Tootfinder

Lower Bounds against the Ideal Proof System in Finite Fields
Tal Elbaz, Nashlen Govindasamy, Jiaqi Lu, Iddo Tzameret
https://arxiv.org/abs/2506.17210 https…

Lower Bounds against the Ideal Proof System in Finite Fields
Lower bounds against strong algebraic proof systems and specifically fragments of the Ideal Proof System (IPS), have been obtained in an ongoing line of work. All of these bounds, however, are proved only over large (or characteristic $0$) fields, yet finite fields are the more natural setting for propositional proof complexity, especially for progress toward lower bounds for Frege systems such as $AC^0[p]$-Frege. This work establishes lower bounds against fragments of IPS over fixed finite fie…

Zero-Knowledge Proof-of-Location Protocols for Vehicle Subsidies and Taxation Compliance
Dan Bogdanov, Eduardo Brito, Annika Jaakson, Peeter Laud, Raul-Martin Rebane
https://arxiv.org/abs/2506.16812

Zero-Knowledge Proof-of-Location Protocols for Vehicle Subsidies and Taxation Compliance
This paper introduces a new set of privacy-preserving mechanisms for verifying compliance with location-based policies for vehicle taxation, or for (electric) vehicle (EV) subsidies, using Zero-Knowledge Proofs (ZKPs). We present the design and evaluation of a Zero-Knowledge Proof-of-Location (ZK-PoL) system that ensures a vehicle's adherence to territorial driving requirements without disclosing specific location data, hence maintaining user privacy. Our findings suggest a promising approach t…

Transformers for Stratified Spectropolarimetric Inversion: Proof of Concept
Ryan James Campbell, Mihalis Mathioudakis, Carlos Quintero Noda
https://arxiv.org/abs/2506.16810

Transformers for Stratified Spectropolarimetric Inversion: Proof of Concept
Solar spectropolarimetric inversion -- inferring atmospheric conditions from the Stokes vector -- is a key diagnostic tool for understanding solar magnetism, but traditional inversion methods are computationally expensive and sensitive to local minima. Advances in artificial intelligence (AI) offer faster solutions, but are often restricted to shallow models or a few spectral lines. We present a proof-of-concept study using a transformer machine learning (ML) model for multi-line, full-Stokes i…

New Bounds for the Ideal Proof System in Positive Characteristic
Amik Raj Behera, Nutan Limaye, Varun Ramanathan, Srikanth Srinivasan
https://arxiv.org/abs/2506.16397

New Bounds for the Ideal Proof System in Positive Characteristic
In this work, we prove upper and lower bounds over fields of positive characteristics for several fragments of the Ideal Proof System (IPS), an algebraic proof system introduced by Grochow and Pitassi (J. ACM 2018). Our results extend the works of Forbes, Shpilka, Tzameret, and Wigderson (Theory of Computing 2021) and also of Govindasamy, Hakoniemi, and Tzameret (FOCS 2022). These works primarily focused on proof systems over fields of characteristic $0$, and we are able to extend these results…

📢 The 2025 GÉANT Innovation Programme has been awarded to the GÉANT Digital Research Environment (DRE) initiative!
Based on the @… Research Cloud, the initiative is a close collaboration between SURF & GÉANT.
Four NRENs —SUNET, Switch, HEAnet & Sikt — will also contribute with their own funding by establishing national tenancies of the GÉANT DRE.

GÉANT Innovation Programme awards its 2025 edition to Digital Research Environment (DRE) initiative | GÉANT CONNECT Online
The GÉANT Innovation Programme is excited to announce the award of its entire 2025 fund to the development of a GÉANT Digital Research Environment (DRE) and of a series of related Proof of Concepts. Based on the SURF Research Cloud, this digital platform will allow researchers and research organisations within NREN communities to build virtual

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

https://www.cbssports.com/fantasy/f…

Generalized Hockey Stick Theorem
Molly Lynch, Michael Weselcouch
https://arxiv.org/abs/2506.16463 https://arxiv.org/pdf/2506.16463

Generalized Hockey Stick Theorem
We give a combinatorial proof via a sign-reversing involution for a new identity that generalizes both the Hockey Stick Identity and the Big Hockey Stick and Pucks Identity.

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.

Coinductive well-foundedness
Iosif Petrakis
https://arxiv.org/abs/2506.16433 https://arxiv.org/pdf/2506.16433

Coinductive well-foundedness
We introduce a coinductive version of the well-foundedness of N that is used in our proof within minimal logic of the constructive counterpart CLNP to the standard least number principle LNP. According to CLNP, an inhabited complemented subset of N has a least element if and only if it is downset located. The use of complemented subsets of N in the formulation of CLNP, instead of subsets of N, allows a positive approach to the subject that avoids negation. Generalising the coinductive well-foun…

Correction to: The Double-Wedge Algebra for Quantum Fields on Schwarzschild and Minkowski Spacetimes
Bernard S. Kay (York)
https://arxiv.org/abs/2506.15731

Correction to: The Double-Wedge Algebra for Quantum Fields on Schwarzschild and Minkowski Spacetimes
There is an error in the proof (but not the truth) of Theorem 3.2 in the author's 1985 paper "The Double-Wedge Algebra for Quantum Fields on Schwarzschild and Minkowski Spacetimes" in "Communications in Mathematical Physics". The author became aware of that error and of how it may be corrected soon after it went to print, and two companion papers published soon afterwards (in Helvetica Physica Acta) refer to an "erratum to appear". This is that erratum. We also take the opportunity to note a fe…

