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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
Researchers are applying evolutionary theory to cancer by changing treatments before tumors have time to develop resistance。 Mathematical models suggest that rapid, carefully timed switches between multiple therapies could improve cure rates
NASA's PACE satellite captured the Black Sea glowing turquoise during its annual phytoplankton bloom。 The vivid color comes from massive numbers of coccolithophores, microscopic organisms whose reflective shells brighten the water enough to be seen from space。 An astronaut aboard the International Space Station also photographed the bloom spreading
NASA is preparing for future astronaut landings on the Moon with an unusually ambitious orbital rehearsal。 During Artemis III in 2027, Orion astronauts will rendezvous and dock separately with prototype lunar landers from Blue Origin and SpaceX, allowing crews and ground teams to test the complex maneuvers needed for later missions
NASA’s Psyche spacecraft aced its Mars flyby, using the planet’s gravity to speed toward its 2029 encounter with a metal-rich asteroid。 The spacecraft tested its cameras, magnetometer, and particle-detecting instruments, capturing unusual views of Mars and measuring its magnetic environment。 It also detected neutrons from the planet and spotted the
Researchers say TikTok, X, and Meta aren't providing data they're legally required to
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 are testing two promising ways to destroy PFAS, the stubborn “forever chemicals” that can accumulate in water and resist normal treatment。 One method uses collapsing vapor bubbles to generate extreme heat and reactive molecules, while the other uses cold plasma and rising gas bubbles to pull PFAS to the surface and break them apart
Scientists have created an “electron lighthouse” that uses laser light to launch and steer electrons through a semiconductor without an applied electrical field。 The quantum effect could eventually improve optical sensors, communications, imaging, and information storage
NASA’s Swift Observatory observed a supermassive black hole ripping apart a star more than 30,000 light-years from the center of a distant galaxy。 The extraordinary flare briefly outshone its entire host galaxy in ultraviolet light and revealed a black hole about a million times the Sun’s mass
JWST has captured unusually detailed images of gas feeding the supermassive black hole at the center of NGC 4696。 A vast filament appears to funnel material into an 800-light-year-wide spinning disk, where gas races around at up to 600 kilometers per second。 The findings suggest black holes may recycle their own fuel by heating gas with jets and la
A catastrophic asteroid breakup may have triggered a huge wave of impacts across the inner solar system about 800 million years ago。 The debris was launched from near a gravitational gateway controlled by Jupiter, sending fragments toward Earth, the Moon, and Mars。 The bombardment may explain ancient lunar craters and could have contributed to majo
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
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
Scientists have uncovered new evidence that Venus may still be tearing itself apart from within。 Advanced 3D simulations indicate that some of the planet's giant rift valleys formed relatively recently and could still be expanding。 The results suggest Venus has a far more active interior than researchers once believed, challenging the long-held vie