Anthropic Claims Claude Refuted ETH

The bigger story is not that AI has settled complexity theory, but that frontier labs are publishing machine-generated mathematical claims faster than independent verification can keep up.

• –Anthropic’s artifact includes a Lean formalization, but its README notes that Lean checks the formal statements—not whether they accurately represent the paper.
• –The claimed result is asymptotic and offers no practical speedup, no direct P-versus-NP result, and no immediate cryptographic implications.
• –Same-day claims from OpenAI and Anthropic create a competitive release cycle where provenance and review matter as much as raw model capability.
• –Developers should treat the math as unverified research while taking PHP2Shell seriously: CISA’s three-day deadline makes patching exposed PHP systems the concrete operational takeaway.