Tootfinder

Beware of snakes like Tricia Cotham in NC who switched parties and gave MAGA a veto-proof majority in the house.
https://ncnewsline.com/2023/04/05/rep-tricia-cothams-party-switch-gives-the-house-gop-a-veto-proof-majority/

Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation
Mohammad Ishzaz Asif Rafid, Morsalin Sakib
https://arxiv.org/abs/2508.12138 https…

Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation
Bitcoin's Proof of Work (PoW) mechanism, while central to achieving decentralized consensus, has long been criticized for excessive energy use and hardware inefficiencies \cite{devries2018bitcoin, truby2018decarbonizing}. This paper introduces a hybrid architecture that replaces Bitcoin's traditional PoW with a centralized, cloud-based collaborative training framework. In this model, miners contribute computing resources to train segments of horizontally scaled machine learning models on prepro…

A proof of the reverse isoperimetric inequality using a geometric-analytic approach
Naman Kumar
https://arxiv.org/abs/2508.13235 https://arxiv.org/pdf/2508…

A proof of the reverse isoperimetric inequality using a geometric-analytic approach
We present the first proof of the reverse isoperimetric inequality for black holes in arbitrary dimension using a two-pronged geometric-analytic approach. The proof holds for compact Riemannian hypersurfaces in AdS space and seems to be a generic property of black holes in the extended phase space formalism. Using Euclidean gravitational action, we show that, among all hypersurfaces of given volume, the round sphere in the $D$-dimensional Anti-de Sitter space maximizes the area (and hence the e…

A New Proof of Fine's Identity using Wildberger's Polynomial Formula
Dean Rubine
https://arxiv.org/abs/2508.12055 https://arxiv.org/pdf/2508.12055

A New Proof of Fine's Identity using Wildberger's Polynomial Formula
In 1959, N. J. Fine showed that the sum of the multinomial coefficients corresponding to the partitions of a natural number $n$ into $r$ parts is a binomial coefficient: $$ \sum_{\substack{k_1 + k_2 + k_3 + {}\ldots = r \\ k_1 + 2k_2 + 3k_3 + {}\ldots = n }} \binom{r}{k_1, k_2, k_3, \ldots } = \binom{n - 1}{r - 1} $$ Fine gives a rather pithy proof, though we're still stuck on the part that says, ``We begin with an important though obvious remark.'' In 2025, Wildberger and Rubine gave the serie…

A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices
Michel Crouzeix (UR), Anne Greenbaum
https://arxiv.org/abs/2508.12768 https://

A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices
In this paper we give an alternative proof that the family of matrices studied by Daeshik Choi in A proof of Crouzeix's conjecture for a class of matrices, Linear Algebra and its Applications, 438, no. 8 (2013), pp. 3247-3257, satisfy Crouzeix's conjecture. We also show that they satisfy the completely bounded version of the conjecture.

I had a coworker proof one of my posts and they said "Well, I think you meant to use the word 'violet' instead of 'violence'..."
To be fair I've probably typed the word "violent" thousands of times more than I've typed the word "violet".

A Formalization of the Reversible Concurrent Calculus CCSKP in Beluga
Gabriele Cecilia (Augusta University)
https://arxiv.org/abs/2508.13612 https://arxiv.…

A Formalization of the Reversible Concurrent Calculus CCSKP in Beluga
Reversible concurrent calculi are abstract models for concurrent systems in which any action can potentially be undone. Over the last few decades, different formalisms have been developed and their mathematical properties have been explored; however, none have been machine-checked within a proof assistant. This paper presents the first Beluga formalization of the Calculus of Communicating Systems with Keys and Proof labels (CCSKP), a reversible extension of CCS. Beyond the syntax and semantic…

A Simpler Proof of Kakutani's Conjecture on Random Subdivision and Its Generalizations
Changqing Liu
https://arxiv.org/abs/2508.12154 https://arxiv.org…

A Simpler Proof of Kakutani's Conjecture on Random Subdivision and Its Generalizations
We shift the perspective on the interval fragmentation problem from division points to division spacings. This leads to a proof that is both simpler and stronger, establishing limiting distributions for partition points and spacings and, more importantly, including large-deviation error bounds. Moreover, the approach is general. We derive the limiting spacing distribution for arbitrary division points, and claim it is independent of splitting scheme. It is shown that, under certain conditions, …

UPS guy's proof of delivery photo yesterday 🤣

Remark on twists of Frobenius algebra and link homology
Noboru Ito, Keita Nakagane, Jun Yoshida
https://arxiv.org/abs/2508.13731 https://arxiv.org/pdf/2508…

Remark on twists of Frobenius algebra and link homology
We discuss twists on Frobenius algebras in the context of link homology. In his paper in 2006, Khovanov asserted that a twist of a Frobenius algebra yields an isomorphic chain complex on each link diagram. Although the result has been widely accepted for nearly two decades, a subtle gap in the original proof was found in the induction step of the construction of the isomorphism. Following discussion with Khovanov, we decided to provide a new proof. Our proof is based on a detailed analysis of c…

Gen AI in Proof-based Math Courses: A Pilot Study
Hannah Klawa, Shraddha Rajpal, Cigole Thomas
https://arxiv.org/abs/2509.13570 https://arxiv.org/pdf/2509.…

Gen AI in Proof-based Math Courses: A Pilot Study
With the rapid rise of generative AI in higher education and the unreliability of current AI detection tools, developing policies that encourage student learning and critical thinking has become increasingly important. This study examines student use and perceptions of generative AI across three proof-based undergraduate mathematics courses: a first-semester abstract algebra course, a topology course and a second-semester abstract algebra course. In each case, course policy permitted some use o…

A convergence proof for a finite element discretization of Chorin's projection method of the incompressible Navier-Stokes equations
Franziska Weber
https://arxiv.org/abs/2508.13416

A convergence proof for a finite element discretization of Chorin's projection method of the incompressible Navier-Stokes equations
We study Chorin's projection method combined with a finite element spatial discretization for the time-dependent incompressible Navier-Stokes equations. The scheme advances the solution in two steps: a prediction step, which computes an intermediate velocity field that is generally not divergence-free, and a projection step, which enforces incompressibility by projecting this velocity onto the divergence-free subspace. We establish convergence, up to a subsequence, of the numerical approximatio…

Just thinking about this OSA thing and I’ve still not come across a site that is blocking me or requiring proof of my age. Maybe I just look at the wrong websites?
#ukpolitics #osa

MAGA Rep may want to see can contact Epstein about that list while he is talking to the dead.
https://flip.it/hVNPmY

Interessant voor iedereen geinteresseerd in AI, wetgeving, van wet naar digitale werking. De proof-of-concept Regelrecht.
#AI

GitHub - MinBZK/poc-machine-law: Proof of Concept RegelRecht
Proof of Concept RegelRecht . Contribute to MinBZK/poc-machine-law development by creating an account on GitHub.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure
Seiji Hattori, Takuya Matsuzaki, Makoto Fujiwara
https://arxiv.org/abs/2509.09726

