{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:5A5INJTJSIPYGMRK3PEWBAMIGJ","short_pith_number":"pith:5A5INJTJ","schema_version":"1.0","canonical_sha256":"e83a86a669921f83322adbc96081883271445a1c5ef5719e30fe615a4b763b52","source":{"kind":"arxiv","id":"0912.3648","version":3},"attestation_state":"computed","paper":{"title":"Geometric Representations of Random Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Edoardo M. Airoldi, Robert L. Wolpert, Sayan Mukherjee, Sim\\'on Lunag\\'omez","submitted_at":"2009-12-18T11:30:15Z","abstract_excerpt":"A parametrization of hypergraphs based on the geometry of points in $\\mathbf{R}^d$ is developed. Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial processes. This prior specification is used to infer conditional independence models or Markov structure of multivariate distributions. Specifically, we can recover both the junction tree factorization as well as the hyper Markov law. This approach offers greater control on the distribution of graph features than Erd\\\"os-R\\'enyi random graphs, supports inference of f"},"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":"0912.3648","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-18T11:30:15Z","cross_cats_sorted":["math.PR","stat.ML","stat.TH"],"title_canon_sha256":"aa410edd034a86fcc35fc25772305aef200c6a25c16d51a84fa1178b1cef991c","abstract_canon_sha256":"2c1f1025baa894e1bf3ea7915aed0f6a4e6583f2578d02585e6f67e4325534a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:06.615051Z","signature_b64":"GCBVtXOGYpQ3Ax/NWuSCLcRJAXktIk7xi4AV2n7MyVOGETBC2+m7X75YA0jgOa6YDCBke1g6oWvLwpA0qahJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e83a86a669921f83322adbc96081883271445a1c5ef5719e30fe615a4b763b52","last_reissued_at":"2026-05-18T02:19:06.614548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:06.614548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Representations of Random Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Edoardo M. Airoldi, Robert L. Wolpert, Sayan Mukherjee, Sim\\'on Lunag\\'omez","submitted_at":"2009-12-18T11:30:15Z","abstract_excerpt":"A parametrization of hypergraphs based on the geometry of points in $\\mathbf{R}^d$ is developed. Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial processes. This prior specification is used to infer conditional independence models or Markov structure of multivariate distributions. Specifically, we can recover both the junction tree factorization as well as the hyper Markov law. This approach offers greater control on the distribution of graph features than Erd\\\"os-R\\'enyi random graphs, supports inference of f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3648","kind":"arxiv","version":3},"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":"0912.3648","created_at":"2026-05-18T02:19:06.614627+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.3648v3","created_at":"2026-05-18T02:19:06.614627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3648","created_at":"2026-05-18T02:19:06.614627+00:00"},{"alias_kind":"pith_short_12","alias_value":"5A5INJTJSIPY","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"5A5INJTJSIPYGMRK","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"5A5INJTJ","created_at":"2026-05-18T12:25:58.837520+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/5A5INJTJSIPYGMRK3PEWBAMIGJ","json":"https://pith.science/pith/5A5INJTJSIPYGMRK3PEWBAMIGJ.json","graph_json":"https://pith.science/api/pith-number/5A5INJTJSIPYGMRK3PEWBAMIGJ/graph.json","events_json":"https://pith.science/api/pith-number/5A5INJTJSIPYGMRK3PEWBAMIGJ/events.json","paper":"https://pith.science/paper/5A5INJTJ"},"agent_actions":{"view_html":"https://pith.science/pith/5A5INJTJSIPYGMRK3PEWBAMIGJ","download_json":"https://pith.science/pith/5A5INJTJSIPYGMRK3PEWBAMIGJ.json","view_paper":"https://pith.science/paper/5A5INJTJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.3648&json=true","fetch_graph":"https://pith.science/api/pith-number/5A5INJTJSIPYGMRK3PEWBAMIGJ/graph.json","fetch_events":"https://pith.science/api/pith-number/5A5INJTJSIPYGMRK3PEWBAMIGJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5A5INJTJSIPYGMRK3PEWBAMIGJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5A5INJTJSIPYGMRK3PEWBAMIGJ/action/storage_attestation","attest_author":"https://pith.science/pith/5A5INJTJSIPYGMRK3PEWBAMIGJ/action/author_attestation","sign_citation":"https://pith.science/pith/5A5INJTJSIPYGMRK3PEWBAMIGJ/action/citation_signature","submit_replication":"https://pith.science/pith/5A5INJTJSIPYGMRK3PEWBAMIGJ/action/replication_record"}},"created_at":"2026-05-18T02:19:06.614627+00:00","updated_at":"2026-05-18T02:19:06.614627+00:00"}