Full paper: arXiv:2603.28846. Two circuits for ECDLP-256 — one at <1,200 logical qubits / 90M Toffoli gates, one at <1,450 / 70M. ~20x reduction in physical qubit requirements over prior estimates. Notably, Google withheld the actual circuits and instead published a ZK proof (SP1 zkVM + Groth16 SNARK) verifying correctness without exposing the implementation. They also pre-coordinated with the U.S. government before release. I wrote a first-principles derivation tracing the full chain from elliptic curve point addition to the 90M gate count: https://darshanfofadiya.com/research-papers/google-ecdlp/