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was applied to formal proof data created in accordance with natural language proofs taken from an undergraduate-level textbook, and the quality of the generated natural language proofs was analyzed in comparison with the original natural language proofs. Furtherm…

Reinforcement Learning-based Adaptive Path Selection for Programmable Networks
Jos\'e Eduardo Zerna Torres, Marios Avgeris, Chrysa Papagianni, Gergely Pongr\'acz, Istv\'an G\'odor, Paola Grosso
https://arxiv.org/abs/2508.13806

Reinforcement Learning-based Adaptive Path Selection for Programmable Networks
This work presents a proof-of-concept implementation of a distributed, in-network reinforcement learning (IN-RL) framework for adaptive path selection in programmable networks. By combining Stochastic Learning Automata (SLA) with real-time telemetry data collected via In-Band Network Telemetry (INT), the proposed system enables local, data-driven forwarding decisions that adapt dynamically to congestion conditions. The system is evaluated on a Mininet-based testbed using P4-programmable BMv2 sw…

Face-hitting dominating sets in planar graphs: Alternative proof and linear-time algorithm
Therese Biedl
https://arxiv.org/abs/2508.11444 https://arxiv.org…

Face-hitting dominating sets in planar graphs: Alternative proof and linear-time algorithm
In a recent paper, Francis, Illickan, Jose and Rajendraprasad showed that every $n$-vertex plane graph $G$ has (under some natural restrictions) a vertex-partition into two sets $V_1$ and $V_2$ such that each $V_i$ is \emph{dominating} (every vertex of $G$ contains a vertex of $V_i$ in its closed neighbourhood) and \emph{face-hitting} (every face of $G$ is incident to a vertex of $V_i$). Their proof works by considering a supergraph $G'$ of $G$ that has certain properties, and among all such gr…

The animation of the opposite of finite sets
Benjamin Antieau
https://arxiv.org/abs/2508.13106 https://arxiv.org/pdf/2508.13106

The animation of the opposite of finite sets
We give a direct proof of the fact that the animation of the opposite of the category of finite sets is a 1-category.

I get to vote, this is proof I’m a real Hamburger now 🍔

Arcs on rational double points in arbitrary characteristic
Tommaso de Fernex, Shih-Hsin Wang
https://arxiv.org/abs/2508.12423 https://arxiv.org/pdf/2508.12…

Arcs on rational double points in arbitrary characteristic
We prove that the Nash problem holds for two-dimensional rational double points in all characteristics. The proof is based on a direct computation of the families of arcs through these singularities.

An elementary proof that linking problems are hard
Shannon Cheng, Anna Chlopecki, Saarah Nazar, Eric Samperton
https://arxiv.org/abs/2509.13120 https://arx…

An elementary proof that linking problems are hard
We give a new, elementary proof of what we believe is the simplest known example of a ``natural'' problem in computational 3-dimensional topology that is $\mathsf{NP}$-hard -- namely, the \emph{Trivial Sublink Problem}: given a diagram $L$ of a link in $S^3$ and a positive integer $k$, decide if $L$ contains a $k$ component sublink that is trivial. This problem was previously shown to be $\mathsf{NP}$-hard in independent works of Koenig-Tsvietkova and de Mesmay-Rieck-Sedgwick-Tancer, both of wh…

The Weyl bound for triple product L-functions in the cubic level
Xinchen Miao, Huimin Zhang
https://arxiv.org/abs/2508.13746 https://arxiv.org/pdf/2508.137…

The Weyl bound for triple product L-functions in the cubic level
In this paper, we focus on the strong subconvexity bounds for triple product L-functions in the cubic level aspect. Our proof on the Weyl-type bound synthesizes techniques from classical analytic number theory with methods in automorphic forms and representation theory. The methods include the refined Petersson trace formula for the newforms of cubic level, classical Voronoi summation formula, Jutila's circle method, Kuznetsov trace formula and the spectral large sieve inequality.

"U.S. District Judge Tim Kelly, a Donald Trump appointee, found the government's "reunification" plan included little proof that any parent or guardian wanted the children returned."
Federal judge blocks deportation of hundreds of Guatemalan children | Courthouse News Service
https://www.courthousenews.com/federal-judge-blocks-deportation-of-hundreds-of-guatemalan-children/

Replaced article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/1]:
- A Proof of Lieb--Wehrl Entropy conjecture for $SU(N,1)$
Mandeep Singh
https:/…

Quantum Corner Polynomials: A Generalization of Super Macdonald Polynomials and Their VOA Correspondence
Panupong Cheewaphutthisakun, Jun'ichi Shiraishi, Keng Wiboonton
https://arxiv.org/abs/2508.12267

Quantum Corner Polynomials: A Generalization of Super Macdonald Polynomials and Their VOA Correspondence
In this paper, we introduce a family of partially symmetric polynomials, which we call quantum corner polynomials, as a generalization of the Sergeev-Veselov super Macdonald polynomials. We show that these quantum corner polynomials are precisely the partially symmetric polynomials corresponding to the quantum corner VOAs. Furthermore, we provide a detailed proof of the partial symmetricity of these polynomials.

On our Tesla we have noticed that the design and construction has tried new methods to save weight, but that those methods have not withstood the test of time (or weather).
For example we've had to replace some of the ball joints in the front suspension because they were not water proof and ended up corroding - a problem solved back in the 1960s by other car makers.
And now there's this...
"Half of Tesla Model 3s Failed Their Mandatory Inspections in Finland&qu…

Half of Tesla Model 3s Failed Their Mandatory Inspections in Finland
The Tesla Model 3, Model S, and Model X all ranked among the bottom five performers in Finland's mandatory vehicle inspections of 4-year-old cars

A proof that all the sliding trajectories of generic inelastic piecewise linear dynamical systems over the torus are closed
Mayara D. A. Caldas, Ricardo M. Martins
https://arxiv.org/abs/2508.11066

A proof that all the sliding trajectories of generic inelastic piecewise linear dynamical systems over the torus are closed
In this article, we consider piecewise smooth differential equations $Z_{X_-X_+}$, where $X_-$ and $X_+$ are linear vector fields in dimension 3, having the torus as discontinuity manifold. We consider that $Z_{X_-X_+}$ is an inelastic vector field over the torus. We classify the set of tangency points on the torus for certain conditions and describe the behavior of the trajectories of the sliding vector field over the torus. We prove that, under generic conditions, all the trajectories of a pi…

Crosslisted article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- A proof of the reverse isoperimetric inequality using a geometric-analytic approach
Naman Kumar

An Unimaginative Proof of Fermat's Two Squares Theorem
Gennady Bachman
https://arxiv.org/abs/2508.10234 https://arxiv.org/pdf/2508.10234

An Unimaginative Proof of Fermat's Two Squares Theorem
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students who are just starting out in math.

Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars
Baptiste Klein, Suzanne Aigrain, Michael Cretignier, Xavier Dumusque, Khaled Al Moulla, Jean-Fran\c{c}ois Donati, Niamh K. O'Sullivan, Haochuan Yu, Andrew Collier Cameron, Oscar Barrag\'an, Annelies Mortier, Alessandro Sozzetti
https://arxi…

Using Doppler Imaging to model stellar activity and search for planets around Sun-like stars
Doppler Imaging (DI) is a well-established technique to map a physical field at a stellar surface from a time series of high-resolution spectra. In this proof-of-concept study, we aim to show that traditional DI algorithms, originally designed for rapidly-rotating stars, have also the ability to model the activity of Sun-like stars, when observed with new-generation highly-stable spectrographs, and search for low-mass planets around them. We used DI to retrieve the relative brightness distribut…

On the equivalence and optimality of transformations of diffusive systems
Davide Gabrielli, Giovanni Jona-Lasinio
https://arxiv.org/abs/2509.14450 https://…

On the equivalence and optimality of transformations of diffusive systems
In this paper we introduce, inspired by Clausius and developing the ideas of \cite{pre}, the concept of equivalence of transformations in non equilibrium theory of diffusive systems within the framework of macroscopic fluctuation theory. Besides providing a new proof of a formula derived in \cite{mft,qc}, which is the basis of the equivalence, we show that equivalent quasistatic transformations can be distinguished in finite terms, by the renormalized work introduced in \cite{45,46,mft,qc}. Thi…

Contractive transport maps from $\mathbb{S}^2$ to nearly spherical surfaces with positive Ricci curvature
Jordan Serres (IMT)
https://arxiv.org/abs/2508.13688 https://

Contractive transport maps from $\mathbb{S}^2$ to nearly spherical surfaces with positive Ricci curvature
We prove that every nearly spherical, positively curved surface is the contractive, volume-preserving image of a round sphere. The proof combines three main tools: the Ricci flow on surfaces, the Kim-Milman construction, and a multiscale Bakry-Émery criterion.

Proof that even the mighty Fleetwood Mac could get it terribly, terribly wrong at times. #TOTP

On definability of C*-tensor norms
Isaac Goldbring, Thomas Sinclair
https://arxiv.org/abs/2509.15086 https://arxiv.org/pdf/2509.15086

On definability of C*-tensor norms
We initiate the study of definability (in the model-theoretic sense) of C*-tensor norms. We show that neither the minimal nor maximal tensor norms are definable uniformly over all C*-algebras. The proof in the case of the minimal tensor product norm uses a deep theorem of Kirchberg characterizing exactness in terms of tensor products with matrix ultraproducts while the case of maximal tensor products uses Pisier's recent characterization of the lifting property in terms of maximal tensor produc…

What's in a Proof? Analyzing Expert Proof-Writing Processes in F* and Verus
Rijul Jain, Shraddha Barke, Gabriel Ebner, Md Rakib Hossain Misu, Shan Lu, Sarah Fakhoury
https://arxiv.org/abs/2508.02733

What's in a Proof? Analyzing Expert Proof-Writing Processes in F* and Verus
Proof-oriented programming languages (POPLs) empower developers to write code alongside formal correctness proofs, providing formal guarantees that the code adheres to specified requirements. Despite their powerful capabilities, POPLs present a steep learning curve and have not yet been adopted by the broader software community. The lack of understanding about the proof-development process and how expert proof developers interact with POPLs has hindered the advancement of effective proof engine…

Implicitly and Differentiably Representing Protein Surfaces and Interfaces
Cory B. Scott, Charlie Rothschild, Benjamin Nye
https://arxiv.org/abs/2508.11641 https://

Implicitly and Differentiably Representing Protein Surfaces and Interfaces
We introduce a pipeline for representing a protein, or protein complex, as the union of signed distance functions (SDFs) by representing each atom as a sphere with the appropriate radius. While this idea has been used previously as a way to render images of proteins, it has not, to our knowledge, been widely adopted in a machine learning setting. Mirroring recent successful work applying SDFs to represent 3D geometry, we present a proof of concept that this representation of proteins could be u…

An introduction to the algebra of rings and fields
Darij Grinberg
https://arxiv.org/abs/2508.13165 https://arxiv.org/pdf/2508.13165

An introduction to the algebra of rings and fields
This is an introduction to rings and fields, written for a quarter-long undergraduate course. It includes the basic properties of ideals, modules, algebras and polynomials, the constructions of ring extensions and finite fields, some number-theoretical applications (such as a proof of quadratic reciprocity and Jacobsthal's formulas for $p = x^2 + y^2$), and tastes of Gröbner bases and the Smith normal form. Familiarity with groups and vector spaces is assumed, though no deep results from eithe…

"McTT: A Verified Kernel for a Proof Assistant"
Presentation by Junyoung Jang, joint work with Antoine Gaulin, Jason Z. S. Hu, Brigitte Pientka.
Repo: https://github.com/Beluga-lang/McTT/tree/icfp25

CoLF Logic Programming as Infinitary Proof Exploration
Zhibo Chen (Carnegie Mellon University), Frank Pfenning (Carnegie Mellon University)
https://arxiv.org/abs/2510.12302 http…

CoLF Logic Programming as Infinitary Proof Exploration
Logical Frameworks such as Automath [de Bruijn, 1968] or LF [Harper et al., 1993] were originally conceived as metalanguages for the specification of foundationally uncommitted deductive systems, yielding generic proof checkers. Their high level of abstraction was soon exploited to also express algorithms over deductive systems such as theorem provers, type-checkers, evaluators, compilers, proof transformers, etc. in the paradigm of computation-as-proof-construction. This has been realized in l…

Coherence for Pseudo Commutative Monads
Diego Manco
https://arxiv.org/abs/2509.15101 https://arxiv.org/pdf/2509.15101…

Coherence for Pseudo Commutative Monads
We prove that the free algebra functor associated to a symmetric, pseudo commutative 2-monad, from the underlying symmetric monoidal 2-category to the 2-category of algebras and pseudo maps over the 2-monad can be enhanced to a multifunctor. Furthermore, we prove that this multifunctor is pseudo symmetric. Our proof implies coherence results for both symmetric and non-symmetric pseudo commutative 2-monads conjectured by Hyland and Power.

