{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:MFZ35AKI23C2VKLKMIBXI7BUTS","short_pith_number":"pith:MFZ35AKI","schema_version":"1.0","canonical_sha256":"6173be8148d6c5aaa96a6203747c349cb890f3b44ff8d2022d2837597a6fa91b","source":{"kind":"arxiv","id":"0911.1176","version":1},"attestation_state":"computed","paper":{"title":"On q-Gaussians and Exchangeability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marjorie G. Hahn, Sabir Umarov, Xinxin Jiang","submitted_at":"2009-11-06T04:56:11Z","abstract_excerpt":"The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that q-Gaussian random variables can be represented as variance mixtures of normals. These variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables; thereby, providing a possible model that has been extensively studied in probability theory. The formulation provided has the additional advantage of y"},"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":"0911.1176","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-11-06T04:56:11Z","cross_cats_sorted":[],"title_canon_sha256":"f508cfab608fe0dcf6839e811d4ff2a676ea2ef26d3bfab7a5be92f7b1690c5a","abstract_canon_sha256":"4a0c42d69e7d2a6336fd3efe35f1c1e9c07b5506f65da81dd9f635422ab8ea9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:59.044809Z","signature_b64":"eL6nS7x/IlTQTHIkssK7hV4dkg3EptbxwlOyyQUPSA0H5vfxEhoQojBVtNg/1ha7nR5Md9fE7QQA7URWLetRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6173be8148d6c5aaa96a6203747c349cb890f3b44ff8d2022d2837597a6fa91b","last_reissued_at":"2026-05-18T02:10:59.043973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:59.043973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On q-Gaussians and Exchangeability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marjorie G. Hahn, Sabir Umarov, Xinxin Jiang","submitted_at":"2009-11-06T04:56:11Z","abstract_excerpt":"The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that q-Gaussian random variables can be represented as variance mixtures of normals. These variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables; thereby, providing a possible model that has been extensively studied in probability theory. The formulation provided has the additional advantage of y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1176","kind":"arxiv","version":1},"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":"0911.1176","created_at":"2026-05-18T02:10:59.044093+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.1176v1","created_at":"2026-05-18T02:10:59.044093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1176","created_at":"2026-05-18T02:10:59.044093+00:00"},{"alias_kind":"pith_short_12","alias_value":"MFZ35AKI23C2","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"MFZ35AKI23C2VKLK","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"MFZ35AKI","created_at":"2026-05-18T12:26:00.592388+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/MFZ35AKI23C2VKLKMIBXI7BUTS","json":"https://pith.science/pith/MFZ35AKI23C2VKLKMIBXI7BUTS.json","graph_json":"https://pith.science/api/pith-number/MFZ35AKI23C2VKLKMIBXI7BUTS/graph.json","events_json":"https://pith.science/api/pith-number/MFZ35AKI23C2VKLKMIBXI7BUTS/events.json","paper":"https://pith.science/paper/MFZ35AKI"},"agent_actions":{"view_html":"https://pith.science/pith/MFZ35AKI23C2VKLKMIBXI7BUTS","download_json":"https://pith.science/pith/MFZ35AKI23C2VKLKMIBXI7BUTS.json","view_paper":"https://pith.science/paper/MFZ35AKI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.1176&json=true","fetch_graph":"https://pith.science/api/pith-number/MFZ35AKI23C2VKLKMIBXI7BUTS/graph.json","fetch_events":"https://pith.science/api/pith-number/MFZ35AKI23C2VKLKMIBXI7BUTS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MFZ35AKI23C2VKLKMIBXI7BUTS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MFZ35AKI23C2VKLKMIBXI7BUTS/action/storage_attestation","attest_author":"https://pith.science/pith/MFZ35AKI23C2VKLKMIBXI7BUTS/action/author_attestation","sign_citation":"https://pith.science/pith/MFZ35AKI23C2VKLKMIBXI7BUTS/action/citation_signature","submit_replication":"https://pith.science/pith/MFZ35AKI23C2VKLKMIBXI7BUTS/action/replication_record"}},"created_at":"2026-05-18T02:10:59.044093+00:00","updated_at":"2026-05-18T02:10:59.044093+00:00"}