References

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Johannes Carmesin · 2026 · online

Causal Flow Equations and the 1/3–2/3 Conjecture: Exact Resolution for Low Bottleneck Count

Juan Pablo Silva Alvarado · 2026 · misc

Current narrowed version under concept DOI 10.5281/zenodo.18985093; the case of four or more bottlenecks is left open

The 1/3–2/3 Poset Conjecture: Proof via Bottleneck Dichotomy and Order Polytope Geometry

Juan Pablo Silva Alvarado · 2026 · misc

Superseded first version; its advertised full theorem is conditional on an unproved Stanley Geometric Identity axiom

Nonlinear stability of subextremal Kerr black holes

Peter Hintz · 2026 · misc

Constraint damping for the Einstein equations in the full subextremal Kerr range

Peter Hintz · 2026 · misc

(Non-)Linear waves on asymptotically Kerr spacetimes. II: Tame forward estimates

Peter Hintz · 2026 · misc

Thin-shell bounds via parallel coupling

Boaz Klartag and Joseph Lehec · 2025 · misc

Digesting the proof of the sharp thin-shell inequality

Yuansi Chen and Boaz Klartag · 2026 · misc

Disjoint multilinear discrete characterizations of the Fourier extension conjecture

Cristian Rios and Eric T. Sawyer · 2026 · misc

Version 8 explicitly retracts the earlier full-proof claim because of an uncontrolled error term

The Spacetime Penrose Inequality: Conditional Results for Stable MOTS and General Trapped Surfaces

Da Xu · 2025 · misc

Current version 5 supersedes the unconditional version 1 claim

The spacetime Penrose inequality under a quasi final state hypothesis

Ahmed Ellithy · 2026 · misc

The three obdurate conjectures of differential geometry

Brendan Guilfoyle and Wilhelm Klingenberg · 2025 · misc

Proof of the Caratheodory Conjecture

Brendan Guilfoyle and Wilhelm Klingenberg · 2008 · misc

Version 4, October 2024, claims the theorem for $C^{3+\alpha}$-smooth surfaces

Inter-universal Teichmüller theory IV: Log-volume computations and set-theoretic foundations

Shinichi Mochizuki · 2021 · article

Why abc is still a conjecture

Peter Scholze and Jakob Stix · 2018 · misc

Project LANA Interim Report on IUT Theory

Project LANA · 2026 · online

New Foundations is consistent

Randall Holmes and Sky Wilshaw · 2026 · misc

New Foundations is consistent: formalization and blueprint

Lean Prover Community · 2026 · online

Inconsistency of Reinhardt cardinals with ZF

Rupert McCallum · 2026 · misc

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Irit Huq-Kuruvilla · 2026 · misc

A five-variable counterexample to the Hessian conjecture, and the low-dimensional status of the Jacobian and Hessian conjectures

Guowu Meng and Liang Yang · 2026 · misc

Ten advances in mathematics

OpenAI · 2026 · online

Announcement page; the bundled 249-page manuscript is at \urlhttps://cdn.openai.com/pdf/ten-proofs-oai.pdf

Open Problems

David W. Masser · 1985 · misc

ABC Allows Us to Count Squarefrees

Andrew Granville · 1998 · article

Sofic Groups and Dynamical Systems

Benjamin Weiss · 2000 · article

Hyperlinear and Sofic Groups: A Brief Guide

Vladimir G. Pestov · 2008 · article

Linear Independence of Time-Frequency Translates

Christopher Heil and Jayakumar Ramanathan and Pankaj Topiwala · 1996 · article

The HRT Conjecture for Symmetric Configurations and Real-Valued Functions

Shuang Guan and Kasso A. Okoudjou · 2026 · misc

The von Neumann Algebra of the Non-Residuated Baumslag Group

Florin R\uadulescu · 2008 · article

Deformation and Rigidity for Group Actions and von Neumann Algebras

Sorin Popa · 2007 · inproceedings

Classification des facteurs

Alain Connes · 1982 · misc

Consequences and Limits of Nonlocal Strategies

Richard Cleve and Peter H\o yer and Ben Toner and John Watrous · 2004 · inproceedings

A Parallel Repetition Theorem for All Entangled Games

Henry Yuen · 2016 · inproceedings

Anchoring Games for Parallel Repetition

Mohammad Bavarian and Thomas Vidick and Henry Yuen · 2017 · inproceedings

Approximating CVP to Within Almost-Polynomial Factors is NP-Hard

Irit Dinur and Guy Kindler and Ran Raz and Shmuel Safra · 2003 · article

Une g\'en\'eralisation probable du th\'eor\`eme fondamental de Minkowski

Eug\`ene Ehrhart · 1964 · article

On the Equality Case in Ehrhart's Volume Conjecture

Benjamin Nill and Andreas Paffenholz · 2014 · article

Compactness Results in Extremal Graph Theory

Paul Erd\Hos and Mikl\'os Simonovits · 1982 · article

The History of Degenerate (Bipartite) Extremal Graph Problems

Zolt\'an F\"uredi and Mikl\'os Simonovits · 2013 · article

Bounds for Packings on a Sphere and in Space

Grigory A. Kabatiansky and Vladimir I. Levenshtein · 1978 · article

Probability of Error for Optimal Codes in a Gaussian Channel

Claude E. Shannon · 1959 · article

Percolation

Geoffrey Grimmett · 1999 · book

A Reduction of the $\theta(p_c)=0$ Problem to a Conjectured Inequality

Gady Kozma and Shahaf Nitzan · 2024 · misc

The Complexity of Computing a Nash Equilibrium

Constantinos Daskalakis and Paul W. Goldberg and Christos H. Papadimitriou · 2009 · article

On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence

Christos H. Papadimitriou · 1994 · article

From Information to Exact Communication

Mark Braverman and Ankit Garg and Ariel Schvartzman · 2017 · inproceedings

Network Coding: The Case of Multiple Unicast Sessions

Zongpeng Li and Baochun Li · 2004 · article

Some General Dynamical Notions

Walter Gottschalk · 1973 · article