A lock that anyone can close but only one person can open sounds impossible, yet it follows directly from Euler's phi ...

A simple, modular agent that proves Lean 4 theorems through iterative refinement. It uses off-the-shelf LLMs (no fine-tuning) with a feedback loop, a memory system, and library search tools to achieve ...

In the realm of science fiction, Dyson spheres and ringworlds have been staples for decades. But it is well known that the simplest designs are unstable against gravitational forces and would thus be ...

After installing this extension, a 'Welcome' page with a setup guide should open automatically. The setup guide provides platform-specific information on the following topics: Books and documentation ...

The Bayesian approach to statistical inference and other data analysis tasks gets its name from Bayes’s theorem (BT). BT specifies that a posterior probability for a hypothesis concerning a data ...

Many biological forms, such as leaves, flowers, and faces, are shaped by complex growth patterns. How can we prescribe the rules of growth on a simple surface so that it will morph into a flower or a ...

ABSTRACT: The proton and electron charge inner structures are considered in the frame of the non-local quantum hydrodynamics based on the non-local physical description. From calculations follow that ...