{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CIZPI6MTYR2AXI67WQ4WFMKB4F","short_pith_number":"pith:CIZPI6MT","canonical_record":{"source":{"id":"1612.03078","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-09T16:26:02Z","cross_cats_sorted":[],"title_canon_sha256":"e81ccbfb23c5d388b74ae1ef724fb571805d6365be86713dcf37f07c3d248891","abstract_canon_sha256":"b9b17e95591bc38fe5daac42975f25529ee96cab204ee5f524bb7a7a53214637"},"schema_version":"1.0"},"canonical_sha256":"1232f47993c4740ba3dfb43962b141e15e942a68b584d016c9c0d197d0ee574a","source":{"kind":"arxiv","id":"1612.03078","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03078","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03078v2","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03078","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"pith_short_12","alias_value":"CIZPI6MTYR2A","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CIZPI6MTYR2AXI67","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CIZPI6MT","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CIZPI6MTYR2AXI67WQ4WFMKB4F","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03078","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-09T16:26:02Z","cross_cats_sorted":[],"title_canon_sha256":"e81ccbfb23c5d388b74ae1ef724fb571805d6365be86713dcf37f07c3d248891","abstract_canon_sha256":"b9b17e95591bc38fe5daac42975f25529ee96cab204ee5f524bb7a7a53214637"},"schema_version":"1.0"},"canonical_sha256":"1232f47993c4740ba3dfb43962b141e15e942a68b584d016c9c0d197d0ee574a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:23.971182Z","signature_b64":"95qBgxaxkCwzXVB55hBx86F5L/BnDB0I9I+jopBn1/D0rWRb6C7Wd2ux+ly8GVxSddgFYzXkgUYt0Iav52zVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1232f47993c4740ba3dfb43962b141e15e942a68b584d016c9c0d197d0ee574a","last_reissued_at":"2026-05-18T00:31:23.970762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:23.970762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03078","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":"2026-05-18T00:31:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9ZjvlMrUx6OyXOUCwKffVu8kbHqFumGHnXQ1zAlMWTpQqD35b1Q7a+Dagg8QYijWrJ2wXr+vKmYhhS+gCqgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:19:37.632792Z"},"content_sha256":"91dbfb877a09ab8bcd2df5b871dba7b32304a9988b5601ff7a5ccae05544fea3","schema_version":"1.0","event_id":"sha256:91dbfb877a09ab8bcd2df5b871dba7b32304a9988b5601ff7a5ccae05544fea3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CIZPI6MTYR2AXI67WQ4WFMKB4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Mecke-type formula and Markov properties for STIT tessellation processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Linh Ngoc Nguyen, Viola Weiss, Werner Nagel","submitted_at":"2016-12-09T16:26:02Z","abstract_excerpt":"An analogue of the classical Mecke formula for Poisson point processes is proved for the class of space-time STIT tessellation processes. From this key identity the Markov property of a class of associated random processes is derived. This in turn is used to determine the distribution of the number of internal vertices of the typical maximal tessellation segment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03078","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":"2026-05-18T00:31:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxLaRSR6gEDSsR4y4K2+5k/caHSZhaqIn0SQoZcSdiUg5pg3AXFtgce8TOrH5N6Q68ROGs7nigLh+aTnfLklDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T06:19:37.633139Z"},"content_sha256":"2891ffca5c6f16b458ce341f4ceca58f7d04083e63dd3d0e1a9b2d3a90c2ab0a","schema_version":"1.0","event_id":"sha256:2891ffca5c6f16b458ce341f4ceca58f7d04083e63dd3d0e1a9b2d3a90c2ab0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CIZPI6MTYR2AXI67WQ4WFMKB4F/bundle.json","state_url":"https://pith.science/pith/CIZPI6MTYR2AXI67WQ4WFMKB4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CIZPI6MTYR2AXI67WQ4WFMKB4F/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":"2026-06-03T06:19:37Z","links":{"resolver":"https://pith.science/pith/CIZPI6MTYR2AXI67WQ4WFMKB4F","bundle":"https://pith.science/pith/CIZPI6MTYR2AXI67WQ4WFMKB4F/bundle.json","state":"https://pith.science/pith/CIZPI6MTYR2AXI67WQ4WFMKB4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CIZPI6MTYR2AXI67WQ4WFMKB4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CIZPI6MTYR2AXI67WQ4WFMKB4F","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":"b9b17e95591bc38fe5daac42975f25529ee96cab204ee5f524bb7a7a53214637","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-09T16:26:02Z","title_canon_sha256":"e81ccbfb23c5d388b74ae1ef724fb571805d6365be86713dcf37f07c3d248891"},"schema_version":"1.0","source":{"id":"1612.03078","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03078","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03078v2","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03078","created_at":"2026-05-18T00:31:23Z"},{"alias_kind":"pith_short_12","alias_value":"CIZPI6MTYR2A","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CIZPI6MTYR2AXI67","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CIZPI6MT","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:2891ffca5c6f16b458ce341f4ceca58f7d04083e63dd3d0e1a9b2d3a90c2ab0a","target":"graph","created_at":"2026-05-18T00:31:23Z","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":"An analogue of the classical Mecke formula for Poisson point processes is proved for the class of space-time STIT tessellation processes. From this key identity the Markov property of a class of associated random processes is derived. This in turn is used to determine the distribution of the number of internal vertices of the typical maximal tessellation segment.","authors_text":"Christoph Thaele, Linh Ngoc Nguyen, Viola Weiss, Werner Nagel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-09T16:26:02Z","title":"A Mecke-type formula and Markov properties for STIT tessellation processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03078","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":"sha256:91dbfb877a09ab8bcd2df5b871dba7b32304a9988b5601ff7a5ccae05544fea3","target":"record","created_at":"2026-05-18T00:31:23Z","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":"b9b17e95591bc38fe5daac42975f25529ee96cab204ee5f524bb7a7a53214637","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-09T16:26:02Z","title_canon_sha256":"e81ccbfb23c5d388b74ae1ef724fb571805d6365be86713dcf37f07c3d248891"},"schema_version":"1.0","source":{"id":"1612.03078","kind":"arxiv","version":2}},"canonical_sha256":"1232f47993c4740ba3dfb43962b141e15e942a68b584d016c9c0d197d0ee574a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1232f47993c4740ba3dfb43962b141e15e942a68b584d016c9c0d197d0ee574a","first_computed_at":"2026-05-18T00:31:23.970762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:23.970762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"95qBgxaxkCwzXVB55hBx86F5L/BnDB0I9I+jopBn1/D0rWRb6C7Wd2ux+ly8GVxSddgFYzXkgUYt0Iav52zVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:23.971182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03078","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91dbfb877a09ab8bcd2df5b871dba7b32304a9988b5601ff7a5ccae05544fea3","sha256:2891ffca5c6f16b458ce341f4ceca58f7d04083e63dd3d0e1a9b2d3a90c2ab0a"],"state_sha256":"fb60084f997880f38b3897a694f895664e20ad401b2da3537be7417082b95942"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCmnKwaMrh2sBWmSLatqcWO2iuai4s8072U+VYU8lcPfku9wP6oJtwoYNBfTi0G5B0vTuxvQk28URwY9f/XAAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T06:19:37.635193Z","bundle_sha256":"ca72ed5fb298a738536520b35e08183f2dfeb8a2db9daadc69461fa1b7614885"}}