Higher dimensional Sacks-Uhlenbeck-type functionals and applications
Gianmichele Di Matteo, Tobias Lamm
https://arxiv.org/abs/2506.17166 https://

Higher dimensional Sacks-Uhlenbeck-type functionals and applications
In this work, we generalize Sacks-Uhlenbeck's existence result for harmonic spheres, constructing for $n \ge 2$, regular, non-trivial, $n$-harmonic $n$-spheres into suitable target manifolds. We obtain an infinite family of new null-homotopic such maps. The proof follows a similar perturbative argument, which in high dimensions leads to a degenerate and double-phase-type Euler-Lagrange system, making the uniform regularity needed to formalize the bubbling harder to achieve. Then, we develop a r…

The Proof Analysis Problem
Noel Arteche, Albert Atserias, Susanna F. de Rezende, Erfan Khaniki
https://arxiv.org/abs/2506.16956 https://

The Proof Analysis Problem
Atserias and Müller (JACM, 2020) proved that for every unsatisfiable CNF formula $φ$, the formula $\operatorname{Ref}(φ)$, stating "$φ$ has small Resolution refutations", does not have subexponential-size Resolution refutations. Conversely, when $φ$ is satisfiable, Pudlák (TCS, 2003) showed how to construct a polynomial-size Resolution refutation of $\operatorname{Ref}(φ)$ given a satisfying assignment of $φ$. A question that remained open is: do all short Resolution refutations of $\op…

#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

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…

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…

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

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

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/

Normal and Dynamical Typicality in a Random Matrix Model
L\'aszl\'o Erd\H{o}s, Joscha Henheik, Cornelia Vogel
https://arxiv.org/abs/2506.17177 http…

Normal and Dynamical Typicality in a Random Matrix Model
We prove normal typicality and dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner type random matrices [arXiv:2403.10359] and an intricate analysis of the deterministic approximation.

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 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.

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…

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…

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…

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

Colimits in the $\infty$-category of $\infty$-topoi and \'etale morphisms
Taichi Uemura
https://arxiv.org/abs/2506.10431 https://…

Colimits in the $\infty$-category of $\infty$-topoi and étale morphisms
We provide an alternative proof of Lurie's result that the wide subcategory of the $\infty$-category of $\infty$-topoi spanned by the étale morphisms is closed under small colimits. Our proof is based on a new characterization of étale morphisms of $\infty$-topoi in relation to univalent families and does not rely on a larger universe. During the proof, we also give an elementary construction of univalent completion.

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…

Scattering of the 2D modified Zakharov-Kuznetsov equation
Philippe Anjolras
https://arxiv.org/abs/2506.17179 https://arxiv.org/pdf/25…

Scattering of the 2D modified Zakharov-Kuznetsov equation
We study the modified Zakharov-Kuznetsov equation in dimension $2$ : \[ \partial_t u + \partial_x \left( Δu + u^3 \right) = 0 \] where $u : (t, (x, y)) \in \mathbb{R} \times \mathbb{R}^2 \mapsto u(t, x, y) \in \mathbb{R}$ and $Δ= \partial_x^2 + \partial_y^2$ is the full Laplacian. We prove that solutions for small and localized initial data scatter for large time. Our proof relies on the method of space-time resonances.

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.

Definitive proof that Trump is in severe mental and cognitive decline , read and judge for yourself.
#trump #israel #iran

An Elementary Proof for the Basel Problem
Jesus Retamozo
https://arxiv.org/abs/2506.11101 https://arxiv.org/pdf/2506.11101

An Elementary Proof for the Basel Problem
We present an astonishingly simple and elegant proof of the celebrated Basel problem.

You know, there are a lot of people of Jewish religion or descent among those in LA being assaulted by DHS/ICE/LAPD.
Since, apparently, any act that is in opposition to Jews is now full, irrefutable, and instant proof of antisemitism I believe we have clear proof that FFOTUS and gang are actively and overtly antisemitic and deserving of instant deportation.

The Darkfield Approach to Measuring Vacuum Birefringence and Light-by-Light Couplings -- A Proof-of-Principle Experiment
Michal Sm\'id, Pooyan Khademi, Carsten B\"ahtz, Erik Brambrink, Jindrich Chalupsky, Tom E. Cowan, Samuele Di Dio Cafiso, Sebastian G\"ode, J\"org Grenzer, Vera Hajkova, Peter Hilz, Willi Hippler, Hauke H\"opner, Alzbeta Horynova, Oliver Humphries, Simon Jelinek, Libor Juha, Felix Karbstein, Alejandro Laso-Garcia, Robert L\"otzsch, Aim\…

The Darkfield Approach to Measuring Vacuum Birefringence and Light-by-Light Couplings -- A Proof-of-Principle Experiment
Vacuum fluctuations give rise to effective nonlinear interactions between electromagnetic fields. These generically modify the characteristics of light traversing a strong-field region. X-ray free-electron lasers constitute a particularly promising probe, due to their brilliance, the possibility of precise control and favourable frequency scaling. However, the nonlinear vacuum response is very small even when probing a tightly focused high-intensity laser field with XFEL radiation and direct me…

