Tootfinder

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

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

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

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

Google launches Antigravity, an "agent-first" coding tool that leverages Gemini 3 Pro and third-party models, available in free public preview (Dominic Preston/The Verge)
https://www.theverge.com/news/822833/google-antigravity-ide-coding-agent-…

Google Antigravity is an ‘agent-first’ coding tool built for Gemini 3
Available in free preview now with Gemini 3 Pro, Google Antigravity supports browser control and provides proof of its work.

On the quadratic complexity of subsets of $\mathbb{F}_p^n$ of bounded $\mathrm{VC_{2}}$-dimension
C. Terry, J. Wolf
https://arxiv.org/abs/2510.12767 https://

On the quadratic complexity of subsets of $\mathbb{F}_p^n$ of bounded $\mathrm{VC_{2}}$-dimension
In prior work, we showed that subsets of $\mathbb{F}_{p}^{n}$ of $\mathrm{VC_{2}}$-dimension at most $k$ are well approximated by a union of atoms of a quadratic factor of complexity $(\ell,q)$, where the complexity $\ell$ of the linear part and the complexity $q$ of the quadratic part are both bounded in terms of $k$, $p$, and the desired level of approximation $μ$. A key tool in the proof of this result was an arithmetic regularity lemma for the Gowers $U^3$-norm by Green and Tao, which resu…

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

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

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

Like today’s ICE,
Depression-era INS agents indiscriminately rounded up Mexicans,
presuming they were here illegally.
In Los Angeles, they targeted parks, hospitals, and work sites in Mexican communities,
demanding proof of citizenship.
High-profile raids and media campaigns announcing impending roundups served as tools of intimidation,
creating widespread fear that led to “voluntary” deportation via free one-way train tickets to Mexico.
Entire famil…

Opinion | When deportation was called repatriation: The US once expelled 1.8 million people to Mexico
Like today, Americans in the 1930s were reeling from economic hard times. Leaders made Latinos scapegoats and deported immigrants and some US citizens.

Mass-Centered GCM Framework in Perturbations of Kerr(-Newman)
Allen Juntao Fang, Elena Giorgi, Jingbo Wan
https://arxiv.org/abs/2510.10811 https://arxiv.or…

Mass-Centered GCM Framework in Perturbations of Kerr(-Newman)
The nonlinear stability problem for black hole solutions of the Einstein equations critically depends on choosing an appropriate geometric gauge. In the vacuum setting, the use of Generally Covariant Modulated (GCM) spheres and hypersurfaces has played a central role in the proof of stability for slowly rotating Kerr spacetime. In this work, we develop an alternative GCM framework, that we call mass-centered, designed to overcome the breakdown of the standard GCM construction in the charged cas…

Proof of the $p$-adic Kazhdan-Lusztig hypothesis for $\mathrm{GL}(n)$
Kristaps John Balodis
https://arxiv.org/abs/2510.09788 https://arxiv.org/pdf/2510.097…

Proof of the $p$-adic Kazhdan-Lusztig hypothesis for $\mathrm{GL}(n)$
In this article, we prove the $p$-adic Kazhdan-Lusztig hypothesis for $\mathrm{GL}_n(F)$. While the approach via graded affine Hecke algebras due to recent work of Solleveld leads to more general results, this article serves to completes and clarifies the approach via affine Hecke algebras of Chriss and Ginzburg. In particular, this article serves as an opportunity to articulate several results which are undoubtedly known to experts, but have not been formally recorded in the literature.

Man-in-the-Middle Proof-of-Concept via Krontiris' Ephemeral Diffie-Hellman Over COSE (EDHOC) in C
Daniel Hennig, Joaquin Garcia-Alfaro
https://arxiv.org/abs/2510.10574 https…

Man-in-the-Middle Proof-of-Concept via Krontiris' Ephemeral Diffie-Hellman Over COSE (EDHOC) in C
This report presents some technical details on the authentication process of a lightweight key exchange protocol, paying attention on how Man-in-the-Middle (MitM) attacks could undermine its security, e.g., under the scope of lawful interception and its risk to facilitate mass surveillance. We focus only on some technical aspects associated to the attack scenario. Perspectives for future work are also discussed. Other specific aspects of the work, mainly focusing on the security implications of…

