Tootfinder

Combinatorial proof of a congruence for partitions into two sizes of part
Eli R. DeWitt, William J. Keith
https://arxiv.org/abs/2507.13566 https://

Combinatorial proof of a congruence for partitions into two sizes of part
Previous work showed that, for $ν_2(n)$ the number of partitions of $n$ into exactly two part sizes, one has $ν_2(16n + 14) \equiv 0 \pmod{4}$. The earlier proof required the technology of modular forms, and a combinatorial proof was desired. This article provides the requested proof, in the process refining divisibility to finer subclasses. Some of these subclasses have counts closely related to the divisor function $d(16n + 14)$, and we offer a conjecture on a potential rank statistic.

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…

Explaining Hitori Puzzles: Neurosymbolic Proof Staging for Sequential Decisions
Maria Leonor Pacheco, Fabio Somenzi, Dananjay Srinivas, Ashutosh Trivedi
https://arxiv.org/abs/2508.14294

Explaining Hitori Puzzles: Neurosymbolic Proof Staging for Sequential Decisions
We propose a neurosymbolic approach to the explanation of complex sequences of decisions that combines the strengths of decision procedures and Large Language Models (LLMs). We demonstrate this approach by producing explanations for the solutions of Hitori puzzles. The rules of Hitori include local constraints that are effectively explained by short resolution proofs. However, they also include a connectivity constraint that is more suitable for visual explanations. Hence, Hitori provides an ex…

Characterizing p-Simulation Between Theories
Hunter Monroe
https://arxiv.org/abs/2507.13576 https://arxiv.org/pdf/2507.13576

Characterizing p-Simulation Between Theories
This paper characterizes when one axiomatic theory, as a proof system for tautologies, $p$-simulates another, by showing: (i)~if c.e. theory $\mathcal{S}$ efficiently interprets $\mathcal{S}{+}ϕ$, then $\mathcal{S}$ $p$-simulates $\mathcal{S}{+}ϕ$ (Jeřábek in Pudlák17 proved simulation), since the interpretation maps an $\mathcal{S}{+}ϕ$-proof whose lines are all theorems into an $\mathcal{S}$-proof; (ii)~$\mathcal{S}$ proves ``$\mathcal{S}$ efficiently interprets $\mathcal{S}{+}ϕ$'' iff…

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…

Proof of a Generalized Ryu-Takayanagi Conjecture
Artem Averin
https://arxiv.org/abs/2508.14877 https://arxiv.org/pdf/2508.14877

Proof of a Generalized Ryu-Takayanagi Conjecture
We derive a generalized version of the Ryu-Takayanagi formula for the entanglement entropy in arbitrary diffeomorphism invariant field theories. We use a recent framework which expresses the measurable quantities of a quantum theory as a weighted sum over paths in the theory's phase space. If this framework is applied to a field theory on a spacetime foliated by a hypersurface $Σ,$ the choice of a codimension-2 surface $B$ without boundary contained in $Σ$ specifies a submanifold in the phase…

Proof the army thinks birds are real.
Army tests robotic coyotes to defend fighter jets
https://www.armytimes.com/news/your-army/2025/07/07/army-tests-robotic-coyotes-to-defend-fighter-jets/

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…

Bust-proof Fantasy Football draft picks for 2025 that the Fantasy Football Today team has pinpointed

https://www.cbssports.com/fantasy/f…

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 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…

Mathematical proof concerning the additivity problem of nonlinear normalized citation counts
Xing Wang, Zhihui Zhang
https://arxiv.org/abs/2508.14595 https://

Mathematical proof concerning the additivity problem of nonlinear normalized citation counts
The issue of whether nonlinear normalized citation counts can be added is critically important in scientometrics because it touches upon the theoretical foundation of underlying computation in the field. In this paper, we provide rigorous mathematical proofs for the key theorems underlying this fundamental issue. Based on these proofs, we ultimately arrive at the following conclusion: a nonlinear normalization method for citation counts must be a non-equidistant transformation; consequently, th…

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

A Million-dollar Proof
Aaron Abrams
https://arxiv.org/abs/2507.13365 https://arxiv.org/pdf/2507.13365

A Million-dollar Proof
We present a new twist on an old identity.