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

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

This https://arxiv.org/abs/2504.11382 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The tangent cone to the real determinantal variety: various expressions and a proof
The set of real matrices of upper-bounded rank is a real algebraic variety called the real generic determinantal variety. An explicit description of the tangent cone to that variety is given in Theorem 3.2 of Schneider and Uschmajew [SIAM J. Optim., 25 (2015), pp. 622-646]. The present paper shows that the proof therein is incomplete and provides a proof. It also reviews equivalent descriptions of the tangent cone to that variety. Moreover, it shows that the tangent cone and the algebraic tange…

A Riemannian Characterization of Compact Affine Manifolds with Parallel Volume
Mihail Cocos
https://arxiv.org/abs/2506.14778 https://…

A Riemannian Characterization of Compact Affine Manifolds with Parallel Volume
We establish that any affine manifold $(M,\nabla)$ endowed with a parallel volume form $ω,$ admits, in any conformal class of Riemannian metrics, a representative $H$ for which $\nabla$ is the Levi-Civita connection. This provides a constructive proof that such manifolds are necessarily complete, generalizing the "if" direction of Markus' conjecture \cite{markus1962}. Moreover, our result demonstrates that these structures are intrinsically Riemannian-flat, a stronger conclusion than the affin…

Profinite rigidity of crystallographic groups arising from Lie theory
Davide Carolillo, Gianluca Paolini
https://arxiv.org/abs/2506.15494 https://

Profinite rigidity of crystallographic groups arising from Lie theory
We prove that every finite direct product of crystallographic groups arising from an irreducible root system (in the sense of Lie theory) is profinitely rigid (equiv. first-order rigid). This is a generalization of recent proofs of profinite rigidity of affine Coxeter groups [1, 7, 22]. Our proof uses model theory.

Bra och underhållande text kring begreppen statistisk signifikans och konfidensintervall.
How a Cup of Tea Laid the Foundations for Modern Statistical Analysis https://www.wired.com/story/how-a-cup-of-t…

How a Cup of Tea Laid the Foundations for Modern Statistical Analysis
Scientific experiments run today are based on research practices that evolved out of a British tea-tasting experiment in the 1920s.

Mathematical proof of errors in Capasso's excess noise factor formula for an n-step staircase multiplier
Ankitha E Bangera
https://arxiv.org/abs/2506.09649

Mathematical proof of errors in Capasso's excess noise factor formula for an n-step staircase multiplier
Solid-state devices such as multistep staircase avalanche photodiodes (APDs) are analogues to the photomultiplier tubes and are considered as a cascade-amplifier. The major source of internal noise in these APDs is due to the randomness in their stepwise impact ionization. Recent literature on staircase APDs by research groups such as Campbell and co-workers have reported the theoretical estimates of total excess noise factors using Capasso's excess noise factor formula. This formula is based o…

Sonnet 117 - CXVII
Accuse me thus: that I have scanted all,
Wherein I should your great deserts repay,
Forgot upon your dearest love to call,
Whereto all bonds do tie me day by day;
That I have frequent been with unknown minds,
And given to time your own dear-purchased right;
That I have hoisted sail to all the winds
Which should transport me farthest from your sight.
Book both my wilfulness and errors down,
And on just proof surmis…

Old-growth forest logging resumed in Finland – Stora Enso breaking its sustainability promises https://www.greenpeace.org/finland/blogit/metsat/old-growth-forest-logging-resumed-in-finland-stora-enso-bre…

Old-growth forest logging resumed in Finland – Stora Enso breaking its sustainability promises - Greenpeace Suomi
In March we warned that forestry giant Stora Enso’s products may contain traces of old growth forests. Well now we know that they do, with fresh proof from Kainuu, Finland.…

Equitable Mechanism Design for Facility Location
Toby Walsh
https://arxiv.org/abs/2506.10460 https://arxiv.org/pdf/2506.10460

Equitable Mechanism Design for Facility Location
We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both d…

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…

I love how the “#ColeValley Town Square” pop-up turns Carl St. into a relaxed oasis. It’s a great proof-of-concept for permanently closing the street where the #NJudah emerges from the Sunset Tunnel (and extending the footprint of Gamble Memorial Park).

Hmm… maybe I should pickup a watch with a "California Dial". 🤔
P.S. For those unfamiliar with this dial layout or even those who have seen it but wondered WTF is going on, this is a nice summary:
https://revolutionwatch.com/california-love/

California Love
With its mix of Roman and Arabic numerals, the so-called California dial has become one of the most sought-after Rolex watches of the modern era.

»Warum Bitcoin nicht umweltfreundlicher wird:
Bitcoin verbraucht mehr Strom als viele Länder – und das ganz bewusst. Ein technologischer Umstieg könnte das ändern, scheitert aber am Widerstand der Community. Warum?«
Auch deswegen sind Krypto-Währungen kein Fortschritt, sondern ein Verlust der Erde von Energie die sie sich Egoisten bezahlt bekommen wollen.
🤑

Warum Bitcoin nicht umweltfreundlicher wird
Bitcoin verbraucht mehr Strom als viele Länder – und das ganz bewusst. Ein technologischer Umstieg könnte das ändern, scheitert aber am Widerstand der Community. Warum?

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}.

