{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SPTP2XIOFLZWX2AK2D2PAGYE6Q","short_pith_number":"pith:SPTP2XIO","schema_version":"1.0","canonical_sha256":"93e6fd5d0e2af36be80ad0f4f01b04f41c4ff8dc9216f17eb155486d61023be5","source":{"kind":"arxiv","id":"1609.09328","version":2},"attestation_state":"computed","paper":{"title":"Proof of Gaussian moment product conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xiangfeng Yang","submitted_at":"2016-09-29T13:31:18Z","abstract_excerpt":"For an $n$-dimensional real-valued centered Gaussian random vector $(X_1,\\ldots,X_n)$ with any covariance matrix, the following moment product conjecture is proved in this paper \\[ \\mathbb{E}\\prod_{j=1}^nX_j^{2m_j}\\geq \\prod_{j=1}^n\\mathbb{E}X_j^{2m_j}, \\] where $m_j\\geq1,1\\leq j\\leq n,$ are any positive integers. Among other important applications, a special case of this conjecture (with $m_j=m,1\\leq j\\leq n$) would give an affirmative answer to another open problem: real linear polarization constant. The proof is based on a very elegant and elementary approach in which only one component $X_"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.09328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-29T13:31:18Z","cross_cats_sorted":[],"title_canon_sha256":"533595f0a6fbab6ad15d7c522a88ae8368dc4669e167006d1aac5fb3041f4dec","abstract_canon_sha256":"59557f83c3c1c095b4b54786c21ac90ba6225fd500a455f685988682890a2b65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:35.904663Z","signature_b64":"WJbkQkSatvXi2QpOJbhwnSbFwEiACR0d+44JBYwMZy4/5dVEe6+xlBN+RLXdPU13OFEUdd2qHq4V4689XGreCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93e6fd5d0e2af36be80ad0f4f01b04f41c4ff8dc9216f17eb155486d61023be5","last_reissued_at":"2026-05-18T01:03:35.903850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:35.903850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of Gaussian moment product conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xiangfeng Yang","submitted_at":"2016-09-29T13:31:18Z","abstract_excerpt":"For an $n$-dimensional real-valued centered Gaussian random vector $(X_1,\\ldots,X_n)$ with any covariance matrix, the following moment product conjecture is proved in this paper \\[ \\mathbb{E}\\prod_{j=1}^nX_j^{2m_j}\\geq \\prod_{j=1}^n\\mathbb{E}X_j^{2m_j}, \\] where $m_j\\geq1,1\\leq j\\leq n,$ are any positive integers. Among other important applications, a special case of this conjecture (with $m_j=m,1\\leq j\\leq n$) would give an affirmative answer to another open problem: real linear polarization constant. The proof is based on a very elegant and elementary approach in which only one component $X_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09328","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.09328","created_at":"2026-05-18T01:03:35.903989+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.09328v2","created_at":"2026-05-18T01:03:35.903989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09328","created_at":"2026-05-18T01:03:35.903989+00:00"},{"alias_kind":"pith_short_12","alias_value":"SPTP2XIOFLZW","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SPTP2XIOFLZWX2AK","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SPTP2XIO","created_at":"2026-05-18T12:30:44.179134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q","json":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q.json","graph_json":"https://pith.science/api/pith-number/SPTP2XIOFLZWX2AK2D2PAGYE6Q/graph.json","events_json":"https://pith.science/api/pith-number/SPTP2XIOFLZWX2AK2D2PAGYE6Q/events.json","paper":"https://pith.science/paper/SPTP2XIO"},"agent_actions":{"view_html":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q","download_json":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q.json","view_paper":"https://pith.science/paper/SPTP2XIO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.09328&json=true","fetch_graph":"https://pith.science/api/pith-number/SPTP2XIOFLZWX2AK2D2PAGYE6Q/graph.json","fetch_events":"https://pith.science/api/pith-number/SPTP2XIOFLZWX2AK2D2PAGYE6Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q/action/storage_attestation","attest_author":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q/action/author_attestation","sign_citation":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q/action/citation_signature","submit_replication":"https://pith.science/pith/SPTP2XIOFLZWX2AK2D2PAGYE6Q/action/replication_record"}},"created_at":"2026-05-18T01:03:35.903989+00:00","updated_at":"2026-05-18T01:03:35.903989+00:00"}