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OpenAI announced the model breakthrough index time hypothesis

OpenAI recently announced that its AI model has cracked the Exponential Time Hypothesis, abbreviated as ETH, which has been a longstanding conjecture in computer science for over twenty years, and is not related to Ethereum. This hypothesis focuses on how difficult particularly hard problems are, using the Boolean Satisfiability Problem (SAT) as an example: given a set of logical conditions, is there an assignment that makes all conditions true simultaneously? As the problem size increases, the best-known methods essentially can only try possible answers one by one, with the time cost growing exponentially with the size. The Exponential Time Hypothesis further asserts that such problems cannot be significantly accelerated, and there are no truly sub-exponential time efficient algorithms.Since its proposal in 1999, this hypothesis has been a crucial cornerstone of theoretical computer science, with numerous papers proving that certain problems are hard and that some algorithms are close to optimal based on it. If the Exponential Time Hypothesis were to be overturned, it would imply that many problems considered nearly impossible to solve faster might theoretically have better solutions. OpenAI claims that its model has found a deterministic algorithm that can accurately count the number of solutions to the k-SAT problem in sub-exponential time, and it has been formally verified using Lean. If this result withstands expert scrutiny, it will directly challenge the Exponential Time Hypothesis.

Strive invested over 500 million USD to increase its holdings of 6,182 BTC, BitMine's Ethereum holdings exceeded 6.05 million

According to BBX data, yesterday and in recent days, global publicly listed companies in the U.S. stock market disclosed the latest official accounts regarding digital asset treasury allocation, stock buybacks, and capital operations. The core updates are as follows:Strive (NASDAQ: $ASST) spent over $500 million to purchase 6,182 BTC, bringing total holdings to 43,000: According to SEC documents, Strive purchased 6,182 bitcoins from October 17 to 23 at an average price of approximately $82,732 (including fees and expenses). As of October 23, Strive's total bitcoin holdings officially reached 43,000 BTC. During the same period, the company's cash and cash equivalents surged to $504.4 million (an increase of $186.9 million compared to October 16); the balance sheet also holds 505,000 shares of Strategy STRC preferred stock (with a fair value of approximately $50.18 million). In terms of equity, the number of Class A common shares outstanding increased by approximately 3.266 million shares to about 118.1 million shares, while the outstanding shares of SATS and SATA preferred stock remained at 7 million shares and approximately 14.03 million shares, respectively.BitMine (NASDAQ: $BMNR) increased its holdings by 10,452 ETH last week, having spent nearly $400 million on stock buybacks this year: Nasdaq-listed mining company BitMine disclosed that it increased its holdings by 10,452 Ethereum in the secondary market last week. As of October 25, 2026, its total Ethereum holdings reached 6,051,933 ETH (approximately 4.95% of the total Ethereum supply). Currently, the total value of BitMine's crypto assets and investments is approximately $15 billion (including $514 million in cash and securities, 215 BTC, $180 million in Beast Industries equity, and $76 million in Eightco investments). Among these, 5,227,037 ETH have been staked (accounting for 86% of total holdings), valued at approximately $12.3 billion based on a price of $2,356 per ETH, with current annual staking yields of about $318 million. Additionally, the company repurchased 2.04 million shares of stock last week at an average price of $22.48; since 2026, it has repurchased a total of 22.9 million shares, amounting to approximately $399.6 million.

first_img Apple is testing its first foldable screen iPad, expected to be launched in 2028

According to a report by the Science and Technology Innovation Board Daily, Apple is testing its first large-screen foldable iPad, with a maximum screen size of about 20 inches, expected to be 18 to 20 inches when fully unfolded, and more portable when folded. It is positioned between a tablet and a laptop, with a launch expected in 2028. The design concept references the Huawei MateBook Fold, which has already been launched in China.This news aligns with analyst Ming-Chi Kuo's previous judgment that Apple plans to launch its first large-screen foldable iPad in 2028, with a focus on minimizing creases. Bloomberg reporter Mark Gurman previously described it as an ultra-large screen similar to two iPad Pros joined side by side, aimed at multitasking and productivity scenarios. It is expected to use ultra-thin glass, and Kuo believes Corning may be the exclusive supplier of the glass. GIS Group is reportedly responsible for cutting, edge finishing, quality inspection, and packaging, and both companies are also involved in other Apple foldable projects, including the foldable iPhone Duo.The report notes that the latest version of the Huawei MateBook Fold was released in August 2026, with an 18-inch unfolded size and a thickness of 7.3 millimeters when fully unfolded. It was launched in China with a starting price of 24,999 yuan. Industry insiders expect Apple's pricing for this device to be relatively high, primarily due to the manufacturing difficulties of large-size flexible screens. Previous industry forecasts estimated first-year shipments to be around 500,000 to 1 million units. This project has not yet been officially confirmed by Apple.
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