Tootfinder

Rational and isolated quadratic points on hyperelliptic curves of rank 0 and small genus
Brice Miayoka Moussolo
https://arxiv.org/abs/2509.20252 https://ar…

Rational and isolated quadratic points on hyperelliptic curves of rank 0 and small genus
In this article, we present a method for computing rational points on hyperelliptic curves of genus~3 and isolated quadratic points on hyperelliptic curves of genus~2 and~3 whose Jacobians have rank~0. Our approach begins by computing the image of the Mordell--Weil group on the associated Kummer variety and then determining which of these points correspond to rational or isolated quadratic points on the curve. We have developed and implemented this algorithm using the computer algebra system \t…

Double-Bracket Algorithmic Cooling
Mohammed Alghadeer, Khanh Uyen Giang, Shuxiang Cao, Simone D. Fasciati, Michele Piscitelli, Nelly Ng, Peter J. Leek, Marek Gluza, Mustafa Bakr
https://arxiv.org/abs/2510.00302

Double-Bracket Algorithmic Cooling
Algorithmic cooling shows that it is possible to locally reduce the entropy of a qubit belonging to an isolated ensemble such as nuclear spins in molecules or nitrogen-vacancy centers in diamonds. In the same physical setting, we introduce double-bracket algorithmic cooling (DBAC), a protocol that systematically suppresses quantum coherence of pure states. DBAC achieves this by simulating quantum imaginary-time evolution through recursive unitary synthesis of Riemannian steepest-descent flows a…

90% Faster, 100% Code-Free: MLLM-Driven Zero-Code 3D Game Development
Runxin Yang, Yuxuan Wan, Shuqing Li, Michael R. Lyu
https://arxiv.org/abs/2509.26161 https://

90% Faster, 100% Code-Free: MLLM-Driven Zero-Code 3D Game Development
Developing 3D games requires specialized expertise across multiple domains, including programming, 3D modeling, and engine configuration, which limits access to millions of potential creators. Recently, researchers have begun to explore automated game development. However, existing approaches face three primary challenges: (1) limited scope to 2D content generation or isolated code snippets; (2) requirement for manual integration of generated components into game engines; and (3) poor performan…