Blockchain-Enabled Explainable AI for Trusted Healthcare Systems
Md Talha Mohsin
https://arxiv.org/abs/2509.14987 https://arxiv.org/pdf/2509.14987

Blockchain-Enabled Explainable AI for Trusted Healthcare Systems
This paper introduces a Blockchain-Integrated Explainable AI Framework (BXHF) for healthcare systems to tackle two essential challenges confronting health information networks: safe data exchange and comprehensible AI-driven clinical decision-making. Our architecture incorporates blockchain, ensuring patient records are immutable, auditable, and tamper-proof, alongside Explainable AI (XAI) methodologies that yield transparent and clinically relevant model predictions. By incorporating security …

Purification of quantum trajectories in infinite dimensions
Federico Girotti, Alessandro Vitale
https://arxiv.org/abs/2509.13377 https://arxiv.org/pdf/2509…

Purification of quantum trajectories in infinite dimensions
In this work we exhibit a class of examples that show that the characterization of purification of quantum trajectories in terms of 'dark' subspaces that was proved for finite dimensional systems fails to hold in infinite dimensional ones. Moreover, we prove that the new phenomenon emerging in our class of models and preventing purification to happen is the only new possibility that emerges in infinite dimensional systems. Our proof strategy points out that the emergence of new phenomena in inf…

Undecidability of Translational Tiling with 2 Polycubes
Yoonhu Kim
https://arxiv.org/abs/2508.11725 https://arxiv.org/pdf/2508.11725

Undecidability of Translational Tiling with 2 Polycubes
In this paper, we prove that it is undecidable whether a set of two polycubes can tile $\mathbb{Z}^3$ by translation. The proof involves a new technique that allows us to simulate two disconnected polycubes with two connected polycubes. By expanding this technique to higher dimensions, we also prove that a set of disconnected tiles in $\mathbb{Z}^n$ can be simulated by the same number of connected tiles in $\mathbb{Z}^n$ for $n \geq 3$.

Every sufficiently large odd integer is a sum of two positive perfect squares and a prime
Ricardo Adonis Caraccioli Abrego
https://arxiv.org/abs/2509.14246 https://

Every sufficiently large odd integer is a sum of two positive perfect squares and a prime
We prove that every sufficiently large odd integer is a sum of two positive squares and a prime. Let R(n) be the number of representations n = x^2 + y^2 + p with x, y >= 1 and p prime. We show that R(n) > 0 for all odd n >= n0 and obtain the asymptotic formula R(n) = S(n) C n / log n, where S(n) > 0 is the singular series and C > 0 is the singular integral. The proof uses the Hardy-Littlewood circle method: on the major arcs we extract the main term, and on the minor arcs we combine an L2 bound…

Well, it turns out that someone very smart gave us definitive proof that #Asus firmware & drivers programmers are not doing a good job.
After seeing this, their dismissiveness towards people complaining now feels a bit more outrageous than before (it has been more than 3 years for some).
Without experience, it's hard to follow the analysis, but there are some easy to understand takes:
1. They force sleeps from 25 to 100ms... in interrupt handlers.
2. They use interrupt handlers as improvised timers/schedulers (re-triggering interruptions from within interruption handling contexts).
#asuslaptops

I made some progress on the Beat Bike!
The magnet mounted on the wheel passes a reed switch which is sensed by the control box (with a Raspberry Pi Pico) and then triggers the drum machine to step through the programmed sequence.
Still a lot of work to do, mostly mounting everything onto the bike, and some more code to write, but the proof of concept is all good.
#bikeTooter

Fact Check: No Proof For Zelenskyy $1.2B Real Estate Empire In 'London Telegraph' Story -- New Website Using Stolen Profile Picture: https://benborges.xyz/2025/08/27/fact-check-no-proof-for.html

Curve semistable Higgs bundles and smooth projective varieties whose canonical bundle is ample
Armando Capasso
https://arxiv.org/abs/2508.12062 https://arx…

Curve semistable Higgs bundles and smooth projective varieties whose canonical bundle is ample
Considering the so-called Simpson system on smooth projective varieties, defined over an algebraically closed field of characteristic $0$, whose canonical bundle is ample, I prove the stability of this Higgs bundle. From this I obtain another proof of the Guggenheimer-Yau inequality. Where the equality holds, I prove that the discriminant class of the Simpson system vanishes. This follows from the study of the relations between ampleness and numerically nefness for Higgs bundles which "feel" th…

Crosslisted article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/1]:
- A proof of the reverse isoperimetric inequality using a geometric-analytic approach
Naman Kumar

Graph-Based Deterministic Polynomial Algorithm for NP Problems
Changryeol Lee (Department of Software, Yonsei University, Mirae Campus)
https://arxiv.org/abs/2508.13166 https://…

Graph-Based Deterministic Polynomial Algorithm for NP Problems
The P = NP problem asks whether every problem whose solution can be verified in polynomial time (NP) can also be solved in polynomial time (P). In this paper, we present a proof that P = NP, demonstrating that every NP problem can be solved deterministically in polynomial time. We introduce a new Computation Model that enables the simulation of a Turing machine, and show that NP problems can be simulated efficiently within this framework. By introducing the concept of a Feasible Graph, we ensur…

Charting GLOBs in Asymptotically Safe Gravity
Francesco Del Porro, Jonas Pfeiffer, Alessia Platania, Samuele Silveravalle
https://arxiv.org/abs/2509.14309 https://

Charting GLOBs in Asymptotically Safe Gravity
Computing the gravitational effective action provides a direct route to charting the landscape of admissible black hole spacetimes and their alternatives, which we will collectively call "gravitationally localized objects" (GLOBs). In this work, we provide a proof of principle of this idea within the framework of asymptotically safe gravity. Focusing on the Einstein-Weyl truncation, we identify the unique ultraviolet-complete trajectory emanating from the asymptotically safe fixed point and use…

Laplace comparison on K\"ahler Ricci flow and convergence
Gang Tian, Qi S. Zhang, Zhenlei Zhang, Meng Zhu, Xiaohua Zhu
https://arxiv.org/abs/2509.14820 https://

Laplace comparison on Kähler Ricci flow and convergence
We first prove a uniform integral Laplace comparison result for the Kähler Ricci flow on Fano manifolds which depends only on the initial metric. As an application, using Cheeger-Colding theory and previous results by some of the authors, we give a direct and independent proof of the Hamilton-Tian conjecture on convergence of Kähler-Ricci flows, modulo a codimension 4 singular set. We also expounded on some existing literature on this conjecture.

Automating the Derivation of Unification Algorithms: A Case Study in Deductive Program Synthesis
Richard Waldinger
https://arxiv.org/abs/2508.11136 https://

Automating the Derivation of Unification Algorithms: A Case Study in Deductive Program Synthesis
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a declarative specification is expressed in logical form and presented to an automatic theorem prover, and a program meeting the specification is extracted from the proof. The correctness of the program is supported by the proof, which also provides an explanation o…

Deformation Quantization on $\mathbb{R}^d$
Haiqi Wu
https://arxiv.org/abs/2509.14235 https://arxiv.org/pdf/2509.14235…

Deformation Quantization on $\mathbb{R}^d$
The primary aim of this essay, drawn from the author's MMath dissertation at Oxford, is to present and explain Kontsevich's formality theorem. The first two sections introduce the main topic. Sections 3 and 4 discuss Hochschild (co)homology, DGLA, and Maurer-Cartan elements. HKR theorem is stated in section 4, while a proof is deferred to appendix. In Section 5 we talk about L-infinity morphisms. The central result of section 5 gives a penultimate step for solving the problem. We prove the main…

Watermarking and Anomaly Detection in Machine Learning Models for LORA RF Fingerprinting
Aarushi Mahajan, Wayne Burleson
https://arxiv.org/abs/2509.15170 https://

