{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KLA36TRYYUTOOIULXZOZNNTLKN","short_pith_number":"pith:KLA36TRY","schema_version":"1.0","canonical_sha256":"52c1bf4e38c526e7228bbe5d96b66b53609b9bae52625273c0aa59768dc39142","source":{"kind":"arxiv","id":"1903.02058","version":2},"attestation_state":"computed","paper":{"title":"Rotatable random sequences in local fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Raban, Steven N. Evans","submitted_at":"2019-03-05T21:16:31Z","abstract_excerpt":"An infinite sequence of real random variables $(\\xi_1, \\xi_2, \\dots)$ is said to be rotatable if every finite subsequence $(\\xi_1, \\dots, \\xi_n)$ has a spherically symmetric distribution. A celebrated theorem of Freedman states that $(\\xi_1, \\xi_2, \\dots)$ is rotatable if and only if $\\xi_j = \\tau \\eta_j$ for all $j$, where $(\\eta_1, \\eta_2, \\dots)$ is a sequence of independent standard Gaussian random variables and $\\tau$ is an independent nonnegative random variable. Freedman's theorem is equivalent to a classical result of Schoenberg which says that a continuous function $\\phi : \\mathbb{R}_"},"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":"1903.02058","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-05T21:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"edc2b3a9c50927283394f643000582eff207f82a81ee94c7ff487d19bf1b8be4","abstract_canon_sha256":"ac95aae41282623b427e391858a7300574a7dba24ed073d7a548ba93ccd10206"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:57.784103Z","signature_b64":"l0QEYEia0OHGkIYiazL0APm4PaDqmjLSdqa1EBD71D6OVuX0Kv6Nl+5stnjZ+Rp7F/KiJAFbKab7MV79goqfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52c1bf4e38c526e7228bbe5d96b66b53609b9bae52625273c0aa59768dc39142","last_reissued_at":"2026-05-17T23:45:57.783620Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:57.783620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rotatable random sequences in local fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Raban, Steven N. Evans","submitted_at":"2019-03-05T21:16:31Z","abstract_excerpt":"An infinite sequence of real random variables $(\\xi_1, \\xi_2, \\dots)$ is said to be rotatable if every finite subsequence $(\\xi_1, \\dots, \\xi_n)$ has a spherically symmetric distribution. A celebrated theorem of Freedman states that $(\\xi_1, \\xi_2, \\dots)$ is rotatable if and only if $\\xi_j = \\tau \\eta_j$ for all $j$, where $(\\eta_1, \\eta_2, \\dots)$ is a sequence of independent standard Gaussian random variables and $\\tau$ is an independent nonnegative random variable. Freedman's theorem is equivalent to a classical result of Schoenberg which says that a continuous function $\\phi : \\mathbb{R}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02058","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":"1903.02058","created_at":"2026-05-17T23:45:57.783686+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.02058v2","created_at":"2026-05-17T23:45:57.783686+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02058","created_at":"2026-05-17T23:45:57.783686+00:00"},{"alias_kind":"pith_short_12","alias_value":"KLA36TRYYUTO","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"KLA36TRYYUTOOIUL","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"KLA36TRY","created_at":"2026-05-18T12:33:21.387695+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/KLA36TRYYUTOOIULXZOZNNTLKN","json":"https://pith.science/pith/KLA36TRYYUTOOIULXZOZNNTLKN.json","graph_json":"https://pith.science/api/pith-number/KLA36TRYYUTOOIULXZOZNNTLKN/graph.json","events_json":"https://pith.science/api/pith-number/KLA36TRYYUTOOIULXZOZNNTLKN/events.json","paper":"https://pith.science/paper/KLA36TRY"},"agent_actions":{"view_html":"https://pith.science/pith/KLA36TRYYUTOOIULXZOZNNTLKN","download_json":"https://pith.science/pith/KLA36TRYYUTOOIULXZOZNNTLKN.json","view_paper":"https://pith.science/paper/KLA36TRY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.02058&json=true","fetch_graph":"https://pith.science/api/pith-number/KLA36TRYYUTOOIULXZOZNNTLKN/graph.json","fetch_events":"https://pith.science/api/pith-number/KLA36TRYYUTOOIULXZOZNNTLKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KLA36TRYYUTOOIULXZOZNNTLKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KLA36TRYYUTOOIULXZOZNNTLKN/action/storage_attestation","attest_author":"https://pith.science/pith/KLA36TRYYUTOOIULXZOZNNTLKN/action/author_attestation","sign_citation":"https://pith.science/pith/KLA36TRYYUTOOIULXZOZNNTLKN/action/citation_signature","submit_replication":"https://pith.science/pith/KLA36TRYYUTOOIULXZOZNNTLKN/action/replication_record"}},"created_at":"2026-05-17T23:45:57.783686+00:00","updated_at":"2026-05-17T23:45:57.783686+00:00"}