{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LHCNFU2OCHTAQM27V4DCWDSBRJ","short_pith_number":"pith:LHCNFU2O","schema_version":"1.0","canonical_sha256":"59c4d2d34e11e608335faf062b0e418a4e0760a3af95f1b4ddc083e3a71780ca","source":{"kind":"arxiv","id":"1202.5262","version":1},"attestation_state":"computed","paper":{"title":"Invariant bipartite random graphs on $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Lopes","submitted_at":"2012-02-23T18:40:39Z","abstract_excerpt":"Suppose that red and blue points occur in $\\mathbb{R}^d$ according to two simple point process with finite intensities $\\lambda_{\\mathcal{R}}$ and $\\lambda_{\\mathcal{B}}$, respectively. Furthermore, let $\\nu$ and $\\mu$ be two probability distributions on the strictly positive integers. Assign independently a random number of stubs (half-edges) to each red and blue point with laws $\\nu$ and $\\mu$, respectively. We are interested in translation-invariant schemes to match stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degre"},"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":"1202.5262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-23T18:40:39Z","cross_cats_sorted":[],"title_canon_sha256":"c77202b56bc25324139297f3051c4cfcfa2f16a7aa676a7420eabb9e4b47f3e7","abstract_canon_sha256":"a1dd62bc7a5dfffc64b0893c8d99d54f9761ab14eb2acfe85d6163d9c632130a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:38.556520Z","signature_b64":"3yDv7p0QVI3WR52vHaBiJq/4rBNs9AbY8WeE7330/MgxxkYbIlc5PZIn45DE36Yrn8sMbcAF9tW9dWO/1ASPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59c4d2d34e11e608335faf062b0e418a4e0760a3af95f1b4ddc083e3a71780ca","last_reissued_at":"2026-05-18T04:01:38.555684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:38.555684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant bipartite random graphs on $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Lopes","submitted_at":"2012-02-23T18:40:39Z","abstract_excerpt":"Suppose that red and blue points occur in $\\mathbb{R}^d$ according to two simple point process with finite intensities $\\lambda_{\\mathcal{R}}$ and $\\lambda_{\\mathcal{B}}$, respectively. Furthermore, let $\\nu$ and $\\mu$ be two probability distributions on the strictly positive integers. Assign independently a random number of stubs (half-edges) to each red and blue point with laws $\\nu$ and $\\mu$, respectively. We are interested in translation-invariant schemes to match stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5262","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":"1202.5262","created_at":"2026-05-18T04:01:38.555814+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.5262v1","created_at":"2026-05-18T04:01:38.555814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5262","created_at":"2026-05-18T04:01:38.555814+00:00"},{"alias_kind":"pith_short_12","alias_value":"LHCNFU2OCHTA","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LHCNFU2OCHTAQM27","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LHCNFU2O","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/LHCNFU2OCHTAQM27V4DCWDSBRJ","json":"https://pith.science/pith/LHCNFU2OCHTAQM27V4DCWDSBRJ.json","graph_json":"https://pith.science/api/pith-number/LHCNFU2OCHTAQM27V4DCWDSBRJ/graph.json","events_json":"https://pith.science/api/pith-number/LHCNFU2OCHTAQM27V4DCWDSBRJ/events.json","paper":"https://pith.science/paper/LHCNFU2O"},"agent_actions":{"view_html":"https://pith.science/pith/LHCNFU2OCHTAQM27V4DCWDSBRJ","download_json":"https://pith.science/pith/LHCNFU2OCHTAQM27V4DCWDSBRJ.json","view_paper":"https://pith.science/paper/LHCNFU2O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.5262&json=true","fetch_graph":"https://pith.science/api/pith-number/LHCNFU2OCHTAQM27V4DCWDSBRJ/graph.json","fetch_events":"https://pith.science/api/pith-number/LHCNFU2OCHTAQM27V4DCWDSBRJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LHCNFU2OCHTAQM27V4DCWDSBRJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LHCNFU2OCHTAQM27V4DCWDSBRJ/action/storage_attestation","attest_author":"https://pith.science/pith/LHCNFU2OCHTAQM27V4DCWDSBRJ/action/author_attestation","sign_citation":"https://pith.science/pith/LHCNFU2OCHTAQM27V4DCWDSBRJ/action/citation_signature","submit_replication":"https://pith.science/pith/LHCNFU2OCHTAQM27V4DCWDSBRJ/action/replication_record"}},"created_at":"2026-05-18T04:01:38.555814+00:00","updated_at":"2026-05-18T04:01:38.555814+00:00"}