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Tencent's official X account stated that its research agent Hyra collaborated with the Hy3 model to explicitly prove an issue that has troubled the mathematical community for over 50 years: the optimal growth rate exponent of the size of the sum set |A+A| and the size of the difference set |A-A| for a finite integer set A is exactly 2. The theorem from 1969 provided an upper bound of 2, but for the following 50 years, the best constructed exponent was only slightly above 1.1.This achievement demonstrates the potential of AI agents in the field of pure mathematical reasoning. Tencent stated that Hyra is an AI research agent developed in-house, specifically designed to assist in the exploration of complex mathematical and scientific problems. This conclusion still requires confirmation through peer review by the mathematical community.

According to Gate market data, the Hong Kong stock market closed with the Hang Seng Index rising by 0.2% and the Technology Index falling by 1.25%. New Oriental rose over 18.8%, JD Logistics rose over 3.5%, Zhihui fell over 16.5%, and Zhongji Xuchuang closed down 2% on its first day of listing.

According to Coinglass data, the cryptocurrency Fear and Greed Index is currently at 27, down 1 point from yesterday. The average over the past 7 days is 27, and the average over the past 30 days is 24.

According to Gate market data, the Hong Kong stock market opened slightly higher today after three consecutive days of gains, with the Hang Seng Index opening up 67 points at 25,875 points, reaching a high of 25,971 points before significant selling pressure emerged, ultimately closing down 0.05%.The tech index fell 1.14% in the morning session, with total market turnover reaching HKD 162.07 billion. In terms of individual stocks, New Oriental surged 17% against the trend, Budweiser APAC rose over 7%, while Zhihu fell over 16%.

According to Gate market data, the Hong Kong Hang Seng Tech Index quickly fell at the beginning of trading, with a decline of over 1%, after previously rising nearly 1%. The Hang Seng Index fell by 0.31%, Hua Hong Semiconductor (01347.HK) fell nearly 7%, Zhizhu (02513.HK) fell over 6%, Sunny Optical Technology (02382.HK) fell over 5%, and SMIC (00981.HK) fell over 4%.

According to Gate market data, the South Korean KOSPI index rose 5% during the day, currently reported at 5,950.55 points.Samsung Electronics rose by 7%, and SK Hynix increased by 3.2%.

According to Gate market data, the Hong Kong stock market opened with the Hang Seng Index rising by 0.26% and the Technology Index rising by 0.43%. New Oriental (09901.HK) increased by over 14.5%, JD Logistics (02618.HK) rose by 2.5%, and Zhongji Xuchuang (03308.HK) fell by 0.92% on its first day of listing.

According to Gate market data, the Dow Jones Index closed down 1,152.46 points on July 29 (Wednesday), a decrease of 2.18%, at 51,594.86 points; the S&P 500 Index closed down 112.4 points, a decrease of 1.51%, at 7,316.38 points; the Nasdaq Composite Index closed down 433.97 points, a decrease of 1.74%, at 24,442.94 points.

According to Gate market data, the Dow Jones Index opened down 398.29 points on July 29 (Wednesday), a decrease of 0.76%, reporting at 52,349.03 points; the S&P 500 Index opened down 10.87 points, a decrease of 0.15%, reporting at 7,418.35 points; the Nasdaq Composite Index opened down 47.14 points, a decrease of 0.19%, reporting at 24,829.77 points.

According to Gate market data, the S&P 500 index futures and Nasdaq 100 index futures have shown a downward trend.

According to Gate market data, the Hong Kong stock market closed with the Hang Seng Index rising by 1.96% and the Technology Index rising by 2.84%. Automotive stocks performed strongly, with Li Auto (02015.HK) rising nearly 10%, Leapmotor (09863.HK) rising by 9.5%, and Xiaomi Group (01810.HK) rising nearly 9%.

According to Coinglass data, the cryptocurrency Fear and Greed Index is currently at 28, up 0 points from yesterday. The average over the past 7 days is 27, and the average over the past 30 days is 24.

