{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:G7WUES6UM7XGG7EWWH5BESCYGA","short_pith_number":"pith:G7WUES6U","schema_version":"1.0","canonical_sha256":"37ed424bd467ee637c96b1fa124858302dfca2fce3ff5abfa86f3d8d6caf3843","source":{"kind":"arxiv","id":"1110.1527","version":1},"attestation_state":"computed","paper":{"title":"Characterization problems for linear forms with free summands","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. G\\\"otze, G. P. Chistyakov","submitted_at":"2011-10-07T13:51:24Z","abstract_excerpt":"Let $T_1,...,T_n$ denote free random variables. For two linear forms $L_1=\\sum_{j=1}^n a_jT_j$ and $L_2=\\sum_{j=1}^n b_jT_j$ with real coefficients $a_j$ and $b_j$ we shall describe all distributions of $T_1,...,T_n$ such that $L_1$ and $L_2$ are free. For identically distributed free random variables $T_1,...,T_n$ with distribution $\\mu$ we establish necessary and sufficient conditions on the coefficients $a_j,b_j,\\,j=1,...,n,$ such that the statements:\\quad $(i)$ $\\mu$ is a centered semicircular distribution; and $(ii)$ \\, $L_1$ and $L_2$ are identically distributed ($L_1\\stackrel{D}{=}L_2$)"},"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":"1110.1527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-07T13:51:24Z","cross_cats_sorted":[],"title_canon_sha256":"139e8b50dc501b15af43add36f0d84da9c60c2e2f243f83706b231b5fff9f838","abstract_canon_sha256":"f47d1195dc63ced6a411cc104c1ecb0823d1bb67e33004cc67afcb16cee8eccc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:29.842057Z","signature_b64":"iGyJ7WvxWCNFi5m7ddKr4BLpAXVaSO6KlYidtVu4UtcUot/XTv6TrGuTY8mFEHZfe0ktfWBv0D83U3XuGRLsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37ed424bd467ee637c96b1fa124858302dfca2fce3ff5abfa86f3d8d6caf3843","last_reissued_at":"2026-05-18T04:11:29.841306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:29.841306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization problems for linear forms with free summands","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. G\\\"otze, G. P. Chistyakov","submitted_at":"2011-10-07T13:51:24Z","abstract_excerpt":"Let $T_1,...,T_n$ denote free random variables. For two linear forms $L_1=\\sum_{j=1}^n a_jT_j$ and $L_2=\\sum_{j=1}^n b_jT_j$ with real coefficients $a_j$ and $b_j$ we shall describe all distributions of $T_1,...,T_n$ such that $L_1$ and $L_2$ are free. For identically distributed free random variables $T_1,...,T_n$ with distribution $\\mu$ we establish necessary and sufficient conditions on the coefficients $a_j,b_j,\\,j=1,...,n,$ such that the statements:\\quad $(i)$ $\\mu$ is a centered semicircular distribution; and $(ii)$ \\, $L_1$ and $L_2$ are identically distributed ($L_1\\stackrel{D}{=}L_2$)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1527","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":"1110.1527","created_at":"2026-05-18T04:11:29.841449+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.1527v1","created_at":"2026-05-18T04:11:29.841449+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1527","created_at":"2026-05-18T04:11:29.841449+00:00"},{"alias_kind":"pith_short_12","alias_value":"G7WUES6UM7XG","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"G7WUES6UM7XGG7EW","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"G7WUES6U","created_at":"2026-05-18T12:26:28.662955+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/G7WUES6UM7XGG7EWWH5BESCYGA","json":"https://pith.science/pith/G7WUES6UM7XGG7EWWH5BESCYGA.json","graph_json":"https://pith.science/api/pith-number/G7WUES6UM7XGG7EWWH5BESCYGA/graph.json","events_json":"https://pith.science/api/pith-number/G7WUES6UM7XGG7EWWH5BESCYGA/events.json","paper":"https://pith.science/paper/G7WUES6U"},"agent_actions":{"view_html":"https://pith.science/pith/G7WUES6UM7XGG7EWWH5BESCYGA","download_json":"https://pith.science/pith/G7WUES6UM7XGG7EWWH5BESCYGA.json","view_paper":"https://pith.science/paper/G7WUES6U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.1527&json=true","fetch_graph":"https://pith.science/api/pith-number/G7WUES6UM7XGG7EWWH5BESCYGA/graph.json","fetch_events":"https://pith.science/api/pith-number/G7WUES6UM7XGG7EWWH5BESCYGA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G7WUES6UM7XGG7EWWH5BESCYGA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G7WUES6UM7XGG7EWWH5BESCYGA/action/storage_attestation","attest_author":"https://pith.science/pith/G7WUES6UM7XGG7EWWH5BESCYGA/action/author_attestation","sign_citation":"https://pith.science/pith/G7WUES6UM7XGG7EWWH5BESCYGA/action/citation_signature","submit_replication":"https://pith.science/pith/G7WUES6UM7XGG7EWWH5BESCYGA/action/replication_record"}},"created_at":"2026-05-18T04:11:29.841449+00:00","updated_at":"2026-05-18T04:11:29.841449+00:00"}