{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-08-04-period-index-conjecture-false/","md":"https://postcutoff.com/e/2026-08-04-period-index-conjecture-false/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":"2026-08-04-period-index-conjecture-false","date":"2026-08-04","date_precision":"day","short_title":"Alexander Perry disproves the period-index conjecture","deck":"A flawed ChatGPT example was the starting point","takeaway":"Alexander Perry posted counterexamples to the period-index conjecture for Brauer classes: d-dimensional varieties (d ≥ 3) with a Brauer class of period 2 and index 2^d (arXiv 2608.03684; v1 4 Aug, v2 3 Sep 2026).","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2608.03684: The period-index conjecture is false for motivic reasons (Perry)","url":"https://arxiv.org/abs/2608.03684","type":"paper","group":"primary","domain":"arxiv.org"}],"official":1,"filed":"2026-09-30","updated":"2026-09-30","orgs":["Alexander Perry","OpenAI"],"title":"Alexander Perry disproves the period-index conjecture (Colliot-Thélène, 2001); a flawed ChatGPT example was the starting point","summary":"Alexander Perry posted counterexamples to the period-index conjecture for Brauer classes: d-dimensional varieties (d ≥ 3) with a Brauer class of period 2 and index 2^d (arXiv 2608.03684; v1 4 Aug, v2 3 Sep 2026). His AI disclosure says the starting point was a flawed ChatGPT example of the right general shape. Perry found the correct construction himself (a generic K3 surface with a symplectic group action), with ChatGPT helping on literature and lattice calculations.","key_facts":["Period-index conjecture: stated by Colliot-Thélène in 2001; predicts the index of a Brauer class on a d-dimensional variety divides period^(d−1)","Result: failures in dimension 3 over Q and F_p(t), and in all dimensions d ≥ 3 over C and F_p((t)); the lower bound on the index uses a motivic obstruction, namely the non-existence of integral Hodge or Tate classes satisfying an equation mod 2","Perry proposes a corrected period-index conjecture with corrections at small primes and proves its Hodge-theoretic counterpart","AI disclosure, §1.7: prompted to use the paper's Hodge-theoretic strategy, ChatGPT 'produced a flawed example of a threefold X and Brauer class α' that 'had some features of our final solution'; 'Drawing inspiration from this failed example, the author eventually discovered Theorem 1.3'; ChatGPT then 'assisted with literature searches and lattice theory calculations'. The paper was written by the author","Status: preprint, not peer-reviewed"],"key_numbers":[],"tags":["math","algebraic-geometry","brauer-group","counterexample","chatgpt"],"science":{"field":"mathematics","subfield":"algebraic geometry / Brauer groups","problem":"Period-index conjecture","result":"Varieties of every dimension d ≥ 3 with a Brauer class of period 2 and index 2^d, contradicting the conjecture; a corrected conjecture is proposed.","open_since":"2001","ai_system":["ChatGPT"],"human_role":"Human-led: a wrong AI example inspired the construction; the human found and proved the correct one, with AI help on literature search and lattice calculations","verification":{"key":"preprint","label":"Preprint only","text":"Preprint by an expert in the field; not peer-reviewed"},"status":"pending","shock":""},"body_md":"## What happened\n\nPerry, who had earlier worked with de Jong on the Hodge theory of the period-index problem, asked ChatGPT to look for a counterexample along that strategy. The model's example was wrong, but its shape pointed Perry to a correct construction built from K3 surfaces with symplectic group actions.\n\n## Why it matters\n\nThe period-index conjecture was a central open question on Brauer groups of function fields. It is also an example of an AI error being productive: the model gave the idea and a human supplied the correct mathematics.","disputed":[{"label":"Verification","text":"Preprint by an expert in the field; not peer-reviewed","sources":[]}],"related":[{"id":"2026-09-30-ai-assisted-conjecture-wave-summer-2026","url":"https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/","date":"2026-09-30","date_precision":"day","short_title":"Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help","deck":null,"takeaway":"This entry catalogues about 50 of them, with the AI role as the authors state it.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":5,"filed":"2026-09-30","updated":"2026-10-19","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-09-30","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-30","run":null,"sources_read":null,"updated":"2026-09-30","human_review":null,"version":{"date":"2026-10-04"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":96,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":35,"in_training_data":false},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":126,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":65,"in_training_data":false}],"short_url":"https://postcutoff.com/s/alexander-perry-disproves"}