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We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest…

Logic · Mathematics 2010-11-24 Shira Kritchman , Ran Raz

Getoor's conjecture that essentially all Levy processes satisfy (H) is a long-standing open problem in potential theory. In the beginning of the paper, we summarize the main results obtained so far for the problem. Then, we present two new…

Probability · Mathematics 2020-03-02 Ze-Chun Hu , Wei Sun

We study the Calabi-Yau equation on symplectic manifolds. We show that Donaldson's conjecture on estimates for this equation in terms of a taming symplectic form can be reduced to an integral estimate of a scalar potential function. Under a…

Differential Geometry · Mathematics 2008-10-06 Valentino Tosatti , Ben Weinkove , Shing-Tung Yau

Multi-round incomplete information tasks are crucial for evaluating the lateral thinking capabilities of large language models (LLMs). Currently, research primarily relies on multiple benchmarks and automated evaluation metrics to assess…

Computation and Language · Computer Science 2025-06-02 Wenhan Dong , Tianyi Hu , Jingyi Zheng , Zhen Sun , Yuemeng Zhao , Yule Liu , Xinlei He , Xinyi Huang

In this paper we introduce a natural model for the realization space of a polytope up to projective equivalence which we call the slack realization space of the polytope. The model arises from the positive part of an algebraic variety…

Combinatorics · Mathematics 2019-08-08 João Gouveia , Antonio Macchia , Rekha R. Thomas , Amy Wiebe

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

Logic in Computer Science · Computer Science 2021-08-17 Ashish Tiwari

We generalize Koll\'ar's conjecture (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to Saito's $S$-sheaves twisted by a $\mathbb{Q}$-divisor. This gives a uniform treatment for various kinds of…

Algebraic Geometry · Mathematics 2022-10-11 Junchao Shentu , Chen Zhao

We consider $(<\lambda)$-support iterations of a version of $(<\lambda)$-strategically complete $\lambda^+$-c.c. definable forcing notions along partial orders. We show that such iterations can be corrected to yield an analog of a result by…

Logic · Mathematics 2024-11-14 Haim Horowitz , Saharon Shelah

lambda-good frame is for us a parallel of the class of models of a superstable theory. Our main line is to start with lambda-good^+ frame s, categorical in lambda, n-successful for n large enough and try to have parallel of stability theory…

Logic · Mathematics 2007-05-23 Saharon Shelah

This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…

Classical Analysis and ODEs · Mathematics 2019-08-02 Dirk Veestraeten

In this article, we consider iteration principles for contraction, with the goal of identifying properties for contractions that respect conditional beliefs. Therefore, we investigate and evaluate four groups of iteration principles for…

Artificial Intelligence · Computer Science 2022-02-08 Kai Sauerwald , Gabriele Kern-Isberner , Christoph Beierle

In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector…

High Energy Physics - Phenomenology · Physics 2008-11-26 S. Actis , A. Ferroglia , G. Passarino , M. Passera

A conference talk discussing the conjecture of Langlands and Rapoport concerning the structure of the points on a Shimura variety modulo a prime of good reduction.

Number Theory · Mathematics 2007-07-24 J. S. Milne

We propose a conjectural $q$-analogue of the classical duality for iterated integrals on $\mathbb{P}^{1}$ minus four points, arising from the involutive M\"{o}bius transformation which exchanges the four marked points in pairs. To this end,…

Number Theory · Mathematics 2026-05-04 Minoru Hirose

The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…

Logic · Mathematics 2024-03-18 Marta Bilkova , Sabine Frittella , Daniil Kozhemiachenko , Ondrej Majer

We prove an explicit form of the Crepant Transformation Conjecture for Grassmannian flops. Our approach uses abelianization to first relate the restrictions of the Lagrangian cones to degree-2 classes, and then deduces the general result…

Algebraic Geometry · Mathematics 2025-04-08 Wendelin Lutz , Qaasim Shafi , Rachel Webb

In a recent article [Phys. Rev. A 94, 052128 (2016)], the authors compute the predictions of two collapse models on the transition probabilities of neutral mesons. Notably, they claim to find an influence on the decay rates and attempt to…

Quantum Physics · Physics 2017-11-09 Antoine Tilloy

In this paper we extend the classical sub-supersolution Sattinger iteration method to $1$-Laplace type boundary value problems of the form \begin{equation*} \begin{cases} \displaystyle -\Delta_1 u = F(x,u) & \text{in}\;\Omega,\\ \newline…

Analysis of PDEs · Mathematics 2024-12-24 Antonio J. Martínez Aparicio , Francescantonio Oliva , Francesco Petitta

We introduce several properties of forcing notions which imply that their lambda-support iterations are lambda-proper. Our methods and techniques refine those studied in math.LO/9906024, math.LO/0210205, math.LO/0508272 and math.LO/0605067,…

Logic · Mathematics 2013-01-04 Andrzej Roslanowski , Saharon Shelah

Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single…

Machine Learning · Statistics 2019-03-04 Rajesh Ranganath , Adler Perotte