Abundance Diagnostics from Slitless Imaging Spectrometer: A Proof-of-Concept for MaGIXS-2
Biswajit Mondal, Amy R. Winebarger, P. S. Athiray
https://arxiv.org/abs/2508.14866 http…

Abundance Diagnostics from Slitless Imaging Spectrometer: A Proof-of-Concept for MaGIXS-2
Elemental abundance diagnostics in the solar corona are crucial for understanding energy transport, plasma heating, and magnetic activity. Most earlier imaging-spectroscopic studies have relied on slit-based spectrometers, which offer high spectral resolution but are limited in spatiotemporal coverage and temperature diagnostics. In contrast, slitless spectrographs like the Marshall Grazing Incidence X-ray Spectrometer (MaGIXS) produce overlapping spatial-spectral data (overlappograms) to enabl…

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…

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.

https://slate.com/technology/2014/07/a-killer-robots-txt-google-easter-egg.html
see this is wrong, the T-1000’s user agent would actually be
Mozilla/5.0 (T-1000; CPU like T-800) Skynet (KHTML, like Gecko) Terminator version 1000 (like Human)…

Is This a Google Easter Egg or Proof That Skynet Is Actually Plotting World Domination?
It's great to be successful, but sometimes being as huge as Google can make a company lose its sense of humor. Google seems determined not to let that...

Reasoning is about giving reasons
Krunal Shah, Dan Roth
https://arxiv.org/abs/2508.14488 https://arxiv.org/pdf/2508.14488

Reasoning is about giving reasons
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to understanding the underlying "reasons" which make up the proof or disproof of the premise - as a function of the "logical atoms" in the argument. While it has been shown that transformers can "chain" rules to derive simple arguments, the challenge of articulating t…

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, …

I will stand on business and say that narcissistic doomers are as bad for discussion surrounding progressive legislation as actual opposition, we saw what PirateSoftware saying "no this isn't feasible" for long enough with no substantive proof did to SKG and how we only saved it by the skin of its teeth.

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.

The government does have an Epstein list -- here's the proof (Chris Truax/The Hill)
https://thehill.com/opinion/white-house/5407135-trump-epstein-files-conspiracy/
http://www.memeorandum.com/250719/p3#a250719p3

On K3 surfaces with hyperbolic automorphism groups
Koji Fujiwara, Keiji Oguiso, Xun Yu
https://arxiv.org/abs/2507.13726 https://arxiv…

On K3 surfaces with hyperbolic automorphism groups
We show the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the assumption that the Picard number $\ge 6$ which is optimal to ensure the finiteness. Our proof of finiteness is based on the study of genus one fibrations on K3 surfaces and recent work of Kikuta and Takatsu.

Optimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factors
Shabarish Chenakkod, Micha{\l} Derezi\'nski, Xiaoyu Dong
https://arxiv.org/abs/2508.14234

Optimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factors
We give a proof of the conjecture of Nelson and Nguyen [FOCS 2013] on the optimal dimension and sparsity of oblivious subspace embeddings, up to sub-polylogarithmic factors: For any $n\geq d$ and $ε\geq d^{-O(1)}$, there is a random $\tilde O(d/ε^2)\times n$ matrix $Π$ with $\tilde O(\log(d)/ε)$ non-zeros per column such that for any $A\in\mathbb{R}^{n\times d}$, with high probability, $(1-ε)\|Ax\|\leq\|ΠAx\|\leq(1+ε)\|Ax\|$ for all $x\in\mathbb{R}^d$, where…

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:/…

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

Matching logic -- proof system $\mathcal{G}^c$
Lauren\c{t}iu Leu\c{s}tean, Dafina Trufa\c{s}
https://arxiv.org/abs/2506.13801 https://

Matching logic -- proof system $\mathcal{G}^c$
We propose in these notes a new proof system for first-order matching logic with application, obtained by adapting to matching logic Gödel's proof system for first-order intuitionistic logic.

