Initio
Research
Reports and notes on our work.
Building the resource frontier for Shor’s algorithm on Elliptic Curves
We continued running autonomous research to further reduce the resources required to run Shor’s algorithm on secp256k1 and P-256. With the same 1,457 logical qubits, our shortest circuit now requires 27.5M Toffoli gates.
Improvements for running Shor’s Algorithm on a 256-bit Elliptic Curve
We're sharing a new autonomous result that further reduces the resources required for running Shor's algorithm on secp256k1, cutting the Toffoli count by 16.5% relative to the best published construction.
Autonomous formal verification of Initio's proof of Ehrhart's Volume Conjecture
We are releasing a formal verification of the Ehrhart Volume Conjecture, generated by AI and validated in Lean, along with the paper and the complete formalization.
An alternative proof of the Ehrhart volume conjecture from a less powerful model
We are releasing an AI-generated alternative proof of the Ehrhart volume conjecture, produced with an older model and no knowledge of a recently published proof, along with a detailed verification and comparison.
Autonomously Extending the SYK Spectral-Edge Theorem with AI
We are releasing a paper on the Sachdev–Ye–Kitaev model (SYK), carried out end-to-end by AI. Our perspective is that higher-order AI discoveries—results built on prior AI results—will soon become the norm.