OpenAI's unreleased Astra model has produced genuine solutions to ten long-standing open problems in mathematics and theoretical computer science, each accompanied by a machine-checkable Lean 4 certificate. The proofs, spanning group theory, von Neumann algebras, high-dimensional geometry, quantum complexity, lattice cryptography, and extremal combinatorics, were published August 1 alongside a 249-page technical manuscript and a 62-page account. Every Lean 4 certificate file is publicly available on OpenAI's GitHub repository under an Apache 2.0 license. This structural change separates this announcement from prior AI-mathematics milestones, as Lean 4's trusted kernel gives a binary verdict: the proof either compiles or it doesn't. Thomas Bloom, the University of Manchester mathematician who curates the Erdős problems catalogue, called the Astra results "big news" on X, rating them more significant than the unit distance counterexample OpenAI published three months earlier. The headline result is the construction of the first known non-sofic group, a counterexample to a question that stood open since Mikhail Gromov introduced the concept of soficity in 1999, answering whether every countable discrete group must be sofic: no. The second major result is a disproof of the Connes Rigidity Conjecture, posed by Fields Medalist Alain Connes in 1980, showing that for at least some class of groups, von Neumann algebras don't "remember" the groups that generated them. Three of the ten results resolve