October 2026

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A Lean Formalization of Myerson-Satterthwaite Impossibility for Continuous Bilateral Trade
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz
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A Finite Coordinate Reduction for Approachability Loss in Lean
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz
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Arrow and Gibbard Satterthwaite Theorems in Lean
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz
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A Lean Formalization of the Shapley Value Characterization for Finite Cooperative Games
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz
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Nash Bargaining Characterization in Lean
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz
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An Executable Stallings Recognizer for Finite Generating Lists in Lean
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz
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Prime-Generated Localization Descent for Unique Factorization in Lean
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz, Anjolina Grisi de Oliveira
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Finite Nash Equilibria and Dependent Mixed Strategies in Lean
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz
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A Lean Certificate for the Single Source Unsplittable Flow Cost Counterexample
Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz
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A contractible open four-manifold with a complete metric of uniformly positive scalar curvature
Jiangcheng You, Heng Zhang
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A generalized Gerver sofa for angled corridors
Henrik Schou Guttesen
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A finite criterion for total sign skew symmetry in order three
琪越唐
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Explicit non-inducible rooted cluster morphisms
琪越唐
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On the escape rate of favorite sites of planar random walks
Heng Ma
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Tilings of an equilateral triangle by at most five lattice trapezoids with 60° base angles: a complete structural classification
Gonzalo Barria
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An Exponent of 1.043 for the Unit Distance Problem
Eric Naslund
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On the ternary pentagonal numbers conjecture
Glenn Bruda
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Linnik's constant is at most $3.99$
Eric Naslund
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The Negative Spherical Perceptron: Capacity, Isostatic Jamming, and Full Replica Symmetry Breaking
P. M. Aronow, Patrick Lopatto
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A Fourier Consequence for Lattice Kissing Numbers and Average Contacts
Scott Kominers
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Continuity of solutions to abstract linear control systems
Frédéric Marbach
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A Finite Polyhedral Construction of the Rank-Two Quantum Greedy Basis
琪越唐
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Reflexive equivalence and reflexive-minimal algebras
Haruhisa Enomoto
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Minimality of the Rank-Two Quantum Greedy Basis
琪越唐
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The Anti-Arithmetic Product of Symmetric Functions
Darij Grinberg
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Theta Bases for Rank-Two Quantum Cluster Algebras of Geometric Type
琪越唐
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Crystalline and infinitesimal Poisson stacks
Aleksandr Karapetyan
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Algebraic dependence of cluster X-variables
琪越唐
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An explicit nonideal rooted cluster morphism
琪越唐
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Strongly positive bases and quantum greedy expansions
琪越唐
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Poisson boundaries of type III factors and the relative bicentralizer conjecture
Shuoxing Zhou
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Improved sum-difference inequalities in abelian groups
Logan Kleinwaks
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The generalized Fermat equation $x^3+y^3=z^n$
Manvir Jaswal
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Proof of the Non-existence of Perfect Cuboids via Mordell-Weil Rank Exhaustion and Minimal Polynomial Irreducibility of the Perfect Cuboid Surface
Jonathan 𝑓(n) Reed
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Weak chromatic splitting fails at n = p for every odd prime p
Agnes Beaudry, Tomer Schlank
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A note of refinements to an algebra of infinite little finitistic dimension
琪越唐
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Constant-Time O(1) AST Reduction and Native Delegate Compilation in RICIS-III
Дмитрий Алейников
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Noncommutative Buzano-Dragomir Inequality and Applications
K. MAHESH KRISHNA
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A note on counterexamples to homological conjectures
琪越唐
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The inverse quiver problem is NP-complete
Paul, Marin, Pierre Coutant--Denord
withdrawn
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Phase retrieval for stationary Schrödinger evolutions
Ben Pineau, João Pedro Ramos, Mitchell A. Taylor
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Moment defects and sharp iid Berry–Esseen bounds
Kacper Rodziewicz, Bartosz Kołodziejek
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Uniform Kazhdan Monsters and Schmidt's Property M
Mehdi Moradi
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Square-difference-free sets of exponent 0.7580758
Eric Naslund
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A Verified Constructive Reduction of the Cook-Levin Theorem in Lean 4: Bridging the Gap Between Complexity Theory and Formal SAT Encodings
Jonathan 𝑓(n) Reed
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The generalized Fermat equation $x^2+y^5=z^7$
Manvir Jaswal
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Parisi formula for Ising and Spherical Perceptrons
Daniel Fu, Youngtak Sohn
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The Parisi Formula for the Edwards–Anderson Model in the High-Dimensional Limit
