{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UB6KNTO7PAE5ZNGDDROT7M2FKA","short_pith_number":"pith:UB6KNTO7","schema_version":"1.0","canonical_sha256":"a07ca6cddf7809dcb4c31c5d3fb345503c6ebe3c97015e0106ae7ce14858dadf","source":{"kind":"arxiv","id":"1205.0933","version":1},"attestation_state":"computed","paper":{"title":"A note on the bivariate distribution representation of two perfectly correlated random variables by Dirac's $\\delta$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NI","authors_text":"Andr\\'es Alay\\'on Glazunov, Jie Zhang","submitted_at":"2012-05-04T12:26:31Z","abstract_excerpt":"In this paper we discuss the representation of the joint probability density function of perfectly correlated continuous random variables, i.e., with correlation coefficients $\\rho=pm1$, by Dirac's $\\delta$-function. We also show how this representation allows to define Dirac's $\\delta$-function as the ratio between bivariate distributions and the marginal distribution in the limit $\\rho\\rightarrow \\pm1$, whenever this limit exists. We illustrate this with the example of the bivariate Rice distribution"},"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":"1205.0933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NI","submitted_at":"2012-05-04T12:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"fcd735b0385a94906748fb5b8d81d3ab09ac5c2a0c01daa2abbfd4d824919f40","abstract_canon_sha256":"50ed0a8bc5303db4a0c4b7f6744905dfacc7a17a14eb37140da175e57051f7fe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:23.524766Z","signature_b64":"STgA26Q5CuidsPCWrLsMQRxbdXK3v6gTRKOwvj8p8DxxrJsqgE+Muw7AGoCyT9PLoQ/qfWUqoK9gyJ7De8kzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a07ca6cddf7809dcb4c31c5d3fb345503c6ebe3c97015e0106ae7ce14858dadf","last_reissued_at":"2026-05-18T03:56:23.524185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:23.524185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the bivariate distribution representation of two perfectly correlated random variables by Dirac's $\\delta$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NI","authors_text":"Andr\\'es Alay\\'on Glazunov, Jie Zhang","submitted_at":"2012-05-04T12:26:31Z","abstract_excerpt":"In this paper we discuss the representation of the joint probability density function of perfectly correlated continuous random variables, i.e., with correlation coefficients $\\rho=pm1$, by Dirac's $\\delta$-function. We also show how this representation allows to define Dirac's $\\delta$-function as the ratio between bivariate distributions and the marginal distribution in the limit $\\rho\\rightarrow \\pm1$, whenever this limit exists. We illustrate this with the example of the bivariate Rice distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0933","kind":"arxiv","version":1},"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":"1205.0933","created_at":"2026-05-18T03:56:23.524267+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.0933v1","created_at":"2026-05-18T03:56:23.524267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0933","created_at":"2026-05-18T03:56:23.524267+00:00"},{"alias_kind":"pith_short_12","alias_value":"UB6KNTO7PAE5","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"UB6KNTO7PAE5ZNGD","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"UB6KNTO7","created_at":"2026-05-18T12:27:23.164592+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/UB6KNTO7PAE5ZNGDDROT7M2FKA","json":"https://pith.science/pith/UB6KNTO7PAE5ZNGDDROT7M2FKA.json","graph_json":"https://pith.science/api/pith-number/UB6KNTO7PAE5ZNGDDROT7M2FKA/graph.json","events_json":"https://pith.science/api/pith-number/UB6KNTO7PAE5ZNGDDROT7M2FKA/events.json","paper":"https://pith.science/paper/UB6KNTO7"},"agent_actions":{"view_html":"https://pith.science/pith/UB6KNTO7PAE5ZNGDDROT7M2FKA","download_json":"https://pith.science/pith/UB6KNTO7PAE5ZNGDDROT7M2FKA.json","view_paper":"https://pith.science/paper/UB6KNTO7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.0933&json=true","fetch_graph":"https://pith.science/api/pith-number/UB6KNTO7PAE5ZNGDDROT7M2FKA/graph.json","fetch_events":"https://pith.science/api/pith-number/UB6KNTO7PAE5ZNGDDROT7M2FKA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UB6KNTO7PAE5ZNGDDROT7M2FKA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UB6KNTO7PAE5ZNGDDROT7M2FKA/action/storage_attestation","attest_author":"https://pith.science/pith/UB6KNTO7PAE5ZNGDDROT7M2FKA/action/author_attestation","sign_citation":"https://pith.science/pith/UB6KNTO7PAE5ZNGDDROT7M2FKA/action/citation_signature","submit_replication":"https://pith.science/pith/UB6KNTO7PAE5ZNGDDROT7M2FKA/action/replication_record"}},"created_at":"2026-05-18T03:56:23.524267+00:00","updated_at":"2026-05-18T03:56:23.524267+00:00"}