Watermarking and Anomaly Detection in Machine Learning Models for LORA RF Fingerprinting
Radio frequency fingerprint identification (RFFI) distinguishes wireless devices by the small variations in their analog circuits, avoiding heavy cryptographic authentication. While deep learning on spectrograms improves accuracy, models remain vulnerable to copying, tampering, and evasion. We present a stronger RFFI system combining watermarking for ownership proof and anomaly detection for spotting suspicious inputs. Using a ResNet-34 on log-Mel spectrograms, we embed three watermarks: a simp…

Nonlinear stability of the Larson-Penston collapse
Yan Guo, Mahir Hadzic, Juhi Jang, Matthew Schrecker
https://arxiv.org/abs/2509.12435 https://arxiv.org/p…

Nonlinear stability of the Larson-Penston collapse
We prove nonlinear stability of the Larson-Penston family of self-similarly collapsing solutions to the isothermal Euler-Poisson system. Our result applies to radially symmetric perturbations and it is the first full nonlinear stability result for radially imploding compressible flows. At the heart of the proof is the ground state character of the Larson-Penston solution, which exhibits important global monotonicity properties used throughout the proof. One of the key challenges is the proof …

As if we needed more proof that "free speech" is dead:
"Disney pulls ‘Jimmy Kimmel Live!’ indefinitely following Kirk comments"
https://www.politico.com/news/2025/09/17/disney-jimmy-kimmel-live-kirk-00570355

Asymptotic expansion of the critical point for oriented percolation in high dimensions
Noe Kawamoto
https://arxiv.org/abs/2508.12299 https://arxiv.org/pdf/…

Asymptotic expansion of the critical point for oriented percolation in high dimensions
We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on $\mathbb Z^d$ in powers of $d^{-1}$ as $d\rightarrow \infty$. The proof relies heavily on the lace expansion.

A discrete approach to Zhang's projection inequality
David Alonso-Guti\'errez, Eduardo Lucas, Javier Mart\'in Go\~ni
https://arxiv.org/abs/2509.14986 https://…

A discrete approach to Zhang's projection inequality
In this paper we will provide a new proof of the fact that for any convex body $K\subseteq\R^n$ $$ \frac{{{2n}\choose{n}}}{n^n}n\int_0^\infty r^{n-1}\vol_n(K\cap(re_n+K))dr\leq\frac{(\vol_n(K))^{n+1}}{(\vol_{n-1}(P_{e_n^\perp}(K)))^n}, $$ where $(e_i)_{i=1}^n$ denotes the canonical orthonormal basis in $\R^n$, $P_{e_n^\perp}(K)$ denotes the orthogonal projection of $K$ onto the linear hyperplane orthogonal to $e_n$, and $\vol_k$ denotes the $k$-dimensional Lebesgue measure. This inequality was …

A generalization of RSK to $d$-complete posets
Son Nguyen, Joseph Vulakh, Dora Woodruff
https://arxiv.org/abs/2508.13988 https://arxiv.org/pdf/2508.13988…

A generalization of RSK to $d$-complete posets
The hook length formula for $d$-complete posets expresses the number of linear extensions of a $d$-complete poset $P$ in terms of hooks of $P$. It generalizes the usual hook length formula for standard Young tableaux, as well as hook length formulas for shifted Young tableaux and trees. We give a new proof of the hook length formula for $d$-complete posets which is elementary and purely combinatorial. Our approach is to define a generalization of the Robinson-Schensted-Knuth bijection for $d$-c…

This was inevitable to happen but still scary, a hacker found ways to avoid safeguards and make GPT-OSS advise on bad things.
https://decrypt.co/333858/openai-jailbreak-proof-new-models-hacked

OpenAI's 'Jailbreak-Proof' New Models? Hacked on Day One
Hours after releasing its first open-weight models in years with claims of robust safety measures, OpenAI's GPT-OSS has been cracked by notorious AI jailbreaker Pliny the Liberator

'We blew it up. And we’ll do it again’.
‘I don’t give a shit what you call it.’
These words, of US Secretary of State Marco Rubio and Vice President J.D. Vance, respectively,
refer to the first of five US bombings of boats in international waters near Venezuela in the last month,
which have reportedly killed twenty-seven people overall.
Washington claims the boats were carrying drugs destined for US shores but has offered no proof;
evidence indica…

Gabriel Hetland, Murder in the Caribbean — Sidecar
The campaign against Venezuela.

'Show Me Your ID!': White Seattle Man Shoots Black Disabled Veteran In the Chest In Broad Daylight After Demanding He Show Him Proof of His Service
https://atlantablackstar.com/2025/08/17/white-seattle-man-shoots-black-disabled-veteran/

Proof of AutoML: SDN based Secure Energy Trading with Blockchain in Disaster Case
Salih Toprak, Muge Erel-Ozcevik
https://arxiv.org/abs/2509.10291 https://…

Proof of AutoML: SDN based Secure Energy Trading with Blockchain in Disaster Case
In disaster scenarios where conventional energy infrastructure is compromised, secure and traceable energy trading between solar-powered households and mobile charging units becomes a necessity. To ensure the integrity of such transactions over a blockchain network, robust and unpredictable nonce generation is vital. This study proposes an SDN-enabled architecture where machine learning regressors are leveraged not for their accuracy, but for their potential to generate randomized values suitab…

From Evaluation to Enhancement: Large Language Models for Zero-Knowledge Proof Code Generation
Zhantong Xue, Pingchuan Ma, Zhaoyu Wang, Shuai Wang
https://arxiv.org/abs/2509.11708

From Evaluation to Enhancement: Large Language Models for Zero-Knowledge Proof Code Generation
Zero-knowledge proofs (ZKPs) are increasingly deployed in domains such as privacy-preserving authentication, blockchain scalability, and secure finance. However, authoring ZK programs remains challenging: unlike mainstream programming, ZK development requires reasoning about finite field arithmetic, constraint systems, and gadgets, making it knowledge-intensive and error-prone. While large language models (LLMs) have demonstrated strong code generation capabilities in general-purpose languages,…

Safe, Untrusted, "Proof-Carrying" AI Agents: toward the agentic lakehouse
Jacopo Tagliabue, Ciro Greco
https://arxiv.org/abs/2510.09567 https://a…

Safe, Untrusted, "Proof-Carrying" AI Agents: toward the agentic lakehouse
Data lakehouses run sensitive workloads, where AI-driven automation raises concerns about trust, correctness, and governance. We argue that API-first, programmable lakehouses provide the right abstractions for safe-by-design, agentic workflows. Using Bauplan as a case study, we show how data branching and declarative environments extend naturally to agents, enabling reproducibility and observability while reducing the attack surface. We present a proof-of-concept in which agents repair data pip…

On localization for the alloy-type Anderson-Bernoulli model with long-range hopping
Shihe Liu, Yunfeng Shi, Zhifei Zhang
https://arxiv.org/abs/2508.12714 https://