Towards Operation Proof Obligation Generation for VDM
Nick Battle, Peter Gorm Larsen
https://arxiv.org/abs/2506.12858 https://arxiv.o…

Towards Operation Proof Obligation Generation for VDM
All formalisms have the ability to ensure that their models are internally consistent. Potential inconsistencies are generally highlighted by assertions called proof obligations, and the generation of these obligations is an important role of the tools that support the method. This capability has been available for VDM tools for many years. However, support for obligation generation for explicit operation bodies has always been limited. This work describes the current state of work to address t…

Singular Perturbations of Hamilton-Jacobi Equations in the Wasserstein Space
Antonios Zitridis
https://arxiv.org/abs/2508.14333 https://arxiv.org/pdf/2508.…

Singular Perturbations of Hamilton-Jacobi Equations in the Wasserstein Space
We study a singular perturbation problem for second-order Hamilton-Jacobi equations in the Wasserstein space. Specifically, we characterize the behavior of the solutions as the perturbation parameter $\varepsilon$ tends to zero. The notion of solution we adopt is that of viscosity solutions in the sense of test functions on the Wasserstein space. Our proof utilizes the perturbed test function method, appropriately adapted to this setting. Finally, we highlight a connection with the homogenizati…

Round-Preserving Asymptotic Compression of Prior-Free Interactive Protocols
Gurleen Padda, Dave Touchette
https://arxiv.org/abs/2507.13464 https://

Round-Preserving Asymptotic Compression of Prior-Free Interactive Protocols
There is a close relationship between the communication complexity and information complexity of communication problems, as demonstrated by results such as Shannon's noiseless source coding theorem, and the Slepian-Wolf theorem. Here, we study this relationship in the prior-free and interactive setting, where we provide an alternate proof for the result of Braverman [SIAM Review, vol. 59, no. 4, 2017], that the amortized communication complexity of simulating a prior-free interactive communicat…

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…

Geometric components of representation spaces via robust families of submanifolds
Gabriele Viaggi
https://arxiv.org/abs/2508.14842 https://arxiv.org/pdf/25…

Geometric components of representation spaces via robust families of submanifolds
We introduce robust families of submanifolds for a linear Lie group $G$. We show that they give rise to geometric subspaces of the representation space ${\rm Hom}(Γ,G)$. As an application, we give a unified short proof of results of Beyrer and Kassel and of Benoist and Koszul about the existence of higher Teichmüller components for $G={\rm SO}(p,q+1),{\rm SL}(p+1,\mathbb{R})$. Being based on very general principles, our approach might be suited for finding geometric components in various ${\r…

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

#ShamelesslySpoofedFromTheOtherSite

Carleman estimates for stationary $Q$-valued maps: a variational approach
Aria Halavati, Luca Spolaor
https://arxiv.org/abs/2508.14388 https://arxiv.org/pd…

Carleman estimates for stationary $Q$-valued maps: a variational approach
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizing multivalued functions, originally due to Almgren and to De Lellis-Spadaro.

#LB Eu demorei um tempo até entender o que raios era isso. Senhoras e senhores, um semi-grupo representado por maçãs e bananas! rs
https://mathstodon.xyz/@slava/114701493754149431

Removing quasiconformal orbits
Jairo Bochi
https://arxiv.org/abs/2507.13519 https://arxiv.org/pdf/2507.13519

Removing quasiconformal orbits
We show that generic continuous linear cocycles over shifts and other zero-dimensional systems admit no quasiconformal orbits, thus providing a partial answer to a question of Nassiri, Rajabzadeh, and Reshadat. The proof relies on a new result about towers for homeomorphisms of zero-dimensional spaces, which may be of independent interest.

Wyoming Is Now Requiring Would-be Voters to Document Their Citizenship | Bolts
https://boltsmag.org/wyoming-voter-registration-proof-of-citizenship-law/

On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter
Guanfu Liu, Pengfei Li, Yukun Liu, Xiaolong Pu
https://arxiv.org/abs/2507.13764

On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter
We provide a general and rigorous proof for the strong consistency of maximum likelihood estimators of the cumulative distribution function of the mixing distribution and structural parameter under finite mixtures of location-scale distributions with a structural parameter. The consistency results do not require the parameter space of location and scale to be compact. We illustrate the results by applying them to finite mixtures of location-scale distributions with the component density functio…

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.