On July 29, Tibo, the product lead for OpenAI Codex, announced on X that all usage limits for ChatGPT Work and Codex users have been reset, and released a statement regarding the issue of rapid consumption of GPT-5.6 Sol usage.In the previous weeks, a large number of users reported that the consumption speed of Codex limits exceeded expectations. OpenAI emphasized that it has not reduced the usage quotas of any subscription plans. After investigation, several reasons were found: Sol is more inclined to work for longer periods, execute more tool calls, and coordinate complex workflows than previous models; it consumes more tokens at the same reasoning level; programmatic tool calls (code mode) allow Sol to execute tool calls in parallel, resulting in more responses and higher usage per round; the distribution of impact is extremely uneven, with median user efficiency being acceptable, but heavy users handling complex tasks consuming far more than expected.OpenAI stated that multiple improvements have been completed, and it is expected that usage endurance will be extended by about 18% in typical usage scenarios. Tomorrow, the five-hour limit that was paused during the investigation will be restored. OpenAI acknowledged that "capabilities and efficiency do not always improve synchronously, and some issues only become apparent after large-scale real-world use; we should have realized this earlier."

According to Gate market data, after two consecutive days of gains, Hong Kong stocks opened high again today, with the Hang Seng Index opening up 176 points at 25,487 points, and then fluctuating upwards, reaching a maximum increase of 426 points to a high of 25,737 points, with the gain slightly narrowing as it approached noon. By the close, the Hang Seng Index rose by 1.37%, the Tech Index rose by 2.2%, and the total market turnover expanded to HKD 173.04 billion.Li Auto surged by 10%, Xiaomi Group rose by over 9%, while Hua Hong Semiconductor and SMIC both fell nearly 8%.

According to Gate market data, the South Korean KOSPI index fell below 5,500 points, down 8.73% during the day.

According to the Dune panel data maintained by the OKX Web3 wallet team, the average daily trading volume of tokenized stocks on the Robinhood Chain reached $29.7 million in the past week, surpassing the combined total of xStocks ($11.1 million) and Backpack Sunrise ($13.4 million) on Solana. The main reason for this growth is that launch platforms like Bankr and long.xyz have allowed users to issue meme coins paired with tokenized stocks for liquidity since mid-July, covering over 90 stock codes. The trading of meme coins generates trading volume for stock tokens while locking the stock tokens in liquidity pools.The tokenized stock with the highest on-chain trading volume is Nvidia (daily trading volume of $13.9 million), followed by SpaceX ($6.2 million) and Apple ($4.5 million). The number of daily active tokenized stock traders peaked at over 20,000 during the week of July 20, the highest among all stock token platforms.However, Binance's bStocks on the BNB Chain has an average daily trading volume of $676.8 million, more than 20 times that of Robinhood. Tokenized stocks still account for only a small portion of the total DEX trading volume on the Robinhood Chain, with most on-chain activity still dominated by meme coins like CASHCAT.

On Tuesday, Apple's stock price reached an all-time high during trading, briefly surpassing a market capitalization of $5 trillion, and continues to hold the top position globally in terms of market value. According to CoinGlass data, the total contract value of Apple (AAPL) across the network is approximately $128 million. From the platform distribution perspective, tradeXYZ, Binance, and Bitget rank in the top three, collectively accounting for about 85.02% of the market share. Among them:tradeXYZ: approximately 219,200 AAPL held, corresponding to a value of $74.9307 million;Binance: approximately 80,300 AAPL held, corresponding to a value of $27.4616 million;Bitget: approximately 18,900 AAPL held, corresponding to a value of $6.4609 million.

According to Jinshi reports, the Korean Exchange has activated the circuit breaker mechanism for the KOSDAQ index, suspending trading for 20 minutes.

According to Gate market data, the Hong Kong Hang Seng Tech Index rose over 3% during the trading session, and the Hang Seng Index increased by 1.66%. MiniMax (00100.HK) rose over 12%, Li Auto (02015.HK) rose over 10.5%, Xiaomi Group (01810.HK) and Leapmotor (09863.HK) both rose over 8%, and Tencent Holdings (00700.HK) rose over 4.5%.

According to Gate market data, the three major U.S. stock index futures have slightly declined in the short term, with Dow futures down 0.13%, S&P 500 futures down 0.08%, and Nasdaq futures down 0.02%.