{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PBDNONUF4FKRQKVUC3SD32DW6J","short_pith_number":"pith:PBDNONUF","canonical_record":{"source":{"id":"1004.2013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-12T17:47:45Z","cross_cats_sorted":[],"title_canon_sha256":"b87b6b0711799d1af8bbdb5248579aa56ac0e4b4451f8f9a1331ea081e780570","abstract_canon_sha256":"2cefc20f76519fd5c770bb75c5fab4dc6cd5eea8f8a247d1788697b3ee2dc2e4"},"schema_version":"1.0"},"canonical_sha256":"7846d73685e155182ab416e43de876f26aff2977d123d18a6948d38bd01fbdef","source":{"kind":"arxiv","id":"1004.2013","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2013","created_at":"2026-05-18T04:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2013v2","created_at":"2026-05-18T04:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2013","created_at":"2026-05-18T04:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"PBDNONUF4FKR","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PBDNONUF4FKRQKVU","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PBDNONUF","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PBDNONUF4FKRQKVUC3SD32DW6J","target":"record","payload":{"canonical_record":{"source":{"id":"1004.2013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-12T17:47:45Z","cross_cats_sorted":[],"title_canon_sha256":"b87b6b0711799d1af8bbdb5248579aa56ac0e4b4451f8f9a1331ea081e780570","abstract_canon_sha256":"2cefc20f76519fd5c770bb75c5fab4dc6cd5eea8f8a247d1788697b3ee2dc2e4"},"schema_version":"1.0"},"canonical_sha256":"7846d73685e155182ab416e43de876f26aff2977d123d18a6948d38bd01fbdef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:11.388924Z","signature_b64":"qh0tCeSkMjb6qcvlZXuV8DvLeUfHq61jEzAwgfBFMzTk4mdwXFVliiU7ppVY9tabzBvTBsuSD40YMPIKNO7LAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7846d73685e155182ab416e43de876f26aff2977d123d18a6948d38bd01fbdef","last_reissued_at":"2026-05-18T04:25:11.388423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:11.388423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.2013","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"grXhROJXcz2uZW+V6+AXk1HYDktpYcpr53TFaRcaljlT1QI3dV2jVcSXv7I1D+p67mU+djyr90Kqqc5+m9aEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:52:24.479551Z"},"content_sha256":"29757d63fcdd3380d5f5fcc469356df41893155adf72af1b70ff29634901156f","schema_version":"1.0","event_id":"sha256:29757d63fcdd3380d5f5fcc469356df41893155adf72af1b70ff29634901156f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PBDNONUF4FKRQKVUC3SD32DW6J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second-Order Properties and Central Limit Theory for the Vertex Process of Iteration Infinitely Divisible and Iteration Stable Random Tessellations in the Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Tomasz Schreiber","submitted_at":"2010-04-12T17:47:45Z","abstract_excerpt":"The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation function as well as the cross-covariance measure and the cross-pair-correlation function of the vertex point process and the random length measure in general non-stationary regime, and we specialize it to the stationary and isotropic setting. Exact formulas are given for vertex count variances in compact and convex sampling windows and asymptotic relations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2013","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTVwM6V+vRFOvfs5J+AWDoZF1vPwHkjBD+BCOD/k5d+KWZKMy2qnxpOrBA6uB4x7Il/jQdKbFbrGQiDYbAUhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:52:24.479914Z"},"content_sha256":"cfc8c3a99256a6132bcbacdf4d71cdc5baed00a0e24fab0a96bceb282bdfe424","schema_version":"1.0","event_id":"sha256:cfc8c3a99256a6132bcbacdf4d71cdc5baed00a0e24fab0a96bceb282bdfe424"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBDNONUF4FKRQKVUC3SD32DW6J/bundle.json","state_url":"https://pith.science/pith/PBDNONUF4FKRQKVUC3SD32DW6J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBDNONUF4FKRQKVUC3SD32DW6J/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T04:52:24Z","links":{"resolver":"https://pith.science/pith/PBDNONUF4FKRQKVUC3SD32DW6J","bundle":"https://pith.science/pith/PBDNONUF4FKRQKVUC3SD32DW6J/bundle.json","state":"https://pith.science/pith/PBDNONUF4FKRQKVUC3SD32DW6J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBDNONUF4FKRQKVUC3SD32DW6J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PBDNONUF4FKRQKVUC3SD32DW6J","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":"2cefc20f76519fd5c770bb75c5fab4dc6cd5eea8f8a247d1788697b3ee2dc2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-12T17:47:45Z","title_canon_sha256":"b87b6b0711799d1af8bbdb5248579aa56ac0e4b4451f8f9a1331ea081e780570"},"schema_version":"1.0","source":{"id":"1004.2013","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2013","created_at":"2026-05-18T04:25:11Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2013v2","created_at":"2026-05-18T04:25:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2013","created_at":"2026-05-18T04:25:11Z"},{"alias_kind":"pith_short_12","alias_value":"PBDNONUF4FKR","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PBDNONUF4FKRQKVU","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PBDNONUF","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:cfc8c3a99256a6132bcbacdf4d71cdc5baed00a0e24fab0a96bceb282bdfe424","target":"graph","created_at":"2026-05-18T04:25:11Z","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":"The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation function as well as the cross-covariance measure and the cross-pair-correlation function of the vertex point process and the random length measure in general non-stationary regime, and we specialize it to the stationary and isotropic setting. Exact formulas are given for vertex count variances in compact and convex sampling windows and asymptotic relations ","authors_text":"Christoph Thaele, Tomasz Schreiber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-12T17:47:45Z","title":"Second-Order Properties and Central Limit Theory for the Vertex Process of Iteration Infinitely Divisible and Iteration Stable Random Tessellations in the Plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2013","kind":"arxiv","version":2},"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":"sha256:29757d63fcdd3380d5f5fcc469356df41893155adf72af1b70ff29634901156f","target":"record","created_at":"2026-05-18T04:25:11Z","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":"2cefc20f76519fd5c770bb75c5fab4dc6cd5eea8f8a247d1788697b3ee2dc2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-12T17:47:45Z","title_canon_sha256":"b87b6b0711799d1af8bbdb5248579aa56ac0e4b4451f8f9a1331ea081e780570"},"schema_version":"1.0","source":{"id":"1004.2013","kind":"arxiv","version":2}},"canonical_sha256":"7846d73685e155182ab416e43de876f26aff2977d123d18a6948d38bd01fbdef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7846d73685e155182ab416e43de876f26aff2977d123d18a6948d38bd01fbdef","first_computed_at":"2026-05-18T04:25:11.388423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:11.388423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qh0tCeSkMjb6qcvlZXuV8DvLeUfHq61jEzAwgfBFMzTk4mdwXFVliiU7ppVY9tabzBvTBsuSD40YMPIKNO7LAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:11.388924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2013","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29757d63fcdd3380d5f5fcc469356df41893155adf72af1b70ff29634901156f","sha256:cfc8c3a99256a6132bcbacdf4d71cdc5baed00a0e24fab0a96bceb282bdfe424"],"state_sha256":"2d50425ec3fa2cb69b94e017d8928f64b76fe771f329c26fb379a6f76126911a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"prfKdi1GOlr8fC1xqs+v2fN22ZLKHRfyzJJ7LRxP+MEg5Bkfo2HM8OHEYBSjgF5kLqMvQS7ZLy0hnz2IYT4pBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:52:24.481940Z","bundle_sha256":"9c7b403787ad563c5472a396353d064cce8e00e1ce873ce4421789796d191b84"}}