{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2025-09-27-aaronson-gpt-5-qma-proof/","md":"https://postcutoff.com/e/2025-09-27-aaronson-gpt-5-qma-proof/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2025-09-27-aaronson-gpt-5-qma-proof","date":"2025-09-27","date_precision":"day","short_title":"Scott Aaronson credits GPT-5 with a key step in a quantum complexity proof","deck":null,"takeaway":"In 'Limits to black-box amplification in QMA' (Aaronson and Witteveen, arXiv 2509.21131), GPT-5-Thinking suggested the key function Tr[(I−E(θ))^−1] used in the proof.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Limits to black-box amplification in QMA (arXiv 2509.21131)","url":"https://arxiv.org/abs/2509.21131","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"The Quantum Insider: GPT-5 serves as research assistant","url":"https://thequantuminsider.com/2025/09/29/gpt-5-serves-as-research-assistant-in-proving-one-of-quantum-computing-theorys-trickiest-theorems/","type":"press","group":"press","domain":"thequantuminsider.com"},{"n":3,"title":"Scott Aaronson: The QMA Singularity","url":"https://scottaaronson.blog/?p=9183","type":"discussion","group":"reactions","domain":"scottaaronson.blog"}],"official":1,"filed":"2026-09-29","updated":"2026-09-29","orgs":["UT Austin","CWI","OpenAI"],"title":"Scott Aaronson credits GPT-5 with a key step in a quantum complexity proof","summary":"In 'Limits to black-box amplification in QMA' (Aaronson and Witteveen, arXiv 2509.21131), GPT-5-Thinking suggested the key function Tr[(I−E(θ))^−1] used in the proof. Aaronson called it the first paper of his where a key technical step came from AI.","key_facts":["Result: black-box amplification cannot push QMA completeness error below doubly exponential or soundness error below exponential","Aaronson: 'Within a half hour, it had suggested to look at the function…'","Aaronson: 'if a student had given it to me, I would've called it clever'","Blog post 'The QMA Singularity', 27 Sep 2025"],"key_numbers":[],"tags":["quantum","complexity-theory","gpt-5","proof"],"science":{"field":"computer-science","subfield":"quantum complexity theory","problem":"Limits of black-box error reduction in QMA","result":"Proof of tight limits on black-box amplification in QMA, with the central analytic idea proposed by GPT-5.","open_since":"","ai_system":["GPT-5-Thinking"],"human_role":"Human-led with AI tools: humans posed the problem, checked and wrote the proof","verification":{"key":"expert","label":"Expert-checked","text":"Expert-checked; arXiv preprint"},"status":"confirmed","shock":"A leading complexity theorist said an LLM supplied the idea he would have called 'clever' from a student."},"body_md":"## What happened\n\nStuck on a technical step, Aaronson asked GPT-5 for help. Within about half an hour it proposed analysing a resolvent-trace function, which worked.\n\n## Why it matters\n\nIt was a credible, first-person account from a top theorist of an LLM contributing a genuine idea to a published result.","disputed":[],"related":[{"id":"2025-11-20-openai-gpt-5-science-acceleration","url":"https://postcutoff.com/e/2025-11-20-openai-gpt-5-science-acceleration/","date":"2025-11-20","date_precision":"day","short_title":"OpenAI publishes 'Early science acceleration experiments with GPT-5'","deck":"Including four new math results","takeaway":"It marked a shift from benchmark claims to documented research contributions, and set the template for OpenAI's 2026 \"OpenAI for Science\" results.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":4,"official":4,"filed":"2026-09-29","updated":"2026-09-29","orgs":["OpenAI"]}],"people":[{"id":"scott-aaronson","name":"Scott Aaronson","url":"https://postcutoff.com/person/scott-aaronson/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-09-29","human_review":null,"version":{"date":"2026-10-04"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":null,"in_training_data":true},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":null,"in_training_data":true},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":null,"in_training_data":true},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":null,"in_training_data":true}],"short_url":null}