{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-03-d-equivalence-generalized-kummer-chatgpt-6/","md":"https://postcutoff.com/e/2026-11-03-d-equivalence-generalized-kummer-chatgpt-6/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":"2026-11-03-d-equivalence-generalized-kummer-chatgpt-6","date":"2026-11-03","date_precision":"day","short_title":"D-equivalence for generalized Kummer hyperkählers (ChatGPT-6 assisted)","deck":null,"takeaway":"Donovan, Wang and Zhang claim that birational hyperkähler varieties of generalized Kummer type are derived equivalent; with earlier work this would settle the D-equivalence conjecture for every known deformation type. ChatGPT 6.0 helped realise the key kernel construction.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Donovan, Wang, Zhang: D-equivalence conjecture for hyperkähler varieties of generalized Kummer type (arXiv 2611.04118)","url":"https://arxiv.org/abs/2611.04118","type":"paper","group":"primary","domain":"arxiv.org"}],"official":1,"filed":"2026-11-08","updated":"2026-11-08","orgs":["Tsinghua University","OpenAI"],"title":"D-equivalence conjecture claimed for hyperkähler varieties of generalized Kummer type, completing all known deformation types; Fourier–Mukai kernel found 'with several rounds of help from ChatGPT 6.0'","summary":"arXiv 2611.04118 (Will Donovan, Chengxi Wang, Nantao Zhang; 3 Nov 2026) claims the Bondal–Orlov/Kawamata D-equivalence conjecture for hyperkähler varieties of generalized Kummer type, which with recent results of others would cover all known deformation types of hyperkähler varieties. The authors write that ChatGPT 6.0 helped them realise their idea for the Fourier–Mukai kernel. Unrefereed preprint.","key_facts":["Claim (abstract): birationally equivalent hyperkähler varieties of generalized Kummer type are derived equivalent; 'Combined with recent results of other authors, this settles the conjecture for all known deformation types'","AI disclosure (PDF): 'we came up with the idea of using lifting and splitting methods from Yang's work … With several rounds of help from ChatGPT 6.0, we realized our idea to obtain a Fourier-Mukai kernel. The authors independently verified the proof … ChatGPT and Claude Opus 5.5 also helped fix typos'","Verification status: preprint (21 pages), human-verified by the authors; not refereed"],"key_numbers":[],"tags":["math","algebraic-geometry","derived-categories","hyperkahler","chatgpt","gpt-6"],"science":{"field":"mathematics","subfield":"algebraic geometry","problem":"D-equivalence conjecture (birational Calabi–Yau/hyperkähler varieties are derived equivalent), generalized Kummer type","result":"Claimed proof for generalized Kummer type; with prior work, all known deformation types","open_since":"","ai_system":["ChatGPT 6.0"],"human_role":"Human-led: authors' idea, ChatGPT helped realise the kernel construction; authors verified","verification":{"key":"preprint","label":"Preprint only","text":"Preprint"},"status":"pending","shock":""},"body_md":"## What happened\n\nWill Donovan, Chengxi Wang and Nantao Zhang posted a 21-page proof that birational hyperkähler varieties of generalized Kummer\ntype have equivalent derived categories, the last known deformation type left open. The authors say the idea was theirs and\nthat ChatGPT 6.0 helped turn it into an explicit Fourier–Mukai kernel over several rounds.\n\n## Why it matters\n\nIf it holds up, the D-equivalence conjecture is settled for every known family of hyperkähler varieties. It is also an example of\na human-led result where the AI's role was a key construction step.","disputed":[{"label":"Verification","text":"Preprint","sources":[]}],"related":[],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-08","type":"filed","text":"Created (science agent; PDF AI statement read)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-08","run":null,"sources_read":"Science agent; PDF AI statement read","updated":"2026-11-08","human_review":null,"version":{"date":"2026-11-08"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":187,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":126,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":217,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":156,"in_training_data":false}],"short_url":null}