tag: formal-verification
articles: 2 · beats: 1
latest: October 7, 2026
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Formal Verification
2 Crashtech articles on Formal Verification, filed under How AI Actually Works, published between August 2026 and October 2026. Every piece is full-text HTML with sources, structured data and an authored FAQ.
All 2 sit in the How AI Actually Works beat. How AI Actually Works
Synthetic Data and Model Collapse: Why Verification Helps but Is Not Enough
Recursive synthetic training can lose distributional diversity. Retaining real data, evaluating coverage and using suitable verifiers can reduce the risk.
OpenAI's Astra Model Solved 10 Open Math Problems — With Machine-Verified Proofs
OpenAI's Astra solved 10 longstanding open math problems with fully verified Lean 4 proofs and zero unproven steps. Total compute cost: roughly $2,000.
Questions we answer about Formal Verification
- Does any use of synthetic training data cause collapse?
- Does passing tests make generated code universally correct?
- What open math problems did OpenAI's Astra model solve?
- What is a Lean proof and why does it matter for AI math?
- How much did it cost OpenAI to solve these math problems with Astra?
- Is Astra publicly available?
- What is a non-sofic group and why was it an important open problem?
Frequently asked questions
What does Crashtech publish about Formal Verification?
2 articles tagged Formal Verification, the most recent published October 7, 2026. All 2 sit in the How AI Actually Works beat. Each carries numbered sources, an authored FAQ and full structured data.
What questions about Formal Verification does Crashtech answer directly?
7 questions have a dedicated answer page under this tag, including “Does any use of synthetic training data cause collapse?”. Each answer is authored prose from the article it belongs to, not a generated summary.
Can AI assistants read Crashtech's Formal Verification coverage?
Yes. Crashtech serves full static HTML to every crawler, allows all major AI user agents in robots.txt, and publishes an llms.txt manifest plus a full-text corpus, so assistants can retrieve and cite these articles directly.