{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-09-13-matroid-secretary-conjecture-resolved-gpt-astra/","md":"https://postcutoff.com/e/2026-09-13-matroid-secretary-conjecture-resolved-gpt-astra/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":"2026-09-13-matroid-secretary-conjecture-resolved-gpt-astra","date":"2026-09-13","date_precision":"day","short_title":"Matroid secretary conjecture resolved, with GPT Astra","deck":null,"takeaway":"Sahil Singla posted \"The Matroid Secretary Conjecture is True\" (arXiv 2609.14555, 13 Sep 2026): a 4-probability-competitive online algorithm for every matroid, settling Babaioff–Immorlica–Kleinberg's 2007 conjecture.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"Abdi, Banihashem, Hajiaghayi, Huang, Mittal, Singla: As Easy as Rank One (arXiv 2611.08869)","url":"https://arxiv.org/abs/2611.08869","type":"paper","group":"primary","domain":"arxiv.org"},{"n":2,"title":"Singla: The Matroid Secretary Conjecture is True (arXiv 2609.14555)","url":"https://arxiv.org/abs/2609.14555","type":"paper","group":"primary","domain":"arxiv.org"},{"n":3,"title":"Abdi, Banihashem, Hajiaghayi, Mittal: On the Strong Matroid Secretary Conjecture and Beyond (arXiv 2609.19118)","url":"https://arxiv.org/abs/2609.19118","type":"paper","group":"primary","domain":"arxiv.org"},{"n":4,"title":"Bérczi, Dughmi, Livanos, Soto: The Strong Secretary Conjecture is True for Linear Matroids (arXiv 2609.20797)","url":"https://arxiv.org/abs/2609.20797","type":"paper","group":"primary","domain":"arxiv.org"},{"n":5,"title":"Implementation (GitHub)","url":"https://github.com/TlatoaniHJ/MatroidSecretary","type":"code","group":"primary","domain":"github.com"},{"n":6,"title":"AI Weekly: Singla preprint claims matroid secretary conjecture resolved","url":"https://aiweekly.co/alerts/singla-preprint-claims-matroid-secretary-conjecture-resolved","type":"press","group":"press","domain":"aiweekly.co"},{"n":7,"title":"Breakthrough Tracker record (kingy.ai)","url":"https://kingy.ai/mathematics-science-breakthrough-tracker/records/cs-strong-matroid-secretary-conjecture-2026/","type":"discussion","group":"reactions","domain":"kingy.ai"}],"official":5,"filed":"2026-11-09","updated":"2026-11-09","orgs":["OpenAI","various researchers"],"title":"Matroid secretary conjecture (2007) claimed resolved, strong form with optimal ratio e; GPT Astra used for the main guarantees","summary":"Sahil Singla posted \"The Matroid Secretary Conjecture is True\" (arXiv 2609.14555, 13 Sep 2026): a 4-probability-competitive online algorithm for every matroid, settling Babaioff–Immorlica–Kleinberg's 2007 conjecture. A merged paper by Abdi, Banihashem, Hajiaghayi, Huang, Mittal and Singla (arXiv 2611.08869, 9 Nov 2026) claims the strong form, ratio e, and the optimal single-sample matroid prophet inequality (ratio 2), stating that ChatGPT Pro models, \"especially GPT Astra\", were used in obtaining the main algorithmic guarantees. Unrefereed.","key_facts":["Conjecture: Babaioff, Immorlica and Kleinberg (SODA 2007) asked for an O(1)-competitive secretary algorithm on every matroid; the strong form asks for ratio e, as for a single item","Singla, arXiv 2609.14555 (v1 13 Sep 2026): accepts each element of the offline optimum with probability at least 1/4; needs only the number of elements and an independence oracle on arrived elements","Abdi, Banihashem, Hajiaghayi, Mittal, arXiv 2609.19118 (16 Sep): strong conjecture for linear matroids via a finite LP; Bérczi, Dughmi, Livanos & Soto, 2609.20797, independently for linear matroids with GPT Astra","Merged paper 2611.08869 (9 Nov): ratio e for every matroid (ordinal, expected polynomially many queries) and ratio 2 single-sample prophet inequality; merges Singla, ABHM and Huang's preprint","AI statement (2611.08869): 'Interactions with models available through ChatGPT Pro, especially GPT Astra, were used in obtaining the main algorithmic guarantees, including Theorems 