The classification of quasi-elliptic fibrations and unexpected plane cubics in characteristics 2 and 3
Jake Kettinger
https://arxiv.org/abs/2510.06365 https://

The classification of quasi-elliptic fibrations and unexpected plane cubics in characteristics 2 and 3
In this paper, we categorize all isomorphism classes of quasi-elliptic surfaces over a field $k$ of characteristic 2 or 3. For every quasi-elliptic surface $X$, we classify all possible sequences of blow-downs from $X$ to the projective plane $\mathbb{P}^2_k$. We then use these categorizations to identify all unexpected plane cubic curves in characteristic 2 and present a proof of the lack of unexpected cubics in characteristic 3. Before the work in this paper -- based partly on the author's th…

The commutative algebra of congruence ideals and applications to number theory
Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning
https://arxiv.org/abs/2510.05418 htt…

The commutative algebra of congruence ideals and applications to number theory
In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick up on Wiles' work and generalize the numerical criterion to ``higher codimension''. A critical ingredient is a notion of congruence module in higher codimension: this has turned out to be a key definition whose utility extends beyond the role it plays in the numerical criterion. In this paper we trace the origin of so…

An efficient iteration method to reconstruct the drift term from the final measurement
Dakang Cen, Wenlong Zhang, Zhidong Zhang
https://arxiv.org/abs/2510.10940 https://

An efficient iteration method to reconstruct the drift term from the final measurement
This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the uniqueness. The proof of uniqueness contains an iteration converging to the drift, which inspires the numerical algorithm. To handle the ill-posedness of the inverse problem, the authors add the mollification on the data first in the iterative algorithm, and then prov…

@… I will probably also post on the original thread when it reopens, but I just wanted to post my thoughts about this thread here as well: https://comm…

Framework supporting far-right racists?
So evidence and proof is the opinion of a known activist with specific political leanings? An activist that has said and done many controversial things as well, I might add.

$\mathsf{P} \neq \mathsf{NP}$: A Non-Relativizing Proof via Quantale Weakness and Geometric Complexity
Ben Goertzel
https://arxiv.org/abs/2510.08814 https://

$\mathsf{P} \neq \mathsf{NP}$: A Non-Relativizing Proof via Quantale Weakness and Geometric Complexity
We give a compositional, information-theoretic framework that turns short programs into locality on many independent blocks, and combine it with symmetry and sparsity of masked random Unique-SAT to obtain distributional lower bounds that contradict the self-reduction upper bound under $\mathsf{P}=\mathsf{NP}$. We work in the weakness quantale $w_Q=K_{\mathrm{poly}}(\cdot\mid\cdot)$. For an efficiently samplable ensemble $D_m$ made by masking random $3$-CNFs with fresh $S_m\ltimes(\mathbb{Z}_2)^…

A Continuum Beck-type Theorem for Hyperplanes
Paige Bright, Alexander Ortiz, Dmitrii Zakharov
https://arxiv.org/abs/2510.10907 https://arxiv.org/pdf/2510.1…

A Continuum Beck-type Theorem for Hyperplanes
We prove a sharp continuum Beck-type theorem for hyperplanes. Our work is inspired by foundational work of Beck on the discrete problem, as well as refinements due to Do and Lund. The inductive proof uses recent breakthrough results in projection theory by Orponen--Shmerkin--Wang and Ren, who proved continuum Beck-type theorems for lines in $\mathbb{R}^2$ and $\mathbb{R}^n$.

Combining relatively hyperbolic groups over a complex of groups
Darius Alizadeh
https://arxiv.org/abs/2510.02602 https://arxiv.org/pdf/2510.02602

Combining relatively hyperbolic groups over a complex of groups
Given a complex of groups $G(\mathcal{Y}) = (G_σ, ψ_a, g_{a,b})$ where all $G_σ$ are relatively hyperbolic, the $ψ_a$ are inclusions of full relatively quasiconvex subgroups, and the universal cover $X$ is CAT$(0)$ and $δ$--hyperbolic, we show $π_1(G(\mathcal{Y}))$ is relatively hyperbolic. The proof extends the work of Dahmani and Martin by constructing a model for the Bowditch boundary of $π_1(G(\mathcal{Y}))$. We prove the model is a compact metrizable space on which $G$ acts as a geo…

