Anthropic and OpenAI are intensifying competition in the large language model market with aggressive pricing moves. Anthropic released Opus 5.5 this week, delivering performance comparable to its more expensive Fable model at significantly lower prices, while OpenAI simultaneously launched two new GPT-6 tiers—Sol and Luna—that undercut current market prices and claim to reduce errors. The simultaneous releases highlight a broader trend of cost reduction and efficiency improvements across the frontier AI market as major players race to dominate enterprise and consumer segments. Meta's Muse AI agent also expanded its reach this week by launching on Mac, demonstrating stronger adoption rates in its early mobile phase than ChatGPT's comparable early launch period. However, the agent faced headwinds when Amazon blocked Muse from its shopping interface, citing policy and security concerns. The moves reflect mounting scrutiny of AI capabilities as they gain traction in consumer applications, alongside ongoing concerns about interpretability and external evaluation visibility. The week also saw broader regulatory and policy developments. OpenAI announced it has solved one of mathematics' "Millennium Problems," though requests for external consultation have raised questions about verification processes. Meanwhile, growing public sentiment shifted against data centers, and a lawsuit was filed against Anthropic, OpenAI, SpaceX, and Google over their advocacy to "pace" AI development, highlighting ongoing tensions between industry progress and regulation.