The Anthropic zeta paper proved 67.25% of Riemann zeta zeros are simple and on the critical line. The community has been tightening it since: 67.30%, then 67.3138%.
GPT-5.6 Sol Pro managed to improve the lower bound: 67.3206%.
The proof uses a local inequality on seven consecutive zeros, with a small "pressure" penalty on each of the six gaps.
Repo with exact rational coefficients, verifier, and certificates: