๐คETH (not Ethereum but the Exponential Time Hypothesis) is false.
A Lean proof, produced by OpenAI says 3-SAT can be solved in subexponential time.
For twenty-five years the field assumed the opposite, and hundreds of "impossible unless ETH fails" results in graphs, biology, databases, and geometry were deduced from a false premise.
The problems are not suddenly easy. We have simply lost a fundamental reason we had for refusing to look for a faster algorithm. Sorry, your SAT solver does not get faster.
ETH was the strong form of P โ NP. Every polynomial is already subexponential, so a true ETH would have implied P โ NP immediately. A false ETH does not imply P = NP. Subexponential is still FAR more than polynomial.
This has no impact on cryptography. Signatures, hashes, discrete logs, and lattices are average-case questions about specific functions. A faster worst-case algorithm for Boolean formulas does not forge a signature, invert SHA-256, or change the cost of a Bitcoin block.
Classical cryptography needs one-way functions, and those cannot exist if P = NP.
Whenever P = NP is proven, our simulation must be reset.