On localization for the alloy-type Anderson-Bernoulli model with long-range hopping
In this paper, we prove the Anderson localization near the spectral edge for some alloy-type Anderson-Bernoulli model on $\mathbb{Z}^d$ with exponential long-range hopping. This extends the work of Bourgain [Geometric Aspects of Functional Analysis, LNM 1850: 77--99, 2004], in which he pioneered a novel multi-scale analysis to treat Bernoulli random variables. Our proof is mainly based on Bourgain's method. However, to establish the initial scales Green's function estimates, we adapt the approa…

Emulating Public Opinion: A Proof-of-Concept of AI-Generated Synthetic Survey Responses for the Chilean Case
Basti\'an Gonz\'alez-Bustamante, Nando Verelst, Carla Cisternas
https://arxiv.org/abs/2509.09871

Emulating Public Opinion: A Proof-of-Concept of AI-Generated Synthetic Survey Responses for the Chilean Case
Large Language Models (LLMs) offer promising avenues for methodological and applied innovations in survey research by using synthetic respondents to emulate human answers and behaviour, potentially mitigating measurement and representation errors. However, the extent to which LLMs recover aggregate item distributions remains uncertain and downstream applications risk reproducing social stereotypes and biases inherited from training data. We evaluate the reliability of LLM-generated synthetic su…

An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function
Karin Ikeda
https://arxiv.org/abs/2510.10598 https://

An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function
In 1997, Báez-Duarte gave a probabilistic proof of the asymptotic formula for the partition function, which had originally been proved by Hardy-Ramanujan. Based on the probabilistic approach, this paper proves an asymptotic formula for the coefficients of the elliptic modular $j$-function using various expressions in terms of modular functions having simple infinite products.

Green's function and volume noncollapsing estimates for the K\"ahler-Ricci flow
Weiqi Zhang, Yashan Zhang
https://arxiv.org/abs/2508.13646 https://

Green's function and volume noncollapsing estimates for the Kähler-Ricci flow
We prove a local volume noncollapsing property for the long-time Kähler-Ricci flow on a minimal Kähler manifold, improving previous results of Guo-Phong-Song-Sturm, Guedj-Tô and Vu. Similar result is also proved for a twisted Kähler-Ricci flow on non-minimal Kähler manifolds. In the course of proof, we develop new Green's function estimates for a general Kähler family under the $L^{p>1}$ and $L^1(\log L)^{q>n}$ volume density conditions.

ToxiEval-ZKP: A Structure-Private Verification Framework for Molecular Toxicity Repair Tasks
Fei Lin, Tengchao Zhang, Ziyang Gong, Fei-Yue Wang
https://arxiv.org/abs/2508.12035 …

ToxiEval-ZKP: A Structure-Private Verification Framework for Molecular Toxicity Repair Tasks
In recent years, generative artificial intelligence (GenAI) has demonstrated remarkable capabilities in high-stakes domains such as molecular science. However, challenges related to the verifiability and structural privacy of its outputs remain largely unresolved. This paper focuses on the task of molecular toxicity repair. It proposes a structure-private verification framework - ToxiEval-ZKP - which, for the first time, introduces zero-knowledge proof (ZKP) mechanisms into the evaluation proce…

A reflection principle for nonintersecting paths and lozenge tilings with free boundaries
Seok Hyun Byun
https://arxiv.org/abs/2508.12135 https://arxiv.org…

A reflection principle for nonintersecting paths and lozenge tilings with free boundaries
Okada and Stembridge's Pfaffian formula for the enumeration of families of nonintersecting paths with fixed starting points and unfixed ending points has been widely used to resolve many challenging problems in enumerative combinatorics. In this paper, we present a new formula that complements Okada and Stembridge's Pfaffian formula. The proof is based on a formula for the square of the sum of maximum minors of matrices obtained from Okada's formula. The combinatorial interpretation of the new …

The asymptotic behavior of simple eigenvalues of particle-in-well systems
Peter Hintz, Aaron Moser
https://arxiv.org/abs/2508.13545 https://arxiv.org/pdf/2…

The asymptotic behavior of simple eigenvalues of particle-in-well systems
The particle in a well in dimension one is a classical problem in quantum mechanics. We study higher-dimensional analogues of the problem, where the well is a smooth domain in $\mathbb{R}^d$. We show that simple eigenvalues and eigenfunctions of the corresponding Schrödinger operator depend smoothly on the square root $h$ of the inverse depth of the well and provide an explicit first-order expansion of the eigenvalues at $h = 0$. Our proof consists of two steps. In the first step, we constru…

Proof Strategy Extraction from LLMs for Enhancing Symbolic Provers
Jian Fang, Yican Sun, Yingfei Xiong
https://arxiv.org/abs/2510.10131 https://arxiv.org/p…

Proof Strategy Extraction from LLMs for Enhancing Symbolic Provers
One important approach to software verification is interactive theorem proving. However, writing formal proofs often requires substantial human effort, making proof automation highly important. Traditionally, proof automation has relied on symbolic provers. Recently, large language models (LLMs) have demonstrated strong capabilities in theorem proving, complementing symbolic provers. Nonetheless, prompting LLMs can be expensive and may pose security risks for confidential codebases. As a result…

Monotone tail functions: definitions, properties, and application to risk-reducing strategies
Hamza Hanbali, Daniel Linders
https://arxiv.org/abs/2508.12608 https://

Monotone tail functions: definitions, properties, and application to risk-reducing strategies
This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the transformed tail quantiles of the original random variable. The main result is intuitive, in that Dhaene et al. (2002a) properties still hold, but only for certain quantile values. However, the proof presents some complications that arise especially when the function i…

A Systematic Study on Generating Web Vulnerability Proof-of-Concepts Using Large Language Models
Mengyao Zhao, Kaixuan Li, Lyuye Zhang, Wenjing Dang, Chenggong Ding, Sen Chen, Zheli Liu
https://arxiv.org/abs/2510.10148

A Systematic Study on Generating Web Vulnerability Proof-of-Concepts Using Large Language Models
Recent advances in Large Language Models (LLMs) have brought remarkable progress in code understanding and reasoning, creating new opportunities and raising new concerns for software security. Among many downstream tasks, generating Proof-of-Concept (PoC) exploits plays a central role in vulnerability reproduction, comprehension, and mitigation. While previous research has focused primarily on zero-day exploitation, the growing availability of rich public information accompanying disclosed CVEs…

Equiangular tight frames in real symplectic space: Zauner's conjecture and the skew Hadamard conjecture
Kean Fallon
https://arxiv.org/abs/2509.14463 https://

Equiangular tight frames in real symplectic space: Zauner's conjecture and the skew Hadamard conjecture
We introduce the notion of equiangular tight frames in real symplectic spaces and formulate a conjecture on their existence in terms of the dimension and number of vectors. Our main results shows the "symplectic Zauner's conjecture" is equivalent to the skew Hadamard conjecture. The proof involves counting subgraphs called "diamonds" in tournaments.

