Research
Research
Research
Research
53,670+ open-access research outputs.
We prove superpolynomial length lower bounds for the semantic tree-like Frege refutation system with bounded line size. Concretely, for any function $n^{2-\varepsilon} \leq s(n) \leq 2^{n^{1-\varepsil…
Long-context large language models (LLMs)-for example, Gemini-3.1-Pro and Qwen-3.5-are widely used to empower many real-world applications, such as retrieval-augmented generation, autonomous agents, a…
Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy explor…
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
In a recent preprint (Mosegaard and Curtis, 2024, arXiv:2411.13570v2) we analyzed the consequences of ignoring the well-known inconsistency of classical conditional probability densities. We explained…
We introduce a fast, one-dimensional Newtonian {reduced model} to capture uniform rotation in cold white dwarfs, encoding centrifugal support as an effective pressure anisotropy. Using $\Delta_{\rm ro…
With the widespread adoption of large language models (LLMs), understanding their personality representation mechanisms has become critical. As a novel paradigm in Personality Editing, most existing m…
We develop the ODE/IM correspondence for the higher-order Mathieu equation arising from the quantum Seiberg-Witten curve of the pure $SU(r+1)$ ${\cal N}=2$ supersymmetric Yang-Mills theory. From the s…
We propose that the size of the universe and its rate of expansion cannot be simultaneously specified with arbitrary precision, a quantum mechanical statement encoded in a deformed commutation relatio…
Crowds have long held a paradoxical place in the human imagination, feared for their destructive potential yet essential for collective expression. This tension was tragically manifested in the 1919 J…
We study the celestial three-gluon amplitude in a dilaton background through the Mellin-Liouville formulation proposed by Stieberger, Taylor and Zhu (STZ). The original map contains an ambiguity in th…
There is a Lie algebra structure on the tensor product of a Leibniz algebra and a Zinbiel algebra for the operads of Leibniz algebras and Zinbiel algebras are Koszul dual. In this paper, we extend suc…
This paper provides a diffeomorphism classification of smooth manifolds homeomorphic to the complex projective space $\mathbb{C}P^m$ for $m \in \{5, 6, 7, 8\}$. The classification is obtained by compu…
Let $Z=\{Z(t): t\in \mathbb R\}$ be a stochastic process with trajectories in space $\mathbb D (\mathbb R)$. It is assumed that there exists an essentially smooth function $A:\mathbb R\to (-\infty, \i…
Computing edge-connected components in directed and undirected graphs is a fundamental and well-studied problem in graph algorithms. In a very recent breakthrough, Korhonen [STOC 2025] showed that for…
Buchbinder and Feldman recently gave a deterministic $(1-1/e-\varepsilon)$-approximation for maximizing a non-negative monotone submodular function subject to a matroid constraint, with query complexi…
Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on th…
We study properties of the following four classes of operators on the Fock space in $\mathbb C^n:$ 1) weakly localized operators; 2) sufficiently localized operators in the sense of Xia and Zheng; 3) …
The inclusive cross section for top quark pair ($\mathrm{t\bar{t}}$) production in lead-lead (PbPb) collisions is reported for the first time at a center-of-mass energy per nucleon pair of 5.36 TeV. T…
We study a generalisation of the set-theoretic Yang-Baxter equation and investigate the connection between its solutions and matrix refactorisation problems. We refer to such solutions as scalene Yang…
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