{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4W5OOLEGGZ36DLFN5FPONCFSDU","short_pith_number":"pith:4W5OOLEG","schema_version":"1.0","canonical_sha256":"e5bae72c863677e1acade95ee688b21d2483a646b6f6924c6f3d6f09795de4b9","source":{"kind":"arxiv","id":"1607.02962","version":1},"attestation_state":"computed","paper":{"title":"On the Ornstein-Zernike equation for stationary cluster processes and the random connection model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"unter Last, Sebastian Ziesche","submitted_at":"2016-07-11T14:08:09Z","abstract_excerpt":"In the first part of this paper we consider a general stationary subcritical cluster model in $\\mathbb{R}^d$. The associated pair-connectedness function can be defined in terms of two-point Palm probabilities of the underlying point process. Using Palm calculus and Fourier theory we solve the Ornstein-Zernike equation (OZE) under quite general distributional assumptions. In the second part of the paper we discuss the analytic and combinatorial properties of the OZE-solution in the special case of a Poisson driven random connection model."},"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":"1607.02962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-11T14:08:09Z","cross_cats_sorted":[],"title_canon_sha256":"e27f7c5d25a23837ec3ceb57852925d03b0dac01ac84458a2e1fa0f852bbb1cb","abstract_canon_sha256":"c2674b7a5a5c3d0011401ecef3e59df9156ee26e2646cd354079eea96612a970"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:14.293825Z","signature_b64":"DQ34DkdCHkMeDIHfCeqz3knxi7u5iDlyaV+Sw51Fmmbb9TEyyADvasKK4YK/Ck+V9NZmHgj89SZ5Xy0eEqDiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5bae72c863677e1acade95ee688b21d2483a646b6f6924c6f3d6f09795de4b9","last_reissued_at":"2026-05-18T01:11:14.293305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:14.293305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Ornstein-Zernike equation for stationary cluster processes and the random connection model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\\"unter Last, Sebastian Ziesche","submitted_at":"2016-07-11T14:08:09Z","abstract_excerpt":"In the first part of this paper we consider a general stationary subcritical cluster model in $\\mathbb{R}^d$. The associated pair-connectedness function can be defined in terms of two-point Palm probabilities of the underlying point process. Using Palm calculus and Fourier theory we solve the Ornstein-Zernike equation (OZE) under quite general distributional assumptions. In the second part of the paper we discuss the analytic and combinatorial properties of the OZE-solution in the special case of a Poisson driven random connection model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02962","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":"1607.02962","created_at":"2026-05-18T01:11:14.293411+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02962v1","created_at":"2026-05-18T01:11:14.293411+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02962","created_at":"2026-05-18T01:11:14.293411+00:00"},{"alias_kind":"pith_short_12","alias_value":"4W5OOLEGGZ36","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4W5OOLEGGZ36DLFN","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4W5OOLEG","created_at":"2026-05-18T12:29:58.707656+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/4W5OOLEGGZ36DLFN5FPONCFSDU","json":"https://pith.science/pith/4W5OOLEGGZ36DLFN5FPONCFSDU.json","graph_json":"https://pith.science/api/pith-number/4W5OOLEGGZ36DLFN5FPONCFSDU/graph.json","events_json":"https://pith.science/api/pith-number/4W5OOLEGGZ36DLFN5FPONCFSDU/events.json","paper":"https://pith.science/paper/4W5OOLEG"},"agent_actions":{"view_html":"https://pith.science/pith/4W5OOLEGGZ36DLFN5FPONCFSDU","download_json":"https://pith.science/pith/4W5OOLEGGZ36DLFN5FPONCFSDU.json","view_paper":"https://pith.science/paper/4W5OOLEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02962&json=true","fetch_graph":"https://pith.science/api/pith-number/4W5OOLEGGZ36DLFN5FPONCFSDU/graph.json","fetch_events":"https://pith.science/api/pith-number/4W5OOLEGGZ36DLFN5FPONCFSDU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4W5OOLEGGZ36DLFN5FPONCFSDU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4W5OOLEGGZ36DLFN5FPONCFSDU/action/storage_attestation","attest_author":"https://pith.science/pith/4W5OOLEGGZ36DLFN5FPONCFSDU/action/author_attestation","sign_citation":"https://pith.science/pith/4W5OOLEGGZ36DLFN5FPONCFSDU/action/citation_signature","submit_replication":"https://pith.science/pith/4W5OOLEGGZ36DLFN5FPONCFSDU/action/replication_record"}},"created_at":"2026-05-18T01:11:14.293411+00:00","updated_at":"2026-05-18T01:11:14.293411+00:00"}