Derivatives of padded Schubert polynomials through pipe dreams
Hugh Dennin
https://arxiv.org/abs/2508.11879 https://arxiv.org/pdf/2508.11879

Derivatives of padded Schubert polynomials through pipe dreams
In recent work, Hamaker, Pechenik, Speyer, and Weigandt showed that a certain differential operator $\nabla$ expands positively in the basis of Schubert polynomials. For $π$ a dominant permutation, Gaetz and Tung showed an analogous positivity result holds for a dual differential operator $Δ$ acting on $π$-padded Schubert polynomials. In this paper, we provide a new proof of the result of Gaetz and Tung using the combinatorics of pipe dreams.

Effective theories for incompressible magnetoelastic shallow shells
Emanuele Tasso, Tobias Unterberger
https://arxiv.org/abs/2508.13916 https://arxiv.org/p…

Effective theories for incompressible magnetoelastic shallow shells
We characterize the asymptotic behaviour, in the sense of $Γ$-convergence, of a thin magnetoelastic shallow shell. The compactness is achieved up to rigid motions. For deformations, it relies on an approximation by rigid movements, whereas for magnetizations it is based on a careful consideration of the geometry of the deformed domain. The result is obtained by a combination of variational methods ($Γ$-convergence) with degree theory, fixed-point and geometrical arguments. The proof strategy …

Determination of the fifth Busy Beaver value
The bbchallenge Collaboration, Justin Blanchard (Skelet), Daniel Briggs (Skelet), Konrad Deka (Skelet), Nathan Fenner (Skelet), Yannick Forster (Skelet), Georgi Georgiev (Skelet), Matthew L. House, Rachel Hunter, Iijil, Maja K\k{a}dzio{\l}ka, Pavel Kropitz, Shawn Ligocki, mxdys, Mateusz Na\'sciszewski, savask, Tristan St\'erin, Chris Xu, Jason Yuen, Th\'eo Zimmermann

Determination of the fifth Busy Beaver value
We prove that $S(5) = 47,176,870$ using the Coq proof assistant. The Busy Beaver value $S(n)$ is the maximum number of steps that an $n$-state 2-symbol Turing machine can perform from the all-zero tape before halting, and $S$ was historically introduced by Tibor Radó in 1962 as one of the simplest examples of an uncomputable function. The proof enumerates $181,385,789$ Turing machines with 5 states and, for each machine, decides whether it halts or not. Our result marks the first determination…

Zk-SNARK Marketplace with Proof of Useful Work
Samuel Oleksak, Richard Gazdik, Martin Peresini, Ivan Homoliak
https://arxiv.org/abs/2510.09729 https://arxi…

Zk-SNARK Marketplace with Proof of Useful Work
Proof of Work (PoW) is widely regarded as the most secure permissionless blockchain consensus protocol. However, its reliance on computationally intensive yet externally useless puzzles results in excessive electric energy wasting. To alleviate this, Proof of Useful Work (PoUW) has been explored as an alternative to secure blockchain platforms while also producing real-world value. Despite this promise, existing PoUW proposals often fail to embed the integrity of the chain and identity of the m…

Necklaces, permutations, and periodic critical orbits for quadratic polynomials
Matthew Baker, Andrea Chen, Sophie Li, Matthew Qian
https://arxiv.org/abs/2508.12924 https://

Necklaces, permutations, and periodic critical orbits for quadratic polynomials
Let $G_n$ denote the $n^{\rm th}$ Gleason polynomial, whose roots correspond to parameters $c$ such that the critical point $0$ is periodic of exact period $n$ under iteration of $z^2 + c$, and let $\bar{G}_n$ denote the reduction of $G_n$ modulo $2$. Buff, Floyd, Koch, and Parry made the surprising observation that the number of real roots of $G_n$ is equal to the number of irreducible factors of $\bar{G}_n$ for all $n$. We provide a bijective proof for this result by first providing explicit …

A Gaussian integral formula for the Hermite polynomials: Combinatorics, Asymptotics and Applications
Mihai Nica, Janosch Ortmann
https://arxiv.org/abs/2508.13910 https://…

A Gaussian integral formula for the Hermite polynomials: Combinatorics, Asymptotics and Applications
The Hermite polynomials are ubiquitous but can be difficult to work with due to their unwieldy definition in terms of derivatives. To remedy this, we showcase an underappreciated Gaussian integral formula for the Hermite polynomials, which is especially useful for generalizing to multivariable Hermite polynomials. Taking this as our definition, we prove many useful consequences, including: 1. Combinatorial interpretations for the Hermite polynomials, including a proof of orthogonality. 2. A mor…

Order denseness in free Banach lattices
Youssef Azouzi, Wassim Dhifaoui
https://arxiv.org/abs/2508.11648 https://arxiv.org/pdf/2508.11648

Order denseness in free Banach lattices
We prove a fundamental property: the free vector lattice $FVL[E]$ over a Banach space E is order dense in the free p-convex Banach lattice $FBL^{(p)}[E],~~1 ^leq p \leq \infty,$ if and only if E is finite-dimensional. In a recent work, Oikhberg, Tradacete, Taylor, and Troitsky claimed that order denseness holds for all Banach spaces. We point out a gap in their proof, and consequently, any conclusions relying on this claim require reexamination -- a task we also undertake in this present paper.…

The Story of Sunflowers
Anup Rao
https://arxiv.org/abs/2509.14790 https://arxiv.org/pdf/2509.14790

The Story of Sunflowers
Sunflowers, or $Δ$-systems, are a fundamental concept in combinatorics introduced by Erdős and Rado in their paper: {\em Intersection theorems for systems of sets}, J. Lond. Math. Soc. (1) {\bf 35} (1960), 85--90. A sunflower is a collection of sets where all pairs have the same intersection. This paper explores the wide-ranging applications of sunflowers in computer science and combinatorics. We discuss recent progress towards the sunflower conjecture and present a short elementary proof of …

Sharp upper bounds on hitting probabilities for the solution to the stochastic heat equation on the line
Robert C. Dalang, David Nualart, Fei Pu
https://arxiv.org/abs/2508.11859

Sharp upper bounds on hitting probabilities for the solution to the stochastic heat equation on the line
For Gaussian random fields with values in $\mathbb{R}^d$, sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in particular to the solutions of systems of linear SPDEs. For non-Gaussian random fields, the available bounds are less sharp. For nonlinear systems of stochastic heat equations, a sharp lower bound was obtained in a previous paper by two of the authors. Here, we obtain the corresponding sharp upper bound. The proof req…

Fractional Sobolev spaces via interpolation, and applications to mixed local-nonlocal operators
Alberto Maione
https://arxiv.org/abs/2509.14703 https://arx…

Fractional Sobolev spaces via interpolation, and applications to mixed local-nonlocal operators
In this note, we present a well-known connection between the Sobolev-Slobodeckij spaces, also known as Fractional Sobolev spaces, and interpolation theory. We show how Sobolev spaces can be equivalently characterized as real and complex interpolation spaces between Lebesgue spaces and integer-order Sobolev spaces. We also state a spectral theorem for the so-called mixed local-nonlocal operators, and show how interpolation theory leads to its proof. This note is intended for early-career researc…

Metric Equational Theories
Radu Mardare (Heriot-Watt University, Edinburgh, Scotland), Neil Ghani (University of Strathclyde, Glasgow, Scotland), Eigil Rischel (University of Strathclyde, Glasgow, Scotland)
https://arxiv.org/abs/2509.14094

Metric Equational Theories
This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET) with the Enriched Lawvere Theories. We extend QETs to Metric Equational Theories (METs) where operations no longer have finite sets as arities (as in QETs and the general theory of universal algebras), but arities are now drawn from countable metric spaces. This extension is inspired by the theory of Enriched Lawvere …

Short proof of Halin's grid theorem for thick ends
Ye Chern
https://arxiv.org/abs/2509.10597 https://arxiv.org/pdf/2509.10597

Short proof of Halin's grid theorem for thick ends
In this paper, we present a short proof of Halin's grid theorem.