Parabolic geometric Eisenstein series and constant term functors
Joakim Faergeman, Andreas Hayash
https://arxiv.org/abs/2507.13930 https://

Parabolic geometric Eisenstein series and constant term functors
We prove a compatibility between parabolic restriction of Whittaker sheaves and restriction of representations under the geometric Casselman-Shalika equivalence. To do this, we establish various Hecke structures on geometric Eisenstein series functors, generalizing results of Braverman-Gaitsgory in the case of a principal parabolic. Moreover, we relate compactified and non-compactified geometric Eisenstein series functors via Koszul duality. We sketch a proof that the spectral-to-automorphic …

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…

On the Carlitz-Mehler formula for Hermite polynomials
Manish Chaurasia
https://arxiv.org/abs/2508.12676 https://arxiv.org/pdf/2508.12676

On the Carlitz-Mehler formula for Hermite polynomials
Carlitz proved a few generalizations of Mehler's formula. Later, Srivastava et al. gave a new proof for some extensions of Carlitz's formula. Here, a direct proof of the further generalization is given.

Israel's government has condemned the strike that hit Soroka Hospital as a criminal act against a civilian target. But since they've offered no proof that it wasn't being secretly used for military purposes, we may have to pause any outrage.

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

Cyclic proof theory of positive inductive definitions
Gianluca Curzi, Lukas Melgaard
https://arxiv.org/abs/2507.13057 https://arxiv.o…

Cyclic proof theory of positive inductive definitions
We study cyclic proof systems for $μ\mathsf{PA}$, an extension of Peano arithmetic by positive inductive definitions that is arithmetically equivalent to the (impredicative) subsystem of second-order arithmetic $Π^1_2$-$\mathsf{CA}_0$ by Möllefeld. The main result of this paper is that cyclic and inductive $μ\mathsf{PA}$ have the same proof-theoretic strength. First, we translate cyclic proofs into an annotated variant based on Sprenger and Dam's systems for first-order $μ$-calculus, whose…

Privacy-preserving and reward-based mechanisms of proof of engagement
Matteo Marco Montanari, Alessandro Aldini
https://arxiv.org/abs/2506.12523 https://…

Privacy-preserving and reward-based mechanisms of proof of engagement
Proof-of-Attendance (PoA) mechanisms are typically employed to demonstrate a specific user's participation in an event, whether virtual or in-person. The goal of this study is to extend such mechanisms to broader contexts where the user wishes to digitally demonstrate her involvement in a specific activity (Proof-of-Engagement, PoE). This work explores different solutions, including DLTs as well as established technologies based on centralized systems. The main aspects we consider include the l…

Future-proofing crops against climate change is crucial for food security. Scientists are developing innovative solutions, but public investment is needed to bring them to fruition. #climatechange #climatesolutions

To future-proof crops, science is half the battle. The other half is getting existing solutions into the field.
A new paper offers a roadmap for integrating crop resilience and carbon mitigation into national and global climate strategies.

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[2/3]:
A classical proof of quantum knowledge for multi-prover interactive proof systems

A federal judge Friday issued a second preliminary injunction blocking some provisions of the sweeping executive order on elections that Donald Trump signed in March.
Judge Denise Casper blocked provisions ordering the U.S. Election Assistance Commission to take steps to require documentary proof of citizenship from people registering to vote and requiring federal voter registration agencies to “assess” the citizenship of individuals who receive public assistance before providing them …

Parts of Trump’s executive order on elections blocked by a federal court
A federal court granted a coalition of states an injunction halting implementation of parts of Trump’s executive order on elections.

Distribution of prime geodesic traces
Anton Deitmar
https://arxiv.org/abs/2507.13679 https://arxiv.org/pdf/2507.13679

Distribution of prime geodesic traces
This note complements a recent paper of Chatzakos, Harcos and Kaneko \cite{CHK}. We use a Dirichlet style Prime Geodesic Theorem to improve the error term estimate in loc. cit. at the cost of lowering the resolution. The proof relies on the Selberg trace formula.

Capacity Matters: a Proof-of-Concept for Transformer Memorization on Real-World Data
Anton Changalidis, Aki H\"arm\"a
https://arxiv.org/abs/2506.14704

Capacity Matters: a Proof-of-Concept for Transformer Memorization on Real-World Data
This paper studies how the model architecture and data configurations influence the empirical memorization capacity of generative transformers. The models are trained using synthetic text datasets derived from the Systematized Nomenclature of Medicine (SNOMED) knowledge graph: triplets, representing static connections, and sequences, simulating complex relation patterns. The results show that embedding size is the primary determinant of learning speed and capacity, while additional layers provi…

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

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…

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…

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.

