Research
Research
Research
Research
59,676+ 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…
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…
The Baik-Ben Arous-Peche (BBP) transition sets fundamental limits for detecting low-rank structure in noisy high-dimensional data and underlies a wide range of spectral methods in many fields from phy…
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…
Concurrent advances across fields such as organoid technology, Microelectrode Arrays (MEAs), neuromorphic computing, and machine learning have given rise to a groundbreaking research paradigm: Synthet…
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…
Accurate localization is a fundamental requirement for autonomous robots operating in indoor environments. Scene graphs encode the spatial structure of an environment as a hierarchy of semantic entiti…
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…
On the flag variety $ \mathcal{F}l_s(E)$ associated to a vector bundle $E,$ , a sequence $s$ and a partition $a,$ there is a line bundle $\it Q^a_s$ on $ \mathcal{F}l_s(E).$ The aim of this pape…
The evolution of protoplanetary disks, especially in the early stages of planetary formation, as dust grows, is the cornerstone of the birth of planets. The mechanisms involved in the growth of sub-mi…
Despite the rise of token communication (TokCom) as a new paradigm beyond traditional bit communication, existing approaches have primarily adopted artificial intelligence (AI)-centric designs that re…
We investigate several aspects of the Bialynicki-Birula decomposition of a smooth complete $\mathbb{G}_m$-variety with finite fixed locus. Our results include novel characterizations of when the Bialy…
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 $P\subset\mathbb R^n$ be a convex polytope and let $\ell$ be a linear functional which is nonconstant on every edge of $P$. The induced acyclic orientation determines positive and negative Bia{\l}…
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…
In this paper, we prove a big monodromy theorem for the monodromy of cyclic coverings of projective line for cohomology with Fp-coefficients. This is a direct generalization of the results of Achter a…
Statistical inference in observational science typically relies on a fundamental assumption: as sample size increases and uncertainties decrease, the inferred results should converge to the true physi…
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…
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