{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZPKYLY4OXWAGJRNXRNAMEXY6F5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b305107186564ac8b55233d60fbd72d0b162a295aaa9b9defb48e46f1d26b313","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T13:12:13Z","title_canon_sha256":"164ac38fe4e9ad27d205688ae30c6f8c6b4a0741c9add6c4c8807949c6410c04"},"schema_version":"1.0","source":{"id":"1608.03784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03784","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03784v2","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03784","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZPKYLY4OXWAG","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZPKYLY4OXWAGJRNX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZPKYLY4O","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:07e627dd7aa9bfa3e4f9867940996fe9e86a82f5e7e2908b65624122fdb5fff4","target":"graph","created_at":"2026-05-18T00:56:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Han Cheng Lie, T. J. Sullivan","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T13:12:13Z","title":"Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03784","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f34ea3820c65892ba36ef228190c1aea657ae68ddc23d23b02a7bf6dc8205049","target":"record","created_at":"2026-05-18T00:56:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b305107186564ac8b55233d60fbd72d0b162a295aaa9b9defb48e46f1d26b313","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T13:12:13Z","title_canon_sha256":"164ac38fe4e9ad27d205688ae30c6f8c6b4a0741c9add6c4c8807949c6410c04"},"schema_version":"1.0","source":{"id":"1608.03784","kind":"arxiv","version":2}},"canonical_sha256":"cbd585e38ebd8064c5b78b40c25f1e2f5b67c152a66c9491ae27b3fc3202109d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbd585e38ebd8064c5b78b40c25f1e2f5b67c152a66c9491ae27b3fc3202109d","first_computed_at":"2026-05-18T00:56:06.189881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:06.189881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lopsolYQv3J5zGzcfgulJogUxyN4cs9VI9V/WK5aUPMCVnoPDAGXcdfPfqwnw17ricIpBJtzdjL0de1f5WYmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:06.190506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f34ea3820c65892ba36ef228190c1aea657ae68ddc23d23b02a7bf6dc8205049","sha256:07e627dd7aa9bfa3e4f9867940996fe9e86a82f5e7e2908b65624122fdb5fff4"],"state_sha256":"00fdaf75c039b1db4216f4d34cbfad3219ef6614d372afa849f1ee383cc28e2b"}