LISA -- A Modern Proof System
Simon Guilloud, Sankalp Gambhir, Viktor Kun\v{c}ak
https://arxiv.org/abs/2507.11167 https://arxiv.org/p…

LISA -- A Modern Proof System
We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic predicate and function symbols. It implements polynomial-time proof checking and uses the axioms of ortholattices (which implies the irrelevance of the order of conjuncts and disjuncts and additional propositional laws). The kernel supports the notion of theorems …

The ASAS-SN Low Surface Brightness Survey I: Proof-of-Concept and Potential Applications
Evan Jennerjahn, Michael A. Tucker, Benjamin J. Shappee, Christopher S. Kochanek, Subo Dong, Annika H. G. Peter, Jose L. Prieto, K. Z. Stanek, Todd A. Thompson
https://arxiv.org/abs/2506.14873

The ASAS-SN Low Surface Brightness Survey I: Proof-of-Concept and Potential Applications
The ASAS-SN Low Surface Brightness Survey utilizes the $\sim7$ years of g-band CCD data from ASAS-SN (The All-Sky Automated Survey for Supernovae) to create stacked images of the entire sky. It is significantly deeper than previous photographic surveys. Our median/95th percentile cumulative exposure time per field is 58.1/86.8 hours, and our median $3σ$ g-band surface brightness limit off the Galactic plane ($|b| > 20°$) is 26.1 mag arcsec$^{-2}$. We image large-scale diffuse struct…

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.

Density of finitely supported invariant measures for automorphisms of compact abelian groups
Rotem Yaari
https://arxiv.org/abs/2507.14113 https://

Density of finitely supported invariant measures for automorphisms of compact abelian groups
We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space of all invariant probability measures, and that if the system is ergodic with respect to Haar measure, then the finitely supported ergodic invariant measures are also dense. A key ingredient in the proof is a variant of the specification property, which we est…

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…

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.

Some concerns on the border rank of Kronecker products of the Coppersmith-Winograd tensor
Daiki Kawabe
https://arxiv.org/abs/2507.13126 https://

Some concerns on the border rank of Kronecker products of the Coppersmith-Winograd tensor
This note provides a detailed proof of Conner--Gesmundo--Landsberg--Ventura's result that the border rank of the Kronecker square of the little Coppersmith--Winograd tensor is $(q+2)^{2}$.We also indicate how the same ideas seem to extend to the case of the Kronecker cube, pointing toward the conjectural value $(q+2)^{m}$ for $m\ge 4$, although a full proof is left for future work.

The convergence proof of the sixth-order compact 9-point FDM for the 2D transport problem
Qiwei Feng
https://arxiv.org/abs/2506.12549 https://

The convergence proof of the sixth-order compact 9-point FDM for the 2D transport problem
It is widely acknowledged that the convergence proof of the error in the $l_{\infty}$ norm of the high-order finite difference method (FDM) and finite element method (FEM) in 2D is challenging. In this paper, we derive the sixth-order compact 9-point FDM with the explicit stencil for the 2D transport problem with the constant coefficient and the Dirichlet boundary condition in a unit square. The proposed sixth-order FDM forms an M-matrix for the any mesh size $h$ employing the uniform Cartesian…

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…

On Pell numbers representable as product of two generalized Fibonacci numbers
Jhon J. Bravo, Pranabesh Das, Jose L. Herrera, John C. Saunders
https://arxiv.org/abs/2507.13674

On Pell numbers representable as product of two generalized Fibonacci numbers
A generalization of the well-known Fibonacci sequence is the $k$-Fibonacci sequence with some fixed integer $k\ge 2$. The first $k$ terms of this sequence are $0,0, \ldots, 1$, and each term afterwards is the sum of the preceding $k$ terms. In this paper, we find all Pell numbers that can be written as a product of two $k$-Fibonacci numbers. The proof of our main theorem uses lower bounds for linear forms in logarithms, properties of continued fractions, and a variation of a result of Dujella a…

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…

Liquid Drop Model for Nuclear Matter in the Low Density Limit
Rupert L. Frank, Mathieu Lewin, Robert Seiringer
https://arxiv.org/abs/2507.14012 https://

Liquid Drop Model for Nuclear Matter in the Low Density Limit
We consider the liquid drop model with a positive background density in the thermodynamic limit. We prove a two-term asymptotics for the ground state energy per unit volume in the dilute limit. Our proof justifies the expectation that optimal configurations consist of droplets of unit size that arrange themselves according to minimizers for the Jellium problem for point particles. In particular, we provide the first rigorous derivation of what is known as the gnocchi phase in astrophysics.

