Google's Cogentic system produced verified proofs for five open problems in theoretical computer science, and Meta's Muse Spark models assisted mathematicians in producing six research papers, five of which answer previously open mathematical questions. Cogentic operates from a problem statement alone, with no expert hints during runs, and was used via the Gemini API. Meta's mathematicians accessed Muse Spark 1.1 and 1.2 in Thinking Mode through the standard meta.ai chat interface, with no custom research scaffold. Domain experts independently verified all five Cogentic proofs. For Meta's work, a second group of mathematicians reviewed each paper, and each paper marks which passages were drafted primarily by humans or AI. Cogentic's architecture centers on an orchestrator allocating independent provers across distinct proof directions, adversarial verification components that treat every step as wrong until proven correct, and a persistent verified ledger of confirmed intermediate results. A dual-verification structure adds a second checker that compares drafts from the same round to catch shared errors. Most Cogentic problems required roughly 100 Gemini API calls; the hardest required approximately 1,000. Developers attribute results more to architectural choices, specifically adversarial verification and persistent lemma memory, than to raw model capability. The work is described in arXiv preprint 2609.40324, with companion papers covering inverse-optimization, two-sided recruitment, anytime experts, and revenue guarantees. Specific Meta results include: a proof that an exact-data-fitting threshold almost certainly does not exist, providing a theoretical benchmark for the limits of exact data fitting, while behavior exactly at the threshold remains unresolved; a counterexample disproving a conjecture about mathematical group classification, found by a GAP software program that Muse Spark generated, with Golich and collaborators verifying the result; and a characterization of when a relaxation of a binary polynomial optimization problem captures the original exactly, answering a question posed by Del Pia and Khajavirad. Three independent concurrent works addressing aspects related to the exact-data-fitting result were posted in August 2026. AI agent Nilradical independently reported a different counterexample to the same group-classification conjecture on September 16, 2026, and Meta's paper acknowledges that independent work. Meta stated its goal was researcher empowerment rather than mass paper production.