{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LHKCINIYJNCKTOQVY5YXGMRKGE","short_pith_number":"pith:LHKCINIY","schema_version":"1.0","canonical_sha256":"59d42435184b44a9ba15c77173322a3114617010451901288d1e9a6ce26f187b","source":{"kind":"arxiv","id":"1204.1633","version":2},"attestation_state":"computed","paper":{"title":"Self-Inverse and Exchangeable Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Nickos Papadatos, Theophilos Cacoullos","submitted_at":"2012-04-07T13:42:52Z","abstract_excerpt":"A random variable Z will be called self-inverse if it has the same distribution as its reciprocal 1/Z. It is shown that if Z is defined as a ratio, X/Y, of two rv's X and Y (with Pr[X=0]=Pr[Y=0]=0), then Z is self-inverse if and only if X and Y are (or can be chosen to be) exchangeable. In general, however, there may not exist iid X and Y in the ratio representation of Z."},"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":"1204.1633","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-04-07T13:42:52Z","cross_cats_sorted":[],"title_canon_sha256":"9746ab0529b72f920de80418c21d8fff0f1a54d91dfd65c09694d17e0a507133","abstract_canon_sha256":"8d9fecdb717d0580adb49fa544e98a4546cd202355f8ba8af8ad4f2b6ea77bac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:04.817339Z","signature_b64":"AM3ynClmznPy6I7vK7/k6F+UPFrgHiUW6x8JcYLsJLqC5vfSPJ0eO4oxpfB9gb3vjEuGU0XdF2MtROW6aSUhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59d42435184b44a9ba15c77173322a3114617010451901288d1e9a6ce26f187b","last_reissued_at":"2026-05-18T00:58:04.816942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:04.816942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-Inverse and Exchangeable Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Nickos Papadatos, Theophilos Cacoullos","submitted_at":"2012-04-07T13:42:52Z","abstract_excerpt":"A random variable Z will be called self-inverse if it has the same distribution as its reciprocal 1/Z. It is shown that if Z is defined as a ratio, X/Y, of two rv's X and Y (with Pr[X=0]=Pr[Y=0]=0), then Z is self-inverse if and only if X and Y are (or can be chosen to be) exchangeable. In general, however, there may not exist iid X and Y in the ratio representation of Z."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1633","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":"1204.1633","created_at":"2026-05-18T00:58:04.817007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.1633v2","created_at":"2026-05-18T00:58:04.817007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1633","created_at":"2026-05-18T00:58:04.817007+00:00"},{"alias_kind":"pith_short_12","alias_value":"LHKCINIYJNCK","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LHKCINIYJNCKTOQV","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LHKCINIY","created_at":"2026-05-18T12:27:14.488303+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/LHKCINIYJNCKTOQVY5YXGMRKGE","json":"https://pith.science/pith/LHKCINIYJNCKTOQVY5YXGMRKGE.json","graph_json":"https://pith.science/api/pith-number/LHKCINIYJNCKTOQVY5YXGMRKGE/graph.json","events_json":"https://pith.science/api/pith-number/LHKCINIYJNCKTOQVY5YXGMRKGE/events.json","paper":"https://pith.science/paper/LHKCINIY"},"agent_actions":{"view_html":"https://pith.science/pith/LHKCINIYJNCKTOQVY5YXGMRKGE","download_json":"https://pith.science/pith/LHKCINIYJNCKTOQVY5YXGMRKGE.json","view_paper":"https://pith.science/paper/LHKCINIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.1633&json=true","fetch_graph":"https://pith.science/api/pith-number/LHKCINIYJNCKTOQVY5YXGMRKGE/graph.json","fetch_events":"https://pith.science/api/pith-number/LHKCINIYJNCKTOQVY5YXGMRKGE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LHKCINIYJNCKTOQVY5YXGMRKGE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LHKCINIYJNCKTOQVY5YXGMRKGE/action/storage_attestation","attest_author":"https://pith.science/pith/LHKCINIYJNCKTOQVY5YXGMRKGE/action/author_attestation","sign_citation":"https://pith.science/pith/LHKCINIYJNCKTOQVY5YXGMRKGE/action/citation_signature","submit_replication":"https://pith.science/pith/LHKCINIYJNCKTOQVY5YXGMRKGE/action/replication_record"}},"created_at":"2026-05-18T00:58:04.817007+00:00","updated_at":"2026-05-18T00:58:04.817007+00:00"}