Algorithmic Perspective on Toda's Theorem
Dror Fried, Etay Segal, Gad E. Yaron
https://arxiv.org/abs/2509.13871 https://arxiv.org/pdf/2509.13871…

Algorithmic Perspective on Toda's Theorem
Toda's Theorem is a fundamental result in computational complexity theory, whose proof relies on a reduction from a QBF problem with a constant number of quantifiers to a model counting problem. While this reduction, henceforth called Toda's reduction, is of a purely theoretical nature, the recent progress of model counting tools raises the question of whether the reduction can be utilized to an efficient algorithm for solving QBF. In this work, we address this question by looking at Toda's red…

A short proof of free energy limit of two spin spherical Sherrington-Kirkpatrick model at any temperature
Debapratim Banerjee
https://arxiv.org/abs/2508.06298 https://

A short proof of free energy limit of two spin spherical Sherrington-Kirkpatrick model at any temperature
In this paper, we present a short proof of the limit of free energy of spherical 2 spin Sherrington-Kirkpatrick (SSK) model without external field. This proof works for all temperatures and is based on the Laplace method of integration and considering a discrete approximation of the whole space. This proof is general enough and can be adapted to any interaction matrix where the eigenvalue distribution has some nice properties. The proof in the high-temperature case is the same as the proof give…

Proof of Cloud: Data Center Execution Assurance for Confidential VMs
Filip Rezabek, Moe Mahhouk, Andrew Miller, Stefan Genchev, Quintus Kilbourn, Georg Carle, Jonathan Passerat-Palmbach
https://arxiv.org/abs/2510.12469

Proof of Cloud: Data Center Execution Assurance for Confidential VMs
Confidential Virtual Machines (CVMs) protect data in use by running workloads inside hardware-isolated environments. In doing so, they also inherit the limitations of the underlying hardware. Trusted Execution Environments (TEEs), which enforce this isolation, explicitly exclude adversaries with physical access from their threat model. Commercial TEEs, e.g., Intel TDX, thus assume infrastructure providers do not physically exploit hardware and serve as safeguards instead. This creates a tension…

Short proofs without interference
Adrian Rebola-Pardo
https://arxiv.org/abs/2508.09851 https://arxiv.org/pdf/2508.09851

Short proofs without interference
Interference is a phenomenon on proof systems for SAT solving that is both counter-intuitive and bothersome when developing proof-logging techniques. However, all existing proof systems that can produce short proofs for all inprocessing techniques deployed by SAT present this feature. Based on insights from propositional dynamic logic, we propose a framework that eliminates interference while preserving the same expressive power of interference-based proofs. Furthermore, we propose a first buil…

An involution for trivariate symmetries of vincular patterns
Joanna N. Chen, Shishuo Fu, Jiang Zeng
https://arxiv.org/abs/2509.13097 https://arxiv.org/pdf/…

An involution for trivariate symmetries of vincular patterns
We provide a bijective proof of the equidistribution of two pairs of vincular patterns in permutations, thereby resolving a recent open problem of Bitonti, Deb, and Sokal (arXiv:2412.10214). Since the bijection is involutive, we also confirm their conjecture on the equidistribution of triple vincular patterns. Somewhat unexpectedly, we show that this involution is closed on the set of Baxter permutations, thereby implying another trivariate symmetries of vincular patterns. The proof of this sec…

Codes on any Cayley Graph have an Interactive Oracle Proof of Proximity
Hugo Delavenne (GRACE), Louise Lallemand (GRACE)
https://arxiv.org/abs/2508.10510 https://

Codes on any Cayley Graph have an Interactive Oracle Proof of Proximity
Interactive Oracle Proofs of Proximity (IOPP) are at the heart of code-based SNARKs, a family of zeroknowledge protocols. The first and most famous one is the FRI protocol [BBHR18a], that efficiently tests proximity to Reed-Solomon codes. This paper generalizes the flowering IOPP introduced in [DMR25] for some specific (2, n)-regular Tanner codes to a much broader variety of codes: any code with symbols indexed on the edges of a Cayley graph. The flowering protocol of [DMR25] had a soundness pa…

Colorful circuits and colorful topes in oriented matroids
Minho Cho, Seunghun Lee, Fr\'ed\'eric Meunier
https://arxiv.org/abs/2509.13718 https://ar…

Colorful circuits and colorful topes in oriented matroids
We provide a short proof of a conic version of the colorful Carathéodory theorem for oriented matroids. Holmsen's extension of the colorful Carathéodory theorem to oriented matroids (Advances in Mathematics, 2016) already encompasses several generalizations of the original result, but not its conic version. Our approach relies on a common generalization of Sperner's lemma and Meshulam's lemma - two closely related results from combinatorial topology that have found a number of applications in…

The lonely runner conjecture holds for eight runners
Matthieu Rosenfeld
https://arxiv.org/abs/2509.14111 https://arxiv.org/pdf/2509.14111

The lonely runner conjecture holds for eight runners
We prove that the lonely runner conjecture holds for eight runners. Our proof relies on a computer verification and on recent results that allow bounding the size of a minimal counterexample. We note that our approach also applies to the known cases with 4, 5, 6, and 7 runners. We expect that minor improvements to our approach could be enough to solve the cases of 9 or 10 runners.

Hodge theory of matroids by star subdivisions
Andy Hsiao
https://arxiv.org/abs/2509.10909 https://arxiv.org/pdf/2509.10909…

Hodge theory of matroids by star subdivisions
It is known that the Chow ring of a matroid satisfies the Hard Lefschetz property and Hodge Riemann relations. We provide a proof of this theorem by decomposition of the deletion operation into star subdivisions at two dimensional cones. This gives a simple combinatorial proof which avoids intersection cohomology or algebraic geometry.

K\H{o}nig = Ramsey, A compactness lemma for Ramsey categories
Maximilian Hadek
https://arxiv.org/abs/2508.11465 https://arxiv.org/pdf/2508.11465

Kőnig = Ramsey, A compactness lemma for Ramsey categories
We prove a new characterization of the Ramsey property of categories in terms of a generalized form of Kőnig's tree lemma. Afterwards, we discuss its applications to structural Ramsey theory. In particular, we provide a new proof of the existence and uniqueness of minimal Ramsey expansions and a new transfer theorem which uses Grothendieck opfibrations and unifies several known Ramsey transfers.