sigma-ai

Python wrapper for MFEM

Core Lean 4 proof that the Bohmian guidance identity clears to Im(dψ conj ψ) = dS |ψ|². Not a Schrödinger solver. Not a winding proof.

Operational System Atlas - Lean 4 Gestalt audit: 7 modules, zero sorry, verbatim imperial session archive

QCut is a quantum circuit knitting package built on top of qiskit for performing gate cuts and resetless wire cuts allowing simulation of larger quantum circuits on smaller quantum devices or simulators at the cost of a circuit/shot overhead.

High-performance quantum computing in pure Rust + WebAssembly: state-vector circuit simulator with SIMD & noise models, VQE, Grover, QAOA, surface-code error correction, and real-time coherence via dynamic min-cut.

Secure symbolic memory vault for Aurora runtime, seeds, and exports

VERY experimental Nintendo Switch 2 emulator

Consumer pilot of scottnarmstrong/MarkovProcess: two Brownian-motion theorems, with lean-pkg receipts

A Lean 4 formalization of quantum systems from an operator-algebraic perspective.

Fast single-cell toolkit

Presentations and slide shows: an open-source, clean-room reimplementation of Microsoft PowerPoint in pure Rust. Part of the ArtCraft Crafting Apps.

Mathematical research, counterexamples, and Lean 4 proofs in mathematics, optimization, quantum information, and theoretical computer science. Fully autonomous agentic research by AI, published by Dev D. Goyal. Includes manuscripts, reproducible checks, and explicit proof limits.

we design new patterns of learning

Three papers on the Grothendieckian Programme — an overview, twelve theses and 57 open problems for mathematics and machine reasoning, with problem cards, problems.json and Lean statements. Take 57.

We're rebuilding and open-sourcing the world’s software from scratch.

2-tag system conjugate to De Mol (2008) computing the accelerated Collatz map T. Halting of B^n is open (≡ 3n+1). Proofs, cycle catalog to length 30, binary analogues. MEPhI Hod Mysli 2026.

Trusted AI mathematics workbench: ProblemContract to Attempt to verified proof/counterexample bundles with SymPy and Lean evidence gates.

Qelm - Quantum Enhanced Language Model

Research-grade N-body gravitational simulator with validated physics, Barnes–Hut approximation, Taichi acceleration, FastAPI backend, convergence testing, and cinematic visualization roadmap.

Bounded-count identifiability: conditional mathematics, Lean proofs and exact reproductions.