Hidden Symmetries: Quantum Physics and the Secrets of Number Theory
![The distribution of exponents within a mass hierarchy, determined through minimum-weight matching, reveals a spectrum of solutions-those exhibiting symmetry in paired exponents [latex]e\_{1}=e\_{2}[/latex] and [latex]e\_{3}=e\_{4}[/latex], alongside non-symmetric alternatives-all normalized to a unified frequency.](https://arxiv.org/html/2603.12320v1/x1.png)
A surprising link between the search for dark matter and a classic problem in number theory is revealing unexpected constraints on particle physics.
Science
Untangling Top Quarks: A New Path to Quantum Insights
![Quantum entanglement persists even in unpolarized systems, as demonstrated by regions satisfying conditions [latex]\mathcal{N}[\rho]>0[/latex], [latex]\mathcal{C}[\rho]>0[/latex], and [latex]D<-1/3[/latex], which indicate entanglement of the [latex]t\bar{t}[/latex] spin state, with particularly dense regions-where [latex]m_{12}>1[/latex]-further revealing a violation of the Bell inequality at energies below 500 GeV.](https://arxiv.org/html/2603.12830v1/x5.png)
Researchers demonstrate how precisely controlled photon collisions can reveal subtle quantum entanglement effects in the production of top quarks, opening doors to tests beyond the Standard Model.
Hidden Threats in Language Models: When Small Changes Add Up
Researchers have discovered a method to bypass safety protocols in large language models by subtly combining seemingly harmless modifications, exposing a new vulnerability in the rapidly evolving AI supply chain.
Trustless Solvency: A New Era for Crypto Exchanges
![The presented results demonstrate performance gains-though inherently optimistic due to the lack of formal inclusion proofs within the codebase-across varied core counts, with instances of equality between 1-core and 32-core values consolidated for clarity, as observed with a dataset size of [latex]n=2^{16}[/latex].](https://arxiv.org/html/2603.12990v1/x8.png)
A novel approach to Proof of Liabilities eliminates reliance on user cooperation, bolstering security and transparency for cryptocurrency platforms.
Designing Solutions: The Link Between Combinatorics and Encryption
New research reveals a surprising connection between the construction of combinatorial designs and the challenge of creating efficient encryption schemes.
Beyond Privacy Budgets: A New Way to Measure Data Leakage
A new metric, Reconstruction Advantage, offers a more precise assessment of privacy risks in differential privacy, challenging existing assumptions about data reconstruction.
Beyond Flatness: Unlocking Robust Topology in Electronic Bands
New research demonstrates how perfectly flat electronic bands can host stable, topologically protected states, overcoming long-standing limitations in materials design.
Unlocking the Collatz Conjecture: A New Approach with Artificial Intelligence
Researchers are combining mathematical analysis with large language models to probe the enduring mystery of the Collatz sequence and reveal hidden patterns in its complex behavior.
Beyond Point Charges: Reconciling Dynamics and Radiation
A new model of charged particles as deformable systems resolves long-standing paradoxes in classical electrodynamics and offers a physical interpretation of radiation reaction.
Defining Subsystems in Gravity: A New Framework for Relational Spacetime
Researchers have developed a novel approach to consistently define subsystems within gravitational theories using dynamical reference frames and carefully imposed ‘soft cutoffs’.