To my knowledge, this is the first formally verified implementation of a 3D constructive solid geometry (CSG) operation: mesh intersection, implemented in Lean 4 and verified against a concise specification that pins down the surface of the resulting mesh exactly and guarantees practical well-formedness conditions on the triangulation。This project
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A team of mathematicians used whimsical "silly sprinklers" to solve a physics mystery that has puzzled scientists for decades。 Their experiments showed that the rotation of both normal and reverse sprinklers is driven by the momentum of flowing water, not by the outside water flow or other long-standing theories。 The results finally provide a clear
Astronomers have found the first confirmed atmosphere around a rocky planet in another star’s habitable zone。 The planet, LHS 1140 b, revealed its atmosphere through helium slowly leaking into space。 Located 48 light-years away, the world may have preserved its atmosphere for billions of years, making it a promising target in the search for potenti
A new particle detector called PLATON could replace millions of tiny detector components with a single block of light-producing material。 Using a light-field camera, highly sensitive photon sensors, and AI, it reconstructs particle paths in fast, detailed 3D。 Simulations suggest it could match or surpass today’s best detectors while being far easie
Scientists have created a programmable optical chip that can slow light on demand, giving engineers far greater control over how optical signals propagate through a circuit。 The technology could provide the delays, synchronization, and buffering functions needed to make light-based computing more practical。 A single chip could eventually perform se
Young Jupiter’s powerful magnetic field may have created a safe zone where several large moons could survive。 Saturn lacked this protection, possibly explaining why Titan stands almost alone among its largest moons
A new review highlights exciting progress in atomically thin quantum materials where light and magnetism work together in ways never before possible。 In these materials, light-generated excitons can interact directly with magnetic behavior, creating opportunities to control magnetic states using light alone。 Scientists believe this could pave the w
Sweden could become an important source of rare earth elements needed for magnets and green technologies。 Instead of extracting one target metal, researchers are cataloging everything contained in Swedish mineral deposits。 They will then develop magnets using those naturally available combinations, potentially reducing pollution, waste, and relianc
NASA astronaut Chris Williams and two Roscosmos cosmonauts are back on Earth after spending 241 days aboard the International Space Station。 Their journey covered more than 102 million miles and included 3,856 trips around the planet
Cosmic expansion allows distant galaxies to move away faster than light, while still letting us see ancient light they emitted when they were much closer。 Eventually, accelerating expansion will push nearly every galaxy beyond our Local Group out of sight, making the Universe appear almost empty