{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:62YWGULD2OPLWVGXNNXNTTKPDO","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":"1d7baed7a57a7fd2b320f7f827bcb971151b3669d03130e8eed2942dda7b00f5","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-02-01T07:11:41Z","title_canon_sha256":"db4bdad7d4d6dae763550cb8bcf485ee51b70d3530aa215c34b58948a94afbbd"},"schema_version":"1.0","source":{"id":"1302.0098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0098","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0098v1","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0098","created_at":"2026-05-18T03:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"62YWGULD2OPL","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"62YWGULD2OPLWVGX","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"62YWGULD","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:fe7a9be8ddb0e1860105e16b26a5aed3ec0b837f0a162ce364cf510f92c86594","target":"graph","created_at":"2026-05-18T03:34:47Z","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":"We introduce a four-parameter extended family of distributions related to the wrapped Cauchy distribution on the circle. The proposed family can be derived by altering the settings of a problem in Brownian motion which generates the wrapped Cauchy. The densities of this family have a closed form and can be symmetric or asymmetric depending on the choice of the parameters. Trigonometric moments are available, and they are shown to have a simple form. Further tractable properties of the model are obtained, many by utilizing the trigonometric moments. Other topics related to the model, including ","authors_text":"M.C. Jones, Shogo Kato","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-02-01T07:11:41Z","title":"An extended family of circular distributions related to wrapped Cauchy distributions via Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0098","kind":"arxiv","version":1},"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:eaec04f37ef38da51c4efd35082e231fae28e03e68e064970086c681591da200","target":"record","created_at":"2026-05-18T03:34:47Z","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":"1d7baed7a57a7fd2b320f7f827bcb971151b3669d03130e8eed2942dda7b00f5","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-02-01T07:11:41Z","title_canon_sha256":"db4bdad7d4d6dae763550cb8bcf485ee51b70d3530aa215c34b58948a94afbbd"},"schema_version":"1.0","source":{"id":"1302.0098","kind":"arxiv","version":1}},"canonical_sha256":"f6b1635163d39ebb54d76b6ed9cd4f1ba059f180d85f6d4bf83957a5bf1b1cd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6b1635163d39ebb54d76b6ed9cd4f1ba059f180d85f6d4bf83957a5bf1b1cd2","first_computed_at":"2026-05-18T03:34:47.460062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:47.460062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fz6/vKef1Rr7HqrxHMVkajGuFPFF2ZUwQqZ8cPZfIj5mC8V2d8JVSg8Ce6dngtKn13qbNnj49YtNkXkR5wuBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:47.460629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eaec04f37ef38da51c4efd35082e231fae28e03e68e064970086c681591da200","sha256:fe7a9be8ddb0e1860105e16b26a5aed3ec0b837f0a162ce364cf510f92c86594"],"state_sha256":"f9aeb98222e7c5fdcd00e8d4c939a2320a227786d5410ff73b922295d188715a"}