Democrats demand proof that Andry Hernšndez Romero is alive
https://www.thepinknews.com/2025/06/11/democrats-demand-proof-that-deported-gay-asylum-seeker-andry-hernandez-romero-is-still-alive/

Quantum-inspired algorithm for simulating viral response
D. O. Konina, D. I. Korbashov, I. V. Kovalchuk, A. A. Nizamieva, D. A. Chermoshentsev, A. K. Fedorov
https://arxiv.org/abs/2506.15671

Quantum-inspired algorithm for simulating viral response
Understanding the properties of biological systems is an exciting avenue for applying advanced approaches to solving corresponding computational tasks. A specific class of problems that arises in the resolution of biological challenges is optimization. In this work, we present the results of a proof-of-concept study that applies a quantum-inspired optimization algorithm to simulate a viral response. We formulate an Ising-type model to describe the patterns of gene activity in host responses. Re…

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

Fair distribution of bundles
Pablo Sober\'on
https://arxiv.org/abs/2507.13421 https://arxiv.org/pdf/2507.13421

Fair distribution of bundles
In this paper, we study the problem of splitting fairly bundles of items. We show that given $n$ bundles with $m$ kinds of items in them, it is possible to distribute the value of each kind of item fairly among $r$ persons by breaking apart at most $(r-1)m$ bundles. Moreover, we can guarantee that each participant will receive roughly $n/r - mr/2$ full bundles. The proof methods are topological and use a modified form of the configuration space/test map scheme. We obtain optimal results when $r…

A uniform cut-elimination theorem for linear logics with fixed points and super exponentials
Esa\"ie Bauer, Alexis Saurin
https://arxiv.org/abs/2506.14327

A uniform cut-elimination theorem for linear logics with fixed points and super exponentials
In the realm of light logics deriving from linear logic, a number of variants of exponential rules have been investigated. The profusion of such proof systems induces the need for cut-elimination theorems for each logic, the proof of which may be redundant. A number of approaches in proof theory have been adopted to cope with this need. In the present paper, we consider this issue from the point of view of enhancing linear logic with least and greatest fixed-points and considering such a variet…

The periodic KdV with control on space-time measurable sets
Jingrui Niu, Ming Wang, Shengquan Xiang
https://arxiv.org/abs/2507.13740 https://

The periodic KdV with control on space-time measurable sets
In this paper, we establish the local exact controllability of the KdV equation on torus around equilibrium states, where both the spatial control region and the temporal control region are sets of positive measure. The proof is based on a novel strategy for proving observability inequalities on space-time measurable sets. This approach is applicable to a broad class of dispersive equations on torus.

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.

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…

An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Rinaldo B. Schinazi
https://arxiv.org/abs/2506.13662

An elementary proof of existence and uniqueness of stationary distributions for irreducible Markov chains
Consider an $n\times n$ matrix $P$ with the following properties. All entries in $P$ are positive or $0$, the sum of each row is 1 and for all $i$ and $j$ in $\{1,\dots,n\}$ there exists a natural number $k$ such that the $(i,j)$ entry of the matrix $P^k$ is strictly positive. Then, there exists a unique row vector $v$ with only strictly positive entries, whose sum of entries is 1 and such that $vP=P$. We present a proof of this well-known result that uses only basic algebra and the Bolzano-Wei…

The Liouville-type equation and an Onofri-type inequality on closed 4-manifolds
Xi-Nan Ma, Tian Wu, Xiao Zhou
https://arxiv.org/abs/2508.14494 https://arxi…

The Liouville-type equation and an Onofri-type inequality on closed 4-manifolds
In this paper, we study the Liouville-type equation \[Δ^2 u-λ_1κΔu+λ_2κ^2(1-\mathrm e^{4u})=0\] on a closed Riemannian manifold \((M^4,g)\) with \(\operatorname{Ric}\geqslant 3κg\) and \(κ>0\). Using the method of invariant tensors, we derive a differential identity to classify solutions within certain ranges of the parameters \(λ_1,λ_2\). A key step in our proof is a second-order derivative estimate, which is established via the continuity method. As an application of the classif…

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…

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.

