-free but deleting any edge or adding any edge creates an induced copy of $H$. There are various graphs $H$, such as $P_4$, for which no finite $H$-induced-saturated graph $G$ exists. We show that for every finite graph $H$ that is not a clique or stable set, there always exists a countable $H$-induced-saturated graph. In fact, a stronger property can be achieved: there is an $H$-free graph $G$ such that $G'$ contains a copy of $H$ whenever $G'\…

Slow convergence almost everywhere of ergodic averages
Valery V. Ryzhikov
https://arxiv.org/abs/2508.00463 https://arxiv.org/pdf/2508.00463

Slow convergence almost everywhere of ergodic averages
For an ergodic action of the group $Z^n$ on a probability space and a given arbitrarily slowly decreasing to zero sequence, there exists an integrable function such that the standard ergodic time averages for it converge almost everywhere to the spatial average of the function at a rate that is not asymptotically majorized by this sequence. This generalizes the Krengel effect about the absence of universal estimates for the rate of convergence in Birkhoff's ergodic theorem. The proof uses a wea…

$\text{NS}_{\omega_1}$ saturated, $\Delta_1 ( \{ \omega_1 \} )$-definable and a $\Delta^1_4$-definable well-order of the reals
Stefan Hoffelner
https://arxiv.org/abs/2507.01183

$\text{NS}_{ω_1}$ saturated, $Δ_1 ( \{ ω_1 \} )$-definable and a $Δ^1_4$-definable well-order of the reals
Assuming $M_1$, the canonical inner model with one Woodin cardinal exists, we construct a model in which the nonstationary ideal on $ω_1$ is $\aleph_2$-saturated, $Δ_1$-definable with $ω_1$ as the only parameter and there is a $Σ^1_{4}$-definable well-order of the reals. This implies that contrary to the assumption that $NS_{ω_1}$ is $\aleph_1$-dense, the assumption of $NS_{ω_1}$ being saturated and $Δ_1$-definable does not imply any nice structural properties for the projective subsets …

This https://arxiv.org/abs/2312.16863 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Existence and spectrality of infinite convolutions generated by infinitely many admissible pairs
In this paper, we study the spectrality of infinite convolutions generated by infinitely many admissible pairs which may not be compactly supported, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. First, we prove that the infinite convolution exists and is a spectral measure if the sequence of admissible pairs satisfies the remainder bounded condition, and it has a subsequence consisting of genera…

Existence of normalized solutions to nonlinear Schr\"{o}dinger equations with potential on lattice graphs
Weiqi Guan
https://arxiv.org/abs/2507.04204 …

Existence of normalized solutions to nonlinear Schrödinger equations with potential on lattice graphs
We study the existence of ground state normalized solution of the following Schrödinger equation: \begin{equation*} \begin{cases} -Δu+V(x)u+λu=f(x,u), & x\in\mathbb{Z}^d \\ \Vert u\Vert_2^2=a \end{cases} \end{equation*} where $V(x)$ is trapping potential or well potential, $f(x,u)$ satisfies Berestycki-Lions type condition and other suitable conditions. We show that there always exists a threshold $α\in[0,\infty)$ such that there do not exist ground state normalized solutions for $a\in (0…

Unique equilibrium states for Viana maps with small potentials
Kecheng Li
https://arxiv.org/abs/2508.00136 https://arxiv.org/pdf/2508.00136

Unique equilibrium states for Viana maps with small potentials
We investigate the thermodynamic formalism for Viana maps-skew products obtained by coupling an expanding circle map with a slightly perturbed quadratic family on the fibers. For every Hölder potential $φ$ whose oscillation is below an explicit threshold, we show that an equilibrium state not only exists but is unique and satisfies an upper level-2 large-deviation principle. All of these conclusions persist under sufficiently small perturbations of the reference map.

The Local Structure Theorem for Graph Minors with Finite Index
Christophe Paul, Evangelos Protopapas, Dimitrios M. Thilikos, Sebastian Wiederrecht
https://arxiv.org/abs/2507.02769

The Local Structure Theorem for Graph Minors with Finite Index
The Local Structure Theorem (LST) for graph minors roughly states that every $H$-minor free graph $G$ that contains a sufficiently large wall $W$, there is a set of few vertices $A$ such that, upon removing $A$, the resulting graph $G':=G - A$ admits an "almost embedding" $δ$ into a surface $Σ$ in which $H$ does not embed. By almost embedding, we mean that there exists a hypergraph $\mathcal{H}$ whose vertex set is a subset of the vertex set of $G$ and an embedding of $\mathcal{H}$ in $Σ$ su…

The Neighbour Sum Problem on Trees
Sayan Dutta, Sohom Gupta
https://arxiv.org/abs/2506.23965 https://arxiv.org/pdf/2506.23965

The Neighbour Sum Problem on Trees
A graph $\mathcal G = (\mathcal V, \mathcal E)$ is said to satisfy the Neighbour Sum Property if there exists some $f:\mathcal V\to\mathbb R$ such that $f\not\equiv 0$ and it maps every vertex to the sum of the values taken by its neighbours. In this article, we provide an algorithm to check whether a given finite tree satisfies the neighbour sum property. We also find a large class of trees on $n$ vertices that satisfy the property.