A Constructive Proof of Existence and Mass Gap for Pure SU(3) Yang-Mills in Four-Dimensional Space-Time
D. C. Jacobsen
https://arxiv.org/abs/2506.00284 htt…

A Constructive Proof of Existence and Mass Gap for Pure SU(3) Yang-Mills in Four-Dimensional Space-Time
In this work we present a constructive proof that pure SU(3) Yang-Mills theory on R^4 exists as a nontrivial Wightman quantum field theory and exhibits a strictly positive mass gap. Our approach embeds the four-dimensional gauge theory as the zero-mode sector of a five-dimensional orbifold regulator that preserves gauge invariance and reflection positivity. A convergent joint polymer expansion on the Wilson lattice provides uniform control of the continuum (a->0) and infinite-volume (L->inf) li…

Oh, absolutely, I live in Norway, because apparently, people need proof before they believe anything these days. Next time you see me, I’ll be casually dropping the phrase “Norsk Syndikalistisk Forbund” in perfect Norwegian, just to remind you that I’m not a figment of your imagination but a real, live, radicalized-by-proxy Norwegian who reads obscure early 20th-century syndicalist newspapers in my spare time.
Don’t worry, I’ll also make sure to quote both Emma Goldman and Rudolf Rocke…

Reconstruction theorems for coadmissible D-cap-modules
Finn Wiersig
https://arxiv.org/abs/2506.12601 https://arxiv.org/pdf/2506.12601…

Reconstruction theorems for coadmissible D-cap-modules
We prove a Riemann-Hilbert correspondence for Ardakov-Wadsley's coadmissible D-cap-modules and, more generally, for Bode's $\mathcal{C}$-complexes. More precisely, we show that any given $\mathcal{C}$-complex can be reconstructed out of its solutions. As a corollary, we find that slight modifications of the solution and de Rham functors introduced by the author are fully faithful on $\mathcal{C}$-complexes and, in particular, on coadmissible D-cap-modules. One of the many steps of our proof is …

On a class of toric manifolds arising from simplicial complexes
Ivan Limonchenko, Marinko Timotijevi\'c, Rade \v{Z}ivaljevi\'c
https://arxiv.org/abs/2506.13547

On a class of toric manifolds arising from simplicial complexes
Given an arbitrary abstract simplicial complex $K$ on $[m]:=\{1,2,\ldots,m\}$, different from the simplex $Δ_{[m]}$ with $m$ vertices, we introduce and study a canonical $(2m-2)$-dimensional toric manifold $X_K$, associated to the canonical $(m-1)$-dimensional complete regular fan $Σ_K$. This construction yields an infinite family of toric manifolds that are not quasitoric and provides a topological proof of the Dehn-Sommerville relations for the associated Bier sphere $\mathrm{Bier}(K)$. Fin…

How Pete Carroll and his philosophy impacted a trio of NFL head coaches https://www.raiders.com/news/pete-carroll-coaching-tree-dan-quinn-dave-canales-brian-schottenheimer

"I name the Emperor himself for ordering the brutal attacks on the people of Ghorman... This massacre is proof that our self-appointed Emperor is little more than a lying executioner, imposing his tyranny under the pretense of security."
▶️ The Ghorman Massacre | #ANDOR

This https://arxiv.org/abs/2504.11666 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on the second supplementary law of rational power residue symbols
As a natural generalization of the Legendre symbol, the $q$-th power residue symbol $(a/p)_q$ is defined for primes $p$ and $q$ with $p\equiv 1 \bmod q$. In this paper, we generalize the second supplementary law by providing an explicit condition for $(q/p)_q = 1$, when $p$ has a special form $p = \sum_{i=0}^{q-1} m^i n^{q-1-i}$. This condition is expressed in terms of the polylogarithm $\mathrm{Li}_{1-q}(x)$ of negative index. Our proof relies on an argument similar to Lemmermeyer's proof of E…

Coalgebraic proof translations for non-wellfounded proofs
Borja Sierra Miranda, Thomas Studer, Lukas Zenger
https://arxiv.org/abs/2506.01711 https://

Coalgebraic proof translations for non-wellfounded proofs
Non-wellfounded proof theory results from allowing proofs of infinite height in proof theory. To guarantee that there is no vicious infinite reasoning, it is usual to add a constraint to the possible infinite paths appearing in a proof. Among these conditions, one of the simplest is enforcing that any infinite path goes through the premise of a rule infinitely often. Systems of this kind appear for modal logics with conversely well-founded frame conditions like GL or Grz. In this paper, we pr…

Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency
Pinaki Mandal
https://arxiv.org/abs/2506.15169 https://

Efficient reallocation of indivisible resources: Pair-efficiency versus Pareto-efficiency
In the object reallocation problem, achieving Pareto-efficiency is desirable, but may be too demanding for implementation purposes. In contrast, pair-efficiency, which is the minimal efficiency requirement, is more suitable. Despite being a significant relaxation, however, pair-efficiency ensures Pareto-efficiency for any strategy-proof and individually rational rule when agents' preferences are unrestricted. What if agents' preferences have specific restricted structures, such as single-peak…

Me: I want to make a bacon, egg, and cheese sandwich but I don’t have any mayonnaise.
Literally two minutes later, I have made some excellent mayo. People should make more mayo at home. Kenji’s method is practically fool proof.
https://www.seriouseats.com/two-minute-mayonnaise

Two-Minute Mayonnaise Recipe
Using an immersion blender, you end up with a cup full of creamy, perfectly emulsified, real-deal, better-than-anything-you-can-buy mayonnaise.

Scientists Find DNA Proof of Swine Feces in North Carolina Homes | The Daily Yonder
https://dailyyonder.com/scientists-find-dna-proof-of-swine-feces-in-north-carolina-homes/2025/06/03/

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…

Canelés are about as close to proof of the existence of the divine as any of us are likely to get.