Two Calabi-Yau theorems for degenerations of compact K\"ahler manifolds
David Witt Nystr\"om
https://arxiv.org/abs/2510.03044 https://arxiv.org/p…

Two Calabi-Yau theorems for degenerations of compact Kähler manifolds
We discuss two closely related Calabi-Yau theorems for degenerations of compact Kähler manifolds. The first is a Calabi-Yau theorem for big test configurations, that generalizes a result in [WN24]. It follows from recent joint work with Mesquita-Piccione [MW25], but is here given a more direct proof. The second result is a Calabi-Yau theorem for a wider class of degenerations, formulated in the language of non-Archimedean Kähler geometry. It was first proved in the algebraic setting by Boucks…

Property B: A Baumgartner-style Property that Applies to Preservation of $\aleph_1$ and $\aleph_2$ under Iterations with Supports of Size $\aleph_1$
Mirna D\v{z}amonja
https://arxiv.org/abs/2509.19519 …

Property B: A Baumgartner-style Property that Applies to Preservation of $\aleph_1$ and $\aleph_2$ under Iterations with Supports of Size $\aleph_1$
We prove a theorem on iterated forcing that can be used for preservation of $\aleph_2$ and $\aleph_1$ in iterations with supports of size $\aleph_1$ of forcings that have amalgamation properties similar to those present in the perfect set forcing. The work is modelled after Baumgartner's Axiom A and his proof that iterations with countable support of the same preserve $\aleph_1$. In honour of James E. Baumgartner, the property introduced here is called Property B$(κ)$. The known additional dif…

Electron-beam-induced Contactless Manipulation of Interlayer Twist in van der Waals Heterostructures
Nicola Curreli, Tero S. Kulmala, Riya Sebait, Nicol\`o Petrini, Matteo Bruno Lodi, Roman Furrer, Alessandro Fanti, Michel Calame, Ilka Kriegel
https://arxiv.org/abs/2510.03347

Electron-beam-induced Contactless Manipulation of Interlayer Twist in van der Waals Heterostructures
The ability to dynamically control the relative orientation of layers in two dimensional (2D) van der Waals (vdW) heterostructures represents a critical step toward the realization of reconfigurable nanoscale devices. Existing actuation methods often rely on mechanical contact, complex architectures, or extreme operating conditions, which limit their applicability and scalability. In this work, we present a proof-of-concept demonstration of contactless electrostatic actuation based on electron-…

Eigenvalues of Universal Covers and the Matching Polynomial
Thom\'as Jung Spier
https://arxiv.org/abs/2510.05041 https://arxiv.org/pdf/2510.05041

Eigenvalues of Universal Covers and the Matching Polynomial
In this work, we prove that the universal and maximal abelian covers of a finite multi-graph have the same eigenvalues. This strengthens a recent result of Li, Magee, Sabri, and Thomas (2025), and answers one of their questions. Our proof relies on the theory of the matching polynomial of a graph, and we further prove new results about its Gallai--Edmonds decomposition.

On convergence of normal form transformations
Valery G. Romanovski, Sebastian Walcher
https://arxiv.org/abs/2510.00925 https://arxiv.org/pdf/2510.00925

On convergence of normal form transformations
We discuss various aspects concerning transformations of local analytic, or formal, vector fields to Poincare-Dulac normal form, and the convergence of such transformations. We first review A.D. Bruno's approach to formal normalization, as well as convergence results in presence of certain (simplified) versions of Bruno's ``Condition A'', and along the way we also identify a large class of systems that satisfy Bruno's diophantine ``Condition omega''. We retrace the proof steps in Bruno's work, …

A Small Collusion is All You Need
Yotam Gafni
https://arxiv.org/abs/2510.05986 https://arxiv.org/pdf/2510.05986

A Small Collusion is All You Need
Transaction Fee Mechanisms (TFMs) study auction design in the Blockchain context, and emphasize robustness against miner and user collusion, moreso than traditional auction theory. \cite{chung2023foundations} introduce the notion of a mechanism being $c$-Side-Contract-Proof ($c$-SCP), i.e., robust to a collusion of the miner and $c$ users. Later work \cite{chung2024collusion,welfareIncreasingCollusion} shows a gap between the $1$-SCP and $2$-SCP classes. We show that the class of $2$-SCP mechan…