Proof of a conjecture on eigenvalues of transposition graph
Cheng Yeaw Ku, Leyou Xu
https://arxiv.org/abs/2506.14419 https://arxiv.or…

Proof of a conjecture on eigenvalues of transposition graph
The transposition graph $Cay(S_n,T_n)$ is the Cayley graph on the symmetric group $S_n$ generated by the set $T_n$ of all transpositions. In this paper, we show that each integer in the interval $\left[-{\lfloor(2n+1)/3 \rfloor\choose 2}, {\lfloor(2n+1)/3 \rfloor\choose 2}\right]$ is an eigenvalue of $Cay(S_n,T_n)$. This proves a recent conjecture by Kravchuk \cite{Kravchuk}.

'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/

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…

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…

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…

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…

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 …

H\"older stability of an inverse spectral problem for the magnetic Schr\"odinger operator on a simple manifold
Boya Liu, Hadrian Quan, Teemu Saksala, Lili Yan
https://arxiv.org/abs/2507.13619

Hölder stability of an inverse spectral problem for the magnetic Schrödinger operator on a simple manifold
We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schrödinger operator can be recovered Hölder stably from the boundary spectral data. This data contains the eigenvalues and the Neumann traces of the corresponding sequence of Dirichlet eigenfunctions of the operator. Our proof contains two parts, which we present in the reverse order. (1) We show that the boundary spectral data can be stably obtaine…

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 $n \geq 3$.

Towards an Analysis of Proofs in Arithmetic
Alexander Leitsch, Anela Loli\'c, Stella Mahler
https://arxiv.org/abs/2506.05837 https://

Towards an Analysis of Proofs in Arithmetic
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata admit (schematic) cut-elimination and the construction of Herbrand systems. This work focuses on the expressivity of proof schemata. We show that proof schemata can simulate primitive recursive arithmetic. The translation of proofs in arithmetic to proof schema…

A short proof of the Alt-Caffarelli-Friedman monotonicity formula
Emanuele Salato
https://arxiv.org/abs/2506.13473 https://arxiv.org/…

A short proof of the Alt-Caffarelli-Friedman monotonicity formula
The Alt-Caffarelli-Friedman monotonicity formula is a cornerstone in the theory of free boundary problems. In this note we provide a short proof of this result. To prove the main stepping stone, namely the Friedland-Hayman inequality, we exploit a useful convexity property.

Abstraction-Based Proof Production in Formal Verification of Neural Networks
Yizhak Yisrael Elboher, Omri Isac, Guy Katz, Tobias Ladner, Haoze Wu
https://arxiv.org/abs/2506.09455 …

Abstraction-Based Proof Production in Formal Verification of Neural Networks
Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN verification results. However, current proofproducing verifiers do not support abstraction-based reasoning, creating a gap between scalability and provable guarantees. We address this gap by introducing a novel framework for proof-producing abstraction-based DNN verif…

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 …

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…

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.

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 …

Proof-Theoretic Functional Completeness for the Connexive Logic C
Sara Ayhan, Hrafn Valt\'yr Oddsson
https://arxiv.org/abs/2507.06854 https://

Proof-Theoretic Functional Completeness for the Connexive Logic C
We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation, expressing a notion of direct refutation, the proof needs to be applied in a bilateralist way in that not only higher-order rule schemata for proofs but also for refutations need to be considered. Secondly, given that C is a connexive logic we need to take a …

Path-filtration for modal logics applied to revisiting quasi-dense logics
Olivier Gasquet
https://arxiv.org/abs/2507.11258 https://ar…

Path-filtration for modal logics applied to revisiting quasi-dense logics
In https://arxiv.org/pdf/2405.10094 (also published at LICS'24 conference), Lyon and Ostropolski-Nalewaja answer the question of the decidability of quasi-dense modallogics, and give an upper bound in EXPSPACE. Unfortunately, their intricate proof contains a major flaw that cannot be fixed, leaving the question wide open. In this paper we provide a correct and rather simple and direct proof of it by introducing a new variant of the well-know filtration method based on paths in a canonical model…