P. M. Aronow, Patrick Lopatto
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Modularity of elliptic curves over totally real field and CM fields not containing \zeta_5
Bao Le Hung
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Nearly Minimax Rates for Functional Estimation Under Rough Random Design
P. M. Aronow, Nathan Kallus, Patrick Lopatto
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The torus with asymptotically the fewest simple closed geodesics
Phuc Thinh Dang, Trong Toan Dao, Nhat Minh Doan
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Binary Regression for BV Class Conditional Probability
Rajesh Dachiraju
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THE CROSS-ENERGY OF DIRICHLET PARTIAL SUMS AND THE ZEROS OF THE RIEMANN ZETA FUNCTION
Pedro Caceres
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Nearly Minimax Variance Estimation Under Rough Random Design
P. M. Aronow, Patrick Lopatto
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An exponential improvement for Borsuk's problem
Andriy Prymak
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Multi-coverings by lattice translates of convex bodies
Scott Kominers
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The Sharp Commutator Bound for the Polymath14 Inequality
Jaeyeon Shim
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Mobility Edge for Sparse Complex Gaussian Matrices
Patrick Lopatto
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Classical infinite divisibility, self-decomposability and bell-shape of free stable laws
Min WANG
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The number of multiplicity sets of n-point plane line collections grows as exp(Theta(sqrt(n)))
Raphael DUCAY
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Measurable Independence Density Equals the Finite Independence-Ratio Infimum in the Euclidean Plane
Ákos Dúcz
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From Snapshots to Processes: Dynamic Contact Algebras as a Foundation for Process-Oriented GIS
John Hessler
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Wave Mechanics
Rajesh Dachiraju
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The Haagerup VOA at Central Charge Eight
Andrew Riesen
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Superexponentially decaying sequences in the Erdos similarity problem
Vjekoslav Kovač
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An $N^{-7/10}$ Bound for the Finite-Size Bias of the Sherrington-Kirkpatrick Free Energy
P. M. Aronow, Patrick Lopatto
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Unconditional implications of the Quasi-Riemann Hypothesis
Shubhrajit Bhattacharya
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Representation embeddings and the third Brauer--Thrall conjecture
Haruhisa Enomoto
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A variational formula for affine semicircular determinants
Sheng Yin
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A counterexample to Han’s conjecture over arbitrary fields
琪越唐
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Arithmetic progressions with prescribed lp gaps
Vjekoslav Kovač
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Stark units for real quadratic fields and reciprocity laws
Danylo Radchenko, Campbell Wheeler
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An Irrationality Measure for Catalan's Constant
Sean Litsey
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A counterexample to Vaught's Conjecture for $L_{\omega_1,\omega}$
Nathanael L. Ackerman, Cameron Freer, Robin W. Knight
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Bruck loops with abelian inner mapping groups: a short proof
Bartosz Naskrecki
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Aging in Spherical Spin Glass Dynamics
P. M. Aronow, Patrick Lopatto
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BRUDNO’S FAMILIES OF EQUAL SUMS OF SIXTH POWERS AND BREMNER’S K3 SURFACE
Alon Amit
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A Machine-Checked Kernel for Federated Automated Adjudication: Credibility Lattice Completion, Certificate Lifecycle Invariants, Certified Numerical Anchors, and a Parameterized Rice Template
Chepin Zhang
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A characterization of cut-percolating bigraphs
Václav Rozhoň
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Strongly regular graphs on 306, 400, 576, 784 and 1296 vertices from multi-orbit coset fusion and Bush-type Hadamard matrices
Anton Kovaľ
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Fröberg's Conjecture through 2d in sufficiently many variables
Vlado Vojdanovski
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Infinitely Many Elliptic Curves of Exact Ranks Five, Six, and Seven
P. M. Aronow, Patrick Lopatto
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Finite Field Riesz-Frechet Representation
K. MAHESH KRISHNA
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A quasi-Riemann hypothesis for Dedekind zeta functions
Dean Cureton, Jesse Thorner
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Finite quantum theta functions for skew-symmetrizable seeds
Qiyue Tang
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Point Density Measures: A Measure-Theoretic Framework with Applications to Geometric Probability
Rajesh Dachiraju
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The Dancing Sand Theorem: the 2-part of the sandpile group of the hypercube, for every n
Rafael Amichis Luengo
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A 23-Point Counterexample to a Modified Half-Frequency Conjecture for Union–Intersection Systems
Jungang Chen
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How long can an off-line zero survive the de Bruijn-Newman heat flow? An explicit unconditional lower bound for Lambda
Pedro Caceres
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Strongly regular graphs on 160, 232, 261 and 280 vertices from fusions of orbitals of PΓL(2,8) and 2^4:(S3×S3)
Anton Kovaľ
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An analogue of the Erdos-Kac theorem for signed Iwasawa invariants of modular forms
Anwesh Ray
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The truncated octahedral conjecture
Thomas Hales, Lark Song
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Axiomatic degree theory on topological manifolds
Stoyan Apostolov
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The Chaise Longue Theorem: Conjecture 1.2 of Degtyarev–Shimada for the Fermat varieties of every degree in every even dimension, and the integral Hodge conjecture for those whose degree is prime, equal to 4, or prime to (n+1)!
