OpenAI released a manuscript titled “The Exponential Time Hypothesis is False,” reportedly generated by an unreleased internal model. Lean, a proof-checking assistant, has verified a version of its main theorem, while an independent group led by ETH’s original proposers Russell Impagliazzo and Ramamohan Paturi, alongside Ryan Williams, reviews the work. Their participation is not an endorsement, so the claim remains unconfirmed. The explainer introduces the issue through 3-SAT: given Boolean variables and rules involving up to three variables, determine whether any assignment satisfies all the rules. Checking an assignment is easy, but exhaustive search takes exponentially many trials; the best known algorithms improve the growth rate without eliminating exponential growth.
Proposed in 1999, ETH asserts that no algorithm can solve 3-SAT in subexponential time - roughly, that the hardest instances require work growing at least as 2 to a fixed positive fraction of the number of variables. It is stronger than P ≠ NP: a subexponential algorithm would refute ETH but would not necessarily make 3-SAT polynomial-time solvable or establish P = NP. ETH matters because reductions connect 3-SAT to problems such as graph colouring, clique, and Hamiltonian cycle, allowing researchers to derive conditional lower bounds for their algorithms. If ETH fails, many such bounds may need reconsideration, but the excerpt provides no details of OpenAI’s proof or its eventual review verdict.
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The Ez-PAVE trial found that targeting LDL below 55 mg/dL reduced cardiovascular events over three years to 6.6%, compared with 9.7% for a target below 70 mg/dL. The benefit came mainly from fewer heart attacks and procedures; the trial did not establish a reduction in cardiovascular deaths. (empirical.health)
U.S. colorectal cancer incidence rose in 2023 after declining for more than two decades, with increases across age groups through 69. The sharpest rise was among adults aged 45-49, highlighting growing needs for screening, treatment, and survivorship care. (uchicagomedicine.org)
The Vera C. Rubin Observatory discovered 2026 ED138, a Kuiper Belt object estimated to be 600-1,500 kilometers wide and a potential dwarf planet. Its orbit stays within Pluto’s range from the Sun, yet it went undetected until now. (sciencealert.com)
Spider silk starts as a liquid protein mixture that rapidly transforms into a strong, flexible fiber tougher than Kevlar. Researchers are probing the molecular changes behind this spinning process to help create high-performance synthetic materials. (quantamagazine.org)
A US-owned commercial satellite photographed China’s Shenlong spaceplane in orbit, revealing a design similar to the US X-37B. A Defense Intelligence Agency assessment says China may soon deploy directed-energy weapons in space. (arstechnica.com)
A four-lane highway is being built through protected Amazon rainforest to ease travel to Belém for the COP30 climate summit. The project has drawn criticism from residents and conservationists, who say the deforestation clashes with the summit’s climate goals. (bbc.com)
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