❝We humans are stability-seeking creatures. Getting accustomed to what used to seem unthinkable can feel like an accomplishment. And when the unthinkable recedes at least a bit…it’s easy to mistake it for proof that the dark times are ending.
But these comparatively small victories don’t alter the direction of our transformation — they don’t even slow it down measurably — even while they appeal to our deep need to normalize.…And so just when we most need to act — while there is indeed room for action and some momentum to the resistance — we tend to be lulled into complacency by the sense of relief on the one hand and boredom on the other.❞
https://www.nytimes.com/2025/05/28/opinion/trump-danger-normalization-shock.html

This https://arxiv.org/abs/2412.09281 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Free ribbon lemma for surface-link
A free surface-link is a surface-link whose fundamental group is a free group not necessarily meridian-based. Free ribbon lemma says that every free sphere-link in the 4-sphere is a ribbon sphere-link. Four different proofs of Free ribbon lemma are explained. The first proof is done in an earlier paper. The second proof is done by showing that there is an O2-handle basis of a ribbon surface-link. The third proof is done by removing the commuter relations from a Wirtinger presentation of a free …

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

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

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…

$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions
Yury Arlinskii, Konrad Schm\"udgen
https://arxiv.org/abs/2506.14357

$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions
Given a conjugation (involution) $C$ on a Hilbert space, $C$-self-adjoint contractive extensions of a non-densely defined $C$-symmetric contraction are studied and parameterizations of all such extensions are obtained. As an application, a proof of an announced result of Glazman \cite{Glazman1} on the existence of maximal dissipative $C$-self-adjoint extensions of a densely defined $C$-symmetric dissipative operator is given.

This https://arxiv.org/abs/2304.05796 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On diagrams of algebras
We present a proof of the formula (given in Lurie's Higher Algebra) for the operad governing diagrams of operad algebras. We believe that our proof corrects a flaw in the original argument. 2nd version: a corrected proof given.

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.

On Effective Banach-Mazur Games and an application to the Poincar\'e Recurrence Theorem for Category
Prajval Koul, Satyadev Nandakumar
https://arxiv.org/abs/2506.11118

On Effective Banach-Mazur Games and an application to the Poincaré Recurrence Theorem for Category
The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we give a proof for the effective Banach Category Theorem. Further, we provide a game-theoretic proof of an effective theorem in dynamical systems, namely the category version of Poincaré Recurrence. The Poincaré Recurrence Theorem for category states that for a hom…

A note on P\'olya urns: the winner may lead all the time
Svante Janson
https://arxiv.org/abs/2506.14859 https://arxiv.org/pdf/250…

A note on Pólya urns: the winner may lead all the time
Consider a Pólya urn where a drawn ball of colour $i$ is replaced together with a fixed number $m_i$ of balls of the same colour. We give a simple proof that if, for example, there are two colours and the urn starts with more balls of colour 1 than 2, and $m_1\ge m_2$, then there is a positive probability that there always will be more balls of colour 1 than colour 2.

Replaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
Proof of the bounded conformal conjecture
https://

Collaborative Beamforming for Communication Applications Using a Two-Element Fully-Wireless Open-Loop Coherent Distributed Array
Jason M. Merlo, Jeffrey A. Nanzer
https://arxiv.org/abs/2506.13014

Collaborative Beamforming for Communication Applications Using a Two-Element Fully-Wireless Open-Loop Coherent Distributed Array
In this work we demonstrate a proof of concept of a fully-wireless two-node open-loop coherent distributed communication system and evaluate its performance by transmitting QPSK , 64-, and 256-QAM constellations at a symbol rate of 2 MBd over a 58 m link in an urban environment. The system is implemented in a distributed manner with on-node processing using software-defined radios (SDRs) and wireless internode communication to share coordination information and does not rely on external time or…

Germany is drawing up plans to rapidly expand its network of bomb-proof bunkers and shelters,
the government’s most senior civilian protection official has said,
warning the state needs to be prepared for an attack from Russia within the next four years.
Ralph Tiesler, the head of the Federal Office of Civil Protection and Disaster Assistance (BBK),
said Europe’s largest economy needed to wake up to the reality of conflict,
and that in its current state Germany w…

Proof of Work With External Utilities
Yogev Bar-On, Ilan Komargodski, Omri Weinstein
https://arxiv.org/abs/2505.21685 https://arxiv.o…

Proof of Work With External Utilities
Proof-of-Work (PoW) consensus is traditionally analyzed under the assumption that all miners incur similar costs per unit of computational effort. In reality, costs vary due to factors such as regional electricity cost differences and access to specialized hardware. These variations in mining costs become even more pronounced in the emerging paradigm of \emph{Proof-of-Useful-Work} (PoUW), where miners can earn additional \emph{external} rewards by performing beneficial computations, such as Art…

How Pete Carroll and his philosophy impacted a trio of NFL head coaches https://www.raiders.com/news/pete-carroll-coaching-tree-dan-quinn-dave-canales-brian-schottenheimer

Rate of metastability of an iterative algorithm for quadratic optimization
Paulo Firmino
https://arxiv.org/abs/2506.11342 https://arx…

Rate of metastability of an iterative algorithm for quadratic optimization
In this paper, relying on methods from proof mining, we provide a quantitative analysis of a theorem due to Xu, stating that an iteration strongly converges to the solution of a well known quadratic optimization problem. Rates of metastability and some rates of asymptotic regularity were obtained. We get quadratic rates of asymptotic regularity for particular sequences.

