An 8.5-minute plain-language explainer of the October 26, 2026 claims by OpenAI and Anthropic that their AI models refuted the Exponential Time Hypothesis: counting steps (n³ vs 2ⁿ at n = 50, 100, 200), 3-SAT as a lock with switches (a real 4-switch example solved by brute force), P vs NP in one sentence, ETH as a floor on the "price per switch", the claimed 2^O(n log log n/√log n) bound, why it changes nothing in practice (Anthropic: no gain over 2ⁿ until n has 10,000+ digits), why it is not P = NP, what falls and what survives, and how it is being checked (Lean, plus open review led by Impagliazzo, Paturi and Williams). Claims shown as made; not yet independently confirmed as of Oct 27, 2026.