{"data":{"event":{"id":"8ba5ab5a-9def-484b-9131-88e51dab9e83","slug":"tu-deng-conjecture-preprint","title":"Liu, Luo, and Xie post a complete proof of the Tu–Deng conjecture","short_summary":"On 30 July 2026 Renzhang Liu, Hengyi Luo, and Tianyuan Xie posted a complete proof of the Tu–Deng combinatorial conjecture on Hamming weights modulo 2^k−1 (arXiv:2608.05187). A compiled dataset records ChatGPT 5.6 Pro assistance; the arXiv abstract does not name a model or split of labor.","full_description":"The Tu–Deng conjecture bounds the number of pairs (a,b) with a+b ≡ t (mod 2^k−1) and wt(a)+wt(b)<k. The preprint gives a complete argument via cyclic-carry enumerators. Because the public abstract does not specify the AI role, attribution is conservative and the ChatGPT 5.6 Pro identification is treated as reported, not as a named-release certainty. Partial Lean formalization is reported in secondary problem indexes.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-07-30T00:00:00.000Z","discovery_date":"2026-07-30T00:00:00.000Z","first_published_date":"2026-07-30T00:00:00.000Z","last_reviewed_date":"2026-07-30T00:00:00.000Z","geographic_scope":"International","affected_population":"Combinatorics and coding-theory research community","base_impact_tier":2,"base_score":"3.00","attribution_multiplier":"0.3500","evidence_multiplier":"0.3500","realization_multiplier":"0.5000","durability_multiplier":"0.7000","current_event_score":"0.128600","confidence_level":"medium","score_explanation":"A complete proof of a named coding-combinatorics conjecture is notable (tier 2). AI share is unspecified in the abstract (0.35). Evidence is a preprint (0.35). Realization is a public complete argument (0.50).","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-07-30T00:00:00.000Z","created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-13T22:56:05.431Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.1"},"contributions":[{"id":"14cb18ea-9f4e-4c83-9b7e-eac8ad932b11","event_id":"8ba5ab5a-9def-484b-9131-88e51dab9e83","model_id":"c56f0731-9e4f-40b1-8887-fa319c5114bf","role_description":"Reported as an assistant on the Tu–Deng proof; the arXiv abstract does not name the model or the split of labor.","attribution_multiplier":"0.3500","credit_share":"1.0000","contribution_score":"0.128600","attribution_rationale":"Secondary compilation credits ChatGPT 5.6 Pro; primary abstract is silent, so attribution stays modest and identity is the 5.6 Pro SKU rather than Sol.","attribution_confidence":"medium","first_used_date":"2026-07-30T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T22:56:05.431Z","model_slug":"gpt-5-6-pro","model_name":"GPT-5.6 Pro","identity_class":"named_release","is_internal":false,"family_name":"GPT-5.6","family_slug":"openai-gpt-5-6","organization_name":"OpenAI","organization_slug":"openai"}],"sources":[{"id":"ea923fe5-8d12-476e-9704-1347ad7b2349","event_id":"8ba5ab5a-9def-484b-9131-88e51dab9e83","url":"https://arxiv.org/abs/2608.05187","canonical_url":"https://arxiv.org/abs/2608.05187","source_type":"preprint","publisher":"arXiv","author":null,"publication_date":"2026-07-30T00:00:00.000Z","retrieved_at":"2026-09-13T22:56:05.431Z","title":"A Complete Proof for Tu-Deng Conjecture","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":true,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T22:56:05.431Z"}],"claims":[{"id":"6e071cfe-b877-4128-a8fc-d4933a0aafe6","event_id":"8ba5ab5a-9def-484b-9131-88e51dab9e83","claim_text":"Liu, Luo, and Xie posted a complete proof of the Tu–Deng conjecture.","claim_type":"outcome","claim_status":"supported","confidence_score":null,"created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-13T22:56:05.431Z"},{"id":"94c1a700-833a-4ef1-b09a-aa95cf8ca634","event_id":"8ba5ab5a-9def-484b-9131-88e51dab9e83","claim_text":"GPT-5.6 Pro was the primary author of the proof.","claim_type":"attribution","claim_status":"disputed","confidence_score":null,"created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-13T22:56:05.431Z"}],"revisions":[{"id":"c0330efe-80a2-46bb-a479-b27e043ec9b0","event_id":"8ba5ab5a-9def-484b-9131-88e51dab9e83","model_id":null,"previous_score":"0.000000","new_score":"0.128600","previous_factors":{},"new_factors":{"evidence":0.35,"base_score":3,"durability":0.7,"attribution":0.35,"realization":0.5},"change_reason":"Imported events under methodology 0.1.","trigger_type":"editorial_import","trigger_source_ids":null,"reviewer_id":null,"review_status":"published","created_at":"2026-09-13T22:56:05.431Z"}],"secondary":[{"name":"Computer Science","slug":"computer-science"}]},"methodology_version":"0.1"}