Pose Estimation of a Thruster-Driven Bioinspired Multi-Link Robot
Nicholas B. Andrews, Yanhao Yang, Sofya Akhetova, Kristi A. Morgansen, Ross L. Hatton
https://arxiv.org/abs/2510.01485

Pose Estimation of a Thruster-Driven Bioinspired Multi-Link Robot
This work demonstrates pose (position and shape) estimation for a free-floating, bioinspired multi-link robot with unactuated joints, link-mounted thrusters for control, and a single gyroscope per link, resulting in an underactuated, minimally sensed platform. Through a proof-of-concept hardware experiment and offline Kalman filter analysis, we show that the robot's pose can be reliably estimated. State estimation is performed using an unscented Kalman filter augmented with Gaussian process res…

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

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

"However, international justice can seem like a faith-based community. We believe in it, but proof of its existence is rare, and almost miraculous when it happens" -- @…
Let's all pray for a miracle, then.

Justice vs Peace
As the world watches the shaky ceasefire in Gaza, the issues of peace and justice intermingle, strain, and collide. For those who work on conflicts, these are familiar tensions, but the underlying debates rarely get wider attention. The basic issue is this: to get any kind of peace deal in

A novel approach through spherical functions in the characterization of invariant polynomials
Roc\'io D\'iaz Mar\'in, Linda Saal
https://arxiv.org/abs/2510.01043 htt…

A novel approach through spherical functions in the characterization of invariant polynomials
Given a compact subgroup K of the orthogonal group acting on the Euclidean space Rn, Gerald Schwarz proved that every smooth K-invariant function on Rn can be expressed as a smooth function of a generating set of $K$-invariant polynomials on n variables. The goal of this work is to provide an alternative and more straightforward proof of this result, based on Gelfand theory, with a particular focus on spherical functions.

PoS-CoPOR: Proof-of-Stake Consensus Protocol with Native Onion Routing Providing Scalability and DoS-Resistance
Ivan Homoliak, Martin Pere\v{s}\'ini, Marek Tama\v{s}kovi\v{c}, Timotej Ponek, Luk\'a\v{s} Hellebrandt, Kamil Malinka
https://arxiv.org/abs/2510.04619

PoS-CoPOR: Proof-of-Stake Consensus Protocol with Native Onion Routing Providing Scalability and DoS-Resistance
Proof-of-Stake (PoS) consensus protocols often face a trade-off between performance and security. Protocols that pre-elect leaders for subsequent rounds are vulnerable to Denial-of-Service (DoS) attacks, which can disrupt the network and compromise liveness. In this work, we present PoS-CoPOR, a single-chain PoS consensus protocol that mitigates this vulnerability by integrating a native onion routing mechanism into the consensus protocol itself. PoS-CoPOR combines stake-weighted probabilistic …

Atypical Hodge Loci
Phillip Griffiths
https://arxiv.org/abs/2510.01155 https://arxiv.org/pdf/2510.01155

Atypical Hodge Loci
In the recent works of a number of people there has emerged a beautiful new perspective on the arithmetic properties of Hodge structures. A central result in that development appears in a paper by Baldi, Klingler, and Ullmo. In this expository work we will explain that result and give a proof. The main conceptual step is to formulate Noether-Lefschetz loci in terms of intersections of period images with Mumford-Tate subdomains of period domains. The main technical step is to use the alignment o…

@… Buttt, proof of work! Years of academic (cryptocurency) research has shown this is the new kid on the block.

Cette tristesse : une orga Š but non-lucratif qui aide des projets open-source, qui s'excuse pour des problèmes entièrement créés par des boîtes extérieures sans foi ni loi.
https://social.anoxinon.de/@Codeberg/115435661014427222

Es ist mir ein Rätsel warum gängige CAPTCHA/Anti-Bot Dienste wie Anubis, ALTCHA etc. auf Proof-of-Work (PoW) setzen. Das (allein) verplempert doch nur Rechenleistung und lässt sich leicht umgehen, oder verstehe ich das nur nicht richtig?

Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified
Martin Dvorak, Tristan Figueroa-Reid, Rida Hamadani, Byung-Hak Hwang, Evgenia Karunus, Vladimir Kolmogorov, Alexander Meiburg, Alexander Nelson, Peter Nelson, Mark Sandey, Ivan Sergeev
https://arxiv.org/abs/2509.20539

Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified
Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited number of notions and results have been implemented so far. In this work, we formalize the proof of the forward (composition) direction of Seymour's theorem for regular matroids. To this end, we develop a library in Lean 4 that implements definitions and result…

Green's functions for magnetic Dirac operators and bulk-edge correspondence
Jean-Marie Barbaroux, Horia D. Cornean, Lo\"ic Le Treust, Nicolas Raymond, Edgardo Stockmeyer
https://arxiv.org/abs/2509.17151

Green's functions for magnetic Dirac operators and bulk-edge correspondence
We study the resolvent kernel (Green's function) of magnetic Dirac operators on a half-plane with boundary conditions interpolating between infinite mass and zigzag cases, excluding the latter. We show that these kernels have all the required properties so that the proof of bulk-edge correspondence from the infinite mass case shown recently can be repeated ad litteram. The zigzag case exhibits qualitatively different behavior and will be addressed in future work.

Secret Leader Election in Ethereum PoS: An Empirical Security Analysis of Whisk and Homomorphic Sortition under DoS on the Leader and Censorship Attacks
Tereza Burianov\'a, Martin Pere\v{s}\'ini, Ivan Homoliak
https://arxiv.org/abs/2509.24955

Secret Leader Election in Ethereum PoS: An Empirical Security Analysis of Whisk and Homomorphic Sortition under DoS on the Leader and Censorship Attacks
Proposer anonymity in Proof-of-Stake (PoS) blockchains is a critical concern due to the risk of targeted attacks such as malicious denial-of-service (DoS) and censorship attacks. While several Secret Single Leader Election (SSLE) mechanisms have been proposed to address these threats, their practical impact and trade-offs remain insufficiently explored. In this work, we present a unified experimental framework for evaluating SSLE mechanisms under adversarial conditions, grounded in a simplified…

The Stein-Weiss inequality in variable exponent Morrey spaces
David Cruz-Uribe, Arash Ghorbanalizadeh, Durvudkhan Suragan
https://arxiv.org/abs/2510.02235 https://

The Stein-Weiss inequality in variable exponent Morrey spaces
In this paper we prove the Stein-Weiss inequality in variable exponent Morrey spaces over a bounded domain. Our work extends earlier results in the variable exponent Lebesgue and Morrey settings, and utilizes new proof techniques applicable to Morrey spaces. We build on the foundational paper by Almeida, Hasanov, and Samko, which introduced Morrey spaces of variable exponents. As an application of our main result, we prove Poincaré-type inequalities using the approach of a recent paper by the …

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

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

Counting $2\times 2$ matrices with fixed determinant and bounded coefficients
Kavita Dhanda, Alan Haynes, Silmi Prasala
https://arxiv.org/abs/2509.16890 https://

Counting $2\times 2$ matrices with fixed determinant and bounded coefficients
Recent work by M. Afifurrahman established the first asymptotic estimates with error terms for the number of $2\times 2$ matrices with fixed non-zero determinant $n\in\mathbb{N}$, and with coefficients bounded in absolute value by $X$. In this paper we present a new proof of this result, which also gives an improved error term as $X\rightarrow\infty$. Similar to Afifurrahman's result, our error term is uniform in both $n$ and $X$, and our estimates are significant for $X$ as small as $n^{1/2+δ…

Unaligned Incentives: Pricing Attacks Against Blockchain Rollups
Stefanos Chaliasos, Conner Swann, Sina Pilehchiha, Nicolas Mohnblatt, Benjamin Livshits, Assimakis Kattis
https://arxiv.org/abs/2509.17126

Unaligned Incentives: Pricing Attacks Against Blockchain Rollups
Rollups have become the de facto scalability solution for Ethereum, securing more than $55B in assets. They achieve scale by executing transactions on a Layer 2 ledger, while periodically posting data and finalizing state on the Layer 1, either optimistically or via validity proofs. Their fees must simultaneously reflect the pricing of three resources: L2 costs (e.g., execution), L1 DA, and underlying L1 gas costs for batch settlement and proof verification. In this work, we identify critical m…