{"data":{"event":{"id":"a5c7f692-39a0-4858-84cd-c8d4ebfb6dfd","slug":"gaussian-moments-conjecture-counterexamples","title":"Long, using Sol Pro and Fable 5, posts low-degree Gaussian Moments counterexamples","short_summary":"On 20 July 2026 Christopher D. Long posted explicit polynomials showing the Gaussian Moments conjecture fails in every dimension n≥3: a cubic in four variables found by GPT-5.6 Sol Pro, then a quartic in three variables found by Claude Fable 5. This is not a Jacobian-conjecture score and not a Clay problem.","full_description":"Derksen, van den Essen, and Zhao (2017) proposed the Gaussian Moments conjecture as a route toward the Jacobian conjecture. After public claims of a Jacobian counterexample, Long asked models for small GMC failures. Sol Pro produced a six-term cubic in four Gaussians; Fable 5 then produced a five-term quartic in three variables. Both satisfy E(P^m)=0 while E(QP^m)=m!≠0. The examples are explicit and checkable by computer algebra; the preprint is unrefereed. The two-variable case is left open here. We do not import the Jacobian n=3 claim as a resolved event.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-07-20T00:00:00.000Z","discovery_date":"2026-07-20T00:00:00.000Z","first_published_date":"2026-07-20T00:00:00.000Z","last_reviewed_date":"2026-07-20T00:00:00.000Z","geographic_scope":"International","affected_population":"Algebra and high-dimensional probability research community","base_impact_tier":2,"base_score":"3.00","attribution_multiplier":"0.7500","evidence_multiplier":"0.3500","realization_multiplier":"0.5500","durability_multiplier":"0.7000","current_event_score":"0.303200","confidence_level":"medium","score_explanation":"Explicit low-degree counterexamples to a 2017 conjecture are notable (tier 2). Dual named-model discovery (0.75). Evidence is an arXiv note with computer-checkable polynomials (0.35). Realization is a public construction (0.55).","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-07-20T00:00:00.000Z","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":"9024c7d6-4dad-4b67-8cfa-ea6fdb26f3b4","event_id":"a5c7f692-39a0-4858-84cd-c8d4ebfb6dfd","model_id":"19e2b5dd-4f37-446a-8344-48196c5acf5a","role_description":"Found the three-variable quartic counterexample after being shown the four-variable example.","attribution_multiplier":"0.7500","credit_share":"0.5000","contribution_score":"0.151600","attribution_rationale":"The paper credits Claude Fable 5 with the three-variable construction and independent algebraic checks.","attribution_confidence":"medium","first_used_date":"2026-07-20T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T22:56:05.431Z","model_slug":"claude-fable-5","model_name":"Claude Fable 5","identity_class":"named_release","is_internal":false,"family_name":"Claude","family_slug":"anthropic-claude","organization_name":"Anthropic","organization_slug":"anthropic"},{"id":"4ae16cb4-4fe1-42e9-8cd4-601cf26a70c4","event_id":"a5c7f692-39a0-4858-84cd-c8d4ebfb6dfd","model_id":"8caf038b-a43c-49d6-bd85-c3ff83dbd402","role_description":"Produced the four-variable cubic counterexample after the initial prompt, according to Long.","attribution_multiplier":"0.7500","credit_share":"0.5000","contribution_score":"0.151600","attribution_rationale":"The paper says the four-variable construction was produced by ChatGPT 5.6 Sol Pro without human intervention after the initial prompt.","attribution_confidence":"medium","first_used_date":"2026-07-20T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T22:56:05.431Z","model_slug":"gpt-5-6-sol","model_name":"GPT-5.6 Sol","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":"25093574-00d7-431f-a141-73298066e864","event_id":"a5c7f692-39a0-4858-84cd-c8d4ebfb6dfd","url":"https://arxiv.org/abs/2607.18186","canonical_url":"https://arxiv.org/abs/2607.18186","source_type":"preprint","publisher":"arXiv","author":null,"publication_date":"2026-07-20T00:00:00.000Z","retrieved_at":"2026-09-13T22:56:05.431Z","title":"Small Counterexamples to the Gaussian Moments 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":"6bfe7042-d529-4f42-a036-316f1aa9344d","event_id":"a5c7f692-39a0-4858-84cd-c8d4ebfb6dfd","claim_text":"Long posted explicit 3- and 4-variable counterexamples showing the Gaussian Moments conjecture fails for every n≥3, crediting Sol Pro and Fable 5.","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":"48bb47f4-dc23-41a5-b46f-e7fa87f3b333","event_id":"a5c7f692-39a0-4858-84cd-c8d4ebfb6dfd","claim_text":"This event records a verified solution of the Jacobian conjecture.","claim_type":"significance","claim_status":"disputed","confidence_score":null,"created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-09-13T22:56:05.431Z"}],"revisions":[{"id":"2f76401c-fb48-4610-8c29-99cda8e4e835","event_id":"a5c7f692-39a0-4858-84cd-c8d4ebfb6dfd","model_id":null,"previous_score":"0.000000","new_score":"0.303200","previous_factors":{},"new_factors":{"evidence":0.35,"base_score":3,"durability":0.7,"attribution":0.75,"realization":0.55},"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":[]},"methodology_version":"0.1"}