2.2, 3.1, 5.2 and 7.2; GPT Sol 5.6 was also used'; the LP of Section 4 was 'devised and carried out without AI models'; 'The authors checked the resulting proofs'","Status: preprints, no peer review; code at github.com/TlatoaniHJ/MatroidSecretary"],"key_numbers":[],"tags":["math","theoretical-computer-science","online-algorithms","matroids","chatgpt","gpt-6-astra","arxiv"],"science":{"field":"computer-science","subfield":"online algorithms","problem":"Matroid secretary conjecture (Babaioff–Immorlica–Kleinberg) and its strong form","result":"O(1) (4-probability-competitive) secretary algorithm for every matroid; merged paper claims the optimal ratio e and a ratio-2 single-sample prophet inequality","open_since":"2007","ai_system":["GPT-6 Astra","GPT-5.6 Sol","ChatGPT Pro"],"human_role":"AI-assisted: authors chose approaches and ran the LP computations; GPT Astra used in obtaining the main theorems; authors checked the proofs","verification":{"key":"preprint","label":"Preprint only","text":"Unrefereed preprints; authors' checks"},"status":"pending","shock":""},"body_md":"## What happened\n\nOn 13 Sep 2026 Sahil Singla posted [arXiv 2609.14555](https://arxiv.org/abs/2609.14555), \"The Matroid Secretary Conjecture is True\", giving an online algorithm that accepts each element of the offline optimum with probability at least 1/4. Within days, [Abdi, Banihashem, Hajiaghayi and Mittal](https://arxiv.org/abs/2609.19118) and [Bérczi, Dughmi, Livanos and Soto](https://arxiv.org/abs/2609.20797) proved the strong (ratio e) conjecture for linear matroids. A tracker also recorded a preprint by Zhiyi Huang claiming ratio e for every matroid.\n\nOn 9 Nov the groups posted a merged paper, [arXiv 2611.08869](https://arxiv.org/abs/2611.08869), claiming the strong conjecture for every matroid and the optimal single-sample matroid prophet inequality. Its AI statement: \"The results came from combining the authors' direction with the technical capabilities of AI models … Interactions with models available through ChatGPT Pro, especially GPT Astra, were used in obtaining the main algorithmic guarantees, including Theorems 2.2, 3.1, 5.2 and 7.2.\" It is not stated in this entry whether Singla's v1 itself used AI; the September preprint was missed by our sweep and found only through the merged paper.\n\n## Why it matters\n\nThe matroid secretary problem was one of the best-known open problems in online algorithms. The result is unrefereed; no expert commentary was found on 9 Nov.","disputed":[{"label":"Verification","text":"Unrefereed preprints; authors' checks","sources":[]}],"related":[{"id":"2026-11-09-ai-assisted-results-november-9-listing","url":"https://postcutoff.com/e/2026-11-09-ai-assisted-results-november-9-listing/","date":"2026-11-09","date_precision":"day","short_title":"AI-assisted results, 9 Nov: arXiv and Hexagon","deck":null,"takeaway":"The 9 Nov sweep listed 175 new arXiv papers mentioning AI. Own entries: the matroid secretary conjecture (strong form, GPT Astra) and Nill's reflexive polytope conjecture disproved with GPT-6.1 Sol.","category":"science","category_label":"Science & math","importance":2,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":44,"official":44,"filed":"2026-11-09","updated":"2026-11-09","orgs":["OpenAI","Anthropic","Google DeepMind","various researchers"]},{"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":"2026-11-09","type":"filed","text":"Created (missed in September)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-09","run":null,"sources_read":null,"updated":"2026-11-09","human_review":null,"version":{"date":"2026-11-09"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":136,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":75,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":166,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":105,"in_training_data":false}],"short_url":"https://postcutoff.com/s/matroid-secretary-conjecture"}