OpenAI published results from an internal, unreleased successor model called Astra showing it produced new proofs or substantial progress on ten open problems spanning high-dimensional sphere packing, coding theory, group theory, operator algebras, quantum complexity, lattice-based cryptography, and extremal combinatorics. Rather than asking readers to take the results on faith, OpenAI had the same model formalize each argument as a Lean 4 certificate, a machine-checkable proof format that a separate proof-verification tool can confirm is logically valid without needing to trust the model's own claims of correctness. That formalization step is the detail worth paying attention to for developers: it demonstrates a repeatable pattern for using an LLM as a mathematical collaborator while keeping a hard, automatable check on its output, rather than relying on human peer review as the only safeguard against hallucinated or subtly wrong proofs. OpenAI also released a companion repository of the Lean certificates on GitHub, so the formal proofs themselves can be independently verified by anyone running the Lean toolchain, separate from any trust in OpenAI's internal evaluation. The company notes that generating all ten solutions would have cost roughly $2,000 at its Sol API pricing, a striking data point on how cheap it currently is to throw frontier-level reasoning at genuinely hard, previously unsolved problems. One of the ten results, an improved bound on high-dimensional sphere-packing density, is the first improvement to that particular bound since 1978, and another disproves a decades-old conjecture from operator algebra theory. For builders, the interesting signal is not the math itself but the workflow: model generates an argument, model formalizes it in Lean, an independent checker verifies it — a template increasingly relevant anywhere correctness matters more than plausibility.