{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZPKYLY4OXWAGJRNXRNAMEXY6F5","short_pith_number":"pith:ZPKYLY4O","schema_version":"1.0","canonical_sha256":"cbd585e38ebd8064c5b78b40c25f1e2f5b67c152a66c9491ae27b3fc3202109d","source":{"kind":"arxiv","id":"1608.03784","version":2},"attestation_state":"computed","paper":{"title":"Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Han Cheng Lie, T. J. Sullivan","submitted_at":"2016-08-12T13:12:13Z","abstract_excerpt":"Given a sequence of Cauchy-distributed random variables defined by a sequence of location parameters and a sequence of scale parameters, we consider another sequence of random variables that is obtained by perturbing the location or scale parameter sequences. Using a result of Kakutani on equivalence of infinite product measures, we provide sufficient conditions for the equivalence of laws of the two sequences."},"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":"1608.03784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T13:12:13Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"164ac38fe4e9ad27d205688ae30c6f8c6b4a0741c9add6c4c8807949c6410c04","abstract_canon_sha256":"b305107186564ac8b55233d60fbd72d0b162a295aaa9b9defb48e46f1d26b313"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:06.190506Z","signature_b64":"lopsolYQv3J5zGzcfgulJogUxyN4cs9VI9V/WK5aUPMCVnoPDAGXcdfPfqwnw17ricIpBJtzdjL0de1f5WYmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbd585e38ebd8064c5b78b40c25f1e2f5b67c152a66c9491ae27b3fc3202109d","last_reissued_at":"2026-05-18T00:56:06.189881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:06.189881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Han Cheng Lie, T. J. Sullivan","submitted_at":"2016-08-12T13:12:13Z","abstract_excerpt":"Given a sequence of Cauchy-distributed random variables defined by a sequence of location parameters and a sequence of scale parameters, we consider another sequence of random variables that is obtained by perturbing the location or scale parameter sequences. Using a result of Kakutani on equivalence of infinite product measures, we provide sufficient conditions for the equivalence of laws of the two sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03784","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":"1608.03784","created_at":"2026-05-18T00:56:06.189979+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.03784v2","created_at":"2026-05-18T00:56:06.189979+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03784","created_at":"2026-05-18T00:56:06.189979+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZPKYLY4OXWAG","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZPKYLY4OXWAGJRNX","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZPKYLY4O","created_at":"2026-05-18T12:30:55.937587+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/ZPKYLY4OXWAGJRNXRNAMEXY6F5","json":"https://pith.science/pith/ZPKYLY4OXWAGJRNXRNAMEXY6F5.json","graph_json":"https://pith.science/api/pith-number/ZPKYLY4OXWAGJRNXRNAMEXY6F5/graph.json","events_json":"https://pith.science/api/pith-number/ZPKYLY4OXWAGJRNXRNAMEXY6F5/events.json","paper":"https://pith.science/paper/ZPKYLY4O"},"agent_actions":{"view_html":"https://pith.science/pith/ZPKYLY4OXWAGJRNXRNAMEXY6F5","download_json":"https://pith.science/pith/ZPKYLY4OXWAGJRNXRNAMEXY6F5.json","view_paper":"https://pith.science/paper/ZPKYLY4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.03784&json=true","fetch_graph":"https://pith.science/api/pith-number/ZPKYLY4OXWAGJRNXRNAMEXY6F5/graph.json","fetch_events":"https://pith.science/api/pith-number/ZPKYLY4OXWAGJRNXRNAMEXY6F5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZPKYLY4OXWAGJRNXRNAMEXY6F5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZPKYLY4OXWAGJRNXRNAMEXY6F5/action/storage_attestation","attest_author":"https://pith.science/pith/ZPKYLY4OXWAGJRNXRNAMEXY6F5/action/author_attestation","sign_citation":"https://pith.science/pith/ZPKYLY4OXWAGJRNXRNAMEXY6F5/action/citation_signature","submit_replication":"https://pith.science/pith/ZPKYLY4OXWAGJRNXRNAMEXY6F5/action/replication_record"}},"created_at":"2026-05-18T00:56:06.189979+00:00","updated_at":"2026-05-18T00:56:06.189979+00:00"}