PoCGen: Generating Proof-of-Concept Exploits for Vulnerabilities in Npm Packages
Deniz Simsek, Aryaz Eghbali, Michael Pradel
https://arxiv.org/abs/2506.04962

PoCGen: Generating Proof-of-Concept Exploits for Vulnerabilities in Npm Packages
Security vulnerabilities in software packages are a significant concern for developers and users alike. Patching these vulnerabilities in a timely manner is crucial to restoring the integrity and security of software systems. However, previous work has shown that vulnerability reports often lack proof-of-concept (PoC) exploits, which are essential for fixing the vulnerability, testing patches, and avoiding regressions. Creating a PoC exploit is challenging because vulnerability reports are info…

Weighted Weak Type estimates for non-integral Square Functions
Dario Mena, Maria Carmen Reguera, Luz Roncal
https://arxiv.org/abs/2506.14897 https://

Weighted Weak Type estimates for non-integral Square Functions
We provide quantitative weighted weak type estimates for non-integral square functions in the critical case $p=2$ in terms of the $A_p$ and reverse Hölder constants associated to the weight. The method of proof uses a decoupling of the role of the weights via a quantitative version of Gehring's lemma. The results can be extended to other $p$ in the range of boundedness of the square function at hand.

Almost uniform convergence for noncommutative Vilenkin-Fourier series
Yong Jiao, Sijie Luo, Tiantian Zhao, Dejian Zhou
https://arxiv.org/abs/2506.14431 htt…

Almost uniform convergence for noncommutative Vilenkin-Fourier series
In the present paper, we study almost uniform convergence for noncommutative Vilenkin-Fourier series. Precisely, we establish several noncommutative (asymmetric) maximal inequalities for the Cesàro means of the noncommutative Vilenkin-Fourier series, which in turn give the corresponding almost uniform convergence. The primary strategy in our proof is to explore a noncommutative generalization of Sunouchi square function operator, and the very recent advance of the noncommutative Calderón-Zygm…

Proof of a conjecture on isolation of graphs with a universal vertex
Peter Borg, Alastair Farrugia
https://arxiv.org/abs/2506.09290 https://

Proof of a conjecture on isolation of graphs with a universal vertex
A copy of a graph $F$ is called an $F$-copy. For any graph $G$, the $F$-isolation number of $G$, denoted by $ι(G,F)$, is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbourhood $N[D]$ of $D$ in $G$ intersects the vertex sets of the $F$-copies contained by $G$ (equivalently, $G-N[D]$ contains no $F$-copy). Thus, $ι(G,K_1)$ is the domination number $γ(G)$ of $G$, and $ι(G,K_2)$ is the vertex-edge domination number of $G$. Settling a conjecture of Zhang an…

Positive Sharing and Abstract Machines
Beniamino Accattoli, Claudio Sacerdoti Coen, Jui-Hsuan Wu
https://arxiv.org/abs/2506.14131 https://

Positive Sharing and Abstract Machines
Wu's positive $λ$-calculus is a recent call-by-value $λ$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of the study of sharing; namely it rules out the recurrent issue of renaming chains, that often causes a quadratic time slowdown. In this paper, we define the natural abstract machine for the positive $λ$-calculus and show that it suffers from an inefficiency: the quad…

Local perturbations of block Toeplitz matrices
Lars Koekenbier, Hermann Schulz-Baldes
https://arxiv.org/abs/2506.12757 https://arxiv.…

Local perturbations of block Toeplitz matrices
This work is about the asymptotic spectral theory of tridiagonal Toeplitz matrices with matrix entries, with periodicity broken on a finite number of entries. Varying the ranks of these perturbations allow to interpolate between open boundary and circulant Toeplitz matrices. While the continuous part of the limit spectrum only depends on these ranks and no other aspect of the perturbation, the outliers of the spectrum depend continuously on the local perturbation. The proof is essentially based…

An Aubin-Yau theorem for transversally K\"ahler foliations
Vlad Marchidanu
https://arxiv.org/abs/2506.03987 https://arxiv.org/pd…

An Aubin-Yau theorem for transversally Kähler foliations
Transversally Kähler foliations are a generalisation of Kähler manifolds, appearing naturally in the complex non-Kähler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem adapt to the transversally Kähler case under the homological orientability condition. We apply this result to obtain a new, simpler proof of the already known Vaisman Aubin-Yau theorem.

The Cost of Restaking vs. Proof-of-Stake
Akaki Mamageishvili, Benny Sudakov
https://arxiv.org/abs/2505.24440 https://arxiv.org/pdf/25…

The Cost of Restaking vs. Proof-of-Stake
We compare the efficiency of restaking and Proof-of-Stake (PoS) protocols in terms of stake requirements. First, we consider the sufficient condition for the restaking graph to be secure. We show that the condition implies that it is always possible to transform such a restaking graph into secure PoS protocols. Next, we derive two main results, giving upper and lower bounds on required extra stakes that one needs to add to validators of the secure restaking graph to be able to transform it into…

This https://arxiv.org/abs/2407.01203 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An elementary proof of a criterion for subfunctors of Ext to be closed
Let $\mathcal{A}$ be an abelian category and let $F$ be a subbifunctor of the additive bifunctor $\text{Ext}_{\mathcal{A}}^{1}(-,-)\colon \mathcal{A}^{\text{op}}\times \mathcal{A}\to \mathsf{Ab}$. Buan proved in [4] that $F$ is closed if, and only if, $F$ has the $3\times 3$-lemma property, a certain diagrammatic property satisfied by the class of $F$-exact sequences. The proof of this result relies on the theory of exact categories and on the Freyd--Mitchell embedding theorem, a very well-know…