Rafael Amichis Luengo
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An order-five Haagerup--Izumi vertex operator algebra at central charge eight
Tzu Chen Huang
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Hilbert functions of chopped ideals of general plane points
Vlado Vojdanovski
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Non-Archimedean Hudzik-Landes-Dragomir-Kato-Saito-Tamura Inequality
K. MAHESH KRISHNA
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A seven-eighths zero-free half-plane for unitary Weil L-functions
Boyang Hu
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Low-discrepancy quasi-uniform digital nets in every dimension
Leonhard Gruenschloss
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A Note on Laminar Presentations and Finite Chain Models for Ample Groupoid Homology
Luciano Melodia
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Gonality and quintic points on intermediate modular curves
Marin Varivoda
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A zero-free strip for the $L$ -functions of the elliptic curves $y^2=x^3+d$
Michael Rubinstein, Mateo Restrepo Borrero
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Deterministic Integer 3SUM in O(n^1.999017) Time via a Sharper Binomial-Tail Analysis
宇轩徐
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Long runs and rare patterns of a random completely multiplicative function
Brice Pouly
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Stable Algebraic Families for $\mathbb{P}^2$
Jit Wu Yap
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The Bannai–Munemasa–Venkov lattice method for strongly regular graphs: a uniform discriminant-form condition and new nonexistence results
Anton Kovaľ
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Milne's rationality conjecture
Keerthi Madapusi
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Marked Positive Handleslide Pentagons in Compression Bodies: Relative Coherence
Hao-Yu Sun
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Every nonsquare integer not equal to $-1$ is a primitive root modulo a positive lower density of primes
Manjul Bhargava
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Non-Archimedean Massera-Schaffer-Maligranda-Pecaric-Rajic Inequality
K. MAHESH KRISHNA
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A Positive Dispersion Optimum for the Rounded Sample Mean: Sufficiency and Necessity of Finite Variance
Mark R. Diamond, Angela O'Brien-Malone
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The Watermark and Double Ladder Theorems: the discriminant group of the Néron–Severi lattice of a Fermat surface of prime degree
Rafael Amichis Luengo
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Another Counterexample to Little Finitistic Dimension Conjecture
Andy Jiang
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An unavoidable set of divisors for the nearest integers to ξ(3/2)^n
Ralf Stephan
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An Arbor Polytope with Nonreal Ehrhart Roots
YURAN XIU
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A counterexample to Haglund's monotonic-zeros conjecture for the Riemann $\Xi$ approximants
Kunal Tyagi
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Unipotent tensor categories and pronilpotent Lie quasibialgebras
Pavel I Etingof
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A nonlinear connectivity code larger than every linear code
Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník
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Small witnesses for eventual Erdős--Straus binomial divisibility
Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník
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A cubic variance bound for matching deficiency
Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník
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A six-spin obstruction to antiferromagnetic biclique maximization
Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník
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Average-radius list decoding of random linear matrix codes at rank-metric capacity
Matěj Kripner, Václav Rozhoň, Robert Šámal, Martin Šindelář, Adrián Zámečník
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Steinhaus Piercing with Slack: The Exact Asymptotic Constant
Anton Joha
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First Proof Third Batch
Mohammed Abouzaid, Nikhil Srivastava, Rachel Ward, Lauren Williams
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Finite Analytic Characters and Tannakian Source Reconstruction: A Finite Tensor–Quiver Framework for Beyond Endoscopy
Shawn Schafer
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Algebraicity of Weil classes on abelian sixfolds of Weil type for $\mathbb{Q}(\sqrt{-3})$ with discriminant $-2$
Benjamin Severn
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Improved Kissing Numbers in Nineteen and Twenty-One Dimensions
Kevin Li
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Explicit positive lower density for the Collatz Conjecture
Kenny Lau