{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4W5OOLEGGZ36DLFN5FPONCFSDU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c2674b7a5a5c3d0011401ecef3e59df9156ee26e2646cd354079eea96612a970","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-11T14:08:09Z","title_canon_sha256":"e27f7c5d25a23837ec3ceb57852925d03b0dac01ac84458a2e1fa0f852bbb1cb"},"schema_version":"1.0","source":{"id":"1607.02962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02962","created_at":"2026-05-18T01:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02962v1","created_at":"2026-05-18T01:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02962","created_at":"2026-05-18T01:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"4W5OOLEGGZ36","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4W5OOLEGGZ36DLFN","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4W5OOLEG","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:f29ac0e4c1e3b192d19d063657a0d8ea3a2fee69f0fc78a501f17e434a831a70","target":"graph","created_at":"2026-05-18T01:11:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"G\\\"unter Last, Sebastian Ziesche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-11T14:08:09Z","title":"On the Ornstein-Zernike equation for stationary cluster processes and the random connection model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02962","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a620513926f286f29e2ace76ebf687360c707eafa6c1ecd280b9ae1c98acb0c6","target":"record","created_at":"2026-05-18T01:11:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c2674b7a5a5c3d0011401ecef3e59df9156ee26e2646cd354079eea96612a970","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-07-11T14:08:09Z","title_canon_sha256":"e27f7c5d25a23837ec3ceb57852925d03b0dac01ac84458a2e1fa0f852bbb1cb"},"schema_version":"1.0","source":{"id":"1607.02962","kind":"arxiv","version":1}},"canonical_sha256":"e5bae72c863677e1acade95ee688b21d2483a646b6f6924c6f3d6f09795de4b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5bae72c863677e1acade95ee688b21d2483a646b6f6924c6f3d6f09795de4b9","first_computed_at":"2026-05-18T01:11:14.293305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:14.293305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DQ34DkdCHkMeDIHfCeqz3knxi7u5iDlyaV+Sw51Fmmbb9TEyyADvasKK4YK/Ck+V9NZmHgj89SZ5Xy0eEqDiCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:14.293825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a620513926f286f29e2ace76ebf687360c707eafa6c1ecd280b9ae1c98acb0c6","sha256:f29ac0e4c1e3b192d19d063657a0d8ea3a2fee69f0fc78a501f17e434a831a70"],"state_sha256":"170ca4ffdfa34f42d7ae5dab7f1384be8084246bcd9487a4d47baa98055d6274"}