Growing a Modular Framework for Modal Systems- HOLMS: a HOL Light Library
Antonella Bilotta
https://arxiv.org/abs/2506.10048 https://…

Growing a Modular Framework for Modal Systems- HOLMS: a HOL Light Library
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an accessible introduction to the library, the fundamentals of modal logic are outlined first, followed by a concise manual for the proof assistant itself. The core contribution of this work on HOLMS is the development of a unified and modular strategy for proving adequ…

Error Rates for Large Deviations in the domain of an $\alpha=1$ stable law
Jonny Imbierski, Dalia Terhesiu
https://arxiv.org/abs/2506.12443 https://…

Error Rates for Large Deviations in the domain of an $α=1$ stable law
We obtain error rates for large deviations of sums of i.i.d. random variables in, a particular case, of the domain of a non-symmetric infinite mean $α=1$-stable law. The focus of this work is on the method of proof via analytic techniques rather than the particular result.

Proof of a conjecture by Starr and log-concavity for random commuting permutations
Abdelmalek Abdesselam
https://arxiv.org/abs/2506.06894 https://

Proof of a conjecture by Starr and log-concavity for random commuting permutations
We prove a conjecture by Shannon Starr regarding the asymptotics for the number of tuples of commuting permutations with given number of joint orbits. These numbers generalize unsigned Stirling numbers of the first kind which count how many single permutations have a given number of cycles. In the case of pairs of permutations, these numbers are related to D'Arcais polynomials and the Nekrasov-Okounkov formula. As a consequence of the above asymptotics, we confirm a log-concavity conjecture in …

A Non-Wellfounded and Labelled Sequent Calculus for Bimodal Provability Logic
Justus Becker
https://arxiv.org/abs/2506.14307 https://…

A Non-Wellfounded and Labelled Sequent Calculus for Bimodal Provability Logic
We present a labelled and non-wellfounded calculus for the bimodal provability logic CS. The system is obtained by modelling the Kripke-like semantics of this logic. As in arXiv:2309.00532, we enforce the second-order property of converse wellfoundedness by using techniques from cyclic proof theory. We will prove soundness and completeness of this system with respect to the semantics and provide a primitive decision procedure together with a way to extract countermodels.

Normal Holonomy of Complex Hyperbolic Submanifolds
Santiago Casta\~neda Montoya, Carlos E. Olmos
https://arxiv.org/abs/2506.11323 https://

Normal Holonomy of Complex Hyperbolic Submanifolds
We prove that the restricted normal holonomy group of a Kähler submanifold of the complex hyperbolic space $\mathbb{C}H^{n}$ is always transitive, provided the index of relative nullity is zero. This contrasts with the case of $\mathbb{C}P^{n}$, where a Berger type result was proved by Console, Di Scala, and the second author. The proof is based on lifting the submanifold to the pseudo-Riemannian space $\mathbb{C}^{n,1}$ and developing new tools to handle the difficulties arising from possible…

On the Vertices of Delta-modular Polyhedra
Bludov Mikhail, Gribanov Dmitry, Klimenko Maxim, Kupavskii Andrey, L\'angi Zsolt, Rogozin Alexander, Voronov Vsevolod
https://arxiv.org/abs/2506.12774

On the Vertices of Delta-modular Polyhedra
Let $P$ be a polytope defined by the system $A x \leq b$, where $A \in R^{m \times n}$, $b \in R^m$, and $\text{rank}(A) = n$. We give a short geometric proof of the following tight upper bound on the number of vertices of $P$: $$ n! \cdot \fracΔ{Δ_{\text{average}}} \cdot \text{vol}(B_2) \sim \frac{1}{\sqrt{πn}} \cdot \left(\frac{2 π}{e}\right)^{n/2} \cdot n^{n/2} \cdot \fracΔ{Δ_{\text{average}}}, $$ where $Δ$ is the maximum absolute value of $n \times n$ subdeterminants of $A$, and $�…

Upper bound on the multiplicity of eigenvalues of the Sch\"odinger-Dirichlet operator in dimension two
Mourad Choulli
https://arxiv.org/abs/2506.14463

Upper bound on the multiplicity of eigenvalues of the Schödinger-Dirichlet operator in dimension two
We establish an upper bound on the multiplicity of eigenvalues of the Schödinger-Dirichlet operator in dimension two. We give a proof based on a generalized Morse Lemma due to Cheng \cite{Ch}.

A Private Smart Wallet with Probabilistic Compliance
Andrea Rizzini, Marco Esposito, Francesco Bruschi, Donatella Sciuto
https://arxiv.org/abs/2506.04853 h…

A Private Smart Wallet with Probabilistic Compliance
We propose a privacy-preserving smart wallet with a novel invitation-based private onboarding mechanism. The solution integrates two levels of compliance in concert with an authority party: a proof of innocence mechanism and an ancestral commitment tracking system using bloom filters for probabilistic UTXO chain states. Performance analysis demonstrates practical efficiency: private transfers with compliance checks complete within seconds on a consumer-grade laptop, and overall with proof gener…

Sums of Schubert structure constants with bounded Coxeter length
Ada Stelzer
https://arxiv.org/abs/2506.13684 https://arxiv.org/pdf/2…

Sums of Schubert structure constants with bounded Coxeter length
Pak-Robichaux recently introduced a signed puzzle rule for Schubert structure constants, which they use to show that sums $γ_k(n)$ of these constants with a bounded number of inversions are polynomial. We give a different, conceptual proof of their theorem. Our argument computes the lead term of $γ_k(n)$ and extends to all classical Lie types.

Level-3 large deviations for the white-forced 2D Navier-Stokes system in a bounded domain
Meng Zhao
https://arxiv.org/abs/2506.14119 https://

Level-3 large deviations for the white-forced 2D Navier-Stokes system in a bounded domain
We study the large deviations principle (LDP) of Donsker-Varadhan type for the white-forced Navier-Stokes system in a bounded domain. Under the assumption that the noise is non-degenerate, we establish level-2 and level-3 LDPs with rate functions given by the Donsker-Varadhan formulas. The proof relies on an improved version of Kifer's criterion, a lift argument inspired from [DV83], an improved abstract result on the large-time asymptotics of generalized Markov semigroups, and a delicate appro…

Covering radii of $3$-zonotopes and the shifted Lonely Runner Conjecture
David Alc\'antara, Francisco Criado, Francisco Santos
https://arxiv.org/abs/2506.13379

Covering radii of $3$-zonotopes and the shifted Lonely Runner Conjecture
We show that the shifted Lonely Runner Conjecture (sLRC) holds for 5 runners. We also determine that there are exactly 3 primitive tight instances of the conjecture, only two of which are tight for the non-shifted conjecture (LRC). Our proof is computational, relying on a rephrasing of the sLRC in terms of covering radii of certain zonotopes (Henze and Malikiosis, 2017), and on an upper bound for the (integer) velocities to be checked (Malikiosis, Santos and Schymura, 2024+). As a tool for th…

Ricci Curvature of Strong Product Graphs
Guiqiang Mou
https://arxiv.org/abs/2506.13269 https://arxiv.org/pdf/2506.13269

Ricci Curvature of Strong Product Graphs
We establish for the first time the explicit curvature formulas for the horizontal and vertical edges of the strong product of two regular graphs. We complement this result with showing that there does not exist a nice formula for the curvatures of diagonal edges, except for a special case in terms of curvatures of the factors. This gives the curvature formulas for all edges of the product of a complete graph and a regular graph. We also present an accessible and simpler proof of the curvature …

IMALL with a Mixed-State Modality: A Logical Approach to Quantum Computation
Kinnari Dave, Alejandro D\'iaz-Caro, Vladimir Zamdzhiev
https://arxiv.org/abs/2506.09545

IMALL with a Mixed-State Modality: A Logical Approach to Quantum Computation
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations, and embeds pure quantum computations within a mixed-state framework via B, interpreted categorically as a functor from a category of Hilbert Spaces to a category of finite-dimensional C*-algebras. Measurement arises as a definable term, not as a constant, and t…

Refuting Perfect Matchings in Spectral Expanders is Hard
Ari Biswas, Rajko Nenadov
https://arxiv.org/abs/2506.07700 https://arxiv.org…

Refuting Perfect Matchings in Spectral Expanders is Hard
This work studies the complexity of refuting the existence of a perfect matching in spectral expanders with an odd number of vertices, in the Polynomial Calculus (PC) and Sum of Squares (SoS) proof system. Austrin and Risse [SODA, 2021] showed that refuting perfect matchings in sparse $d$-regular \emph{random} graphs, in the above proof systems, with high probability requires proofs with degree $Ω(n/\log n)$. We extend their result by showing the same lower bound holds for \emph{all} $d$-regul…

Combinatorics of descent algebras and graph coverings
Philippe Biane
https://arxiv.org/abs/2506.05528 https://arxiv.org/pdf/2506.0552…

Combinatorics of descent algebras and graph coverings
We give a direct combinatorial proof that the product of two descent classes in a symmetric group is a sum of descent classes. The proof is based on the fact that the group product gives a covering map when descent classes are endowed with the graph structure coming from the weak order. The main geometric argument is valid for any Coxeter group, even infinite ones for which the descent algebra does not exist.

On the cut-elimination of the modal $\mu$-calculus: Linear Logic to the rescue
Esa\"ie Bauer, Alexis Saurin
https://arxiv.org/abs/2506.09791 https://

On the cut-elimination of the modal $μ$-calculus: Linear Logic to the rescue
This paper presents a proof-theoretic analysis of the modal $μ$-calculus. More precisely, we prove a syntactic cut-elimination for the non-wellfounded modal $μ$-calculus, using methods from linear logic and its exponential modalities. To achieve this, we introduce a new system, \muLLmodinf{}, which is a linear version of the modal $μ$-calculus, intertwining the modalities from the modal $μ$-calculus with the exponential modalities from linear logic. Our strategy for proving cut-elimination …

A proof of the Fields Conjectures
Satoshi Murai, Brendon Rhoades, Andy Wilson
https://arxiv.org/abs/2505.24027 https://arxiv.org/pdf/…

A proof of the Fields Conjectures
The {\em superspace ring} of rank $n$ is the algebra $Ω_n$ of differential forms on affine $n$-space. The algebra $Ω_n$ is bigraded with respect to polynomial and exterior degree and carries a natural action of the symmetric group $\mathfrak{S}_n$. Modding out by $\mathfrak{S}_n$-invariants with vanishing constant term yields the {\em superspace coinvariant ring} $SR_n$. We prove that, as an ungraded $\mathfrak{S}_n$-module, the space $SR_n$ is isomorphic to the sign-twisted permutation actio…