{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5DC6M6PUF5VXOTST6KRLRYBPJB","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":"9b7db59fd71c8d0b8c43f67b75bdfe86d23e1e5e6e524d7fa618264857fee8ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-03T18:07:55Z","title_canon_sha256":"470bdad2a590bb5fc5eee6c93ef6567af3f58c38c722a387b410a4d23d22b0ae"},"schema_version":"1.0","source":{"id":"1209.0423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0423","created_at":"2026-05-18T03:46:29Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0423v1","created_at":"2026-05-18T03:46:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0423","created_at":"2026-05-18T03:46:29Z"},{"alias_kind":"pith_short_12","alias_value":"5DC6M6PUF5VX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5DC6M6PUF5VXOTST","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5DC6M6PU","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:600bda86c4df40567e522ee8ab9a0a71628339ef32003e6f775ed7aa05dc568b","target":"graph","created_at":"2026-05-18T03:46:29Z","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 lower-dimensional maximal polytopes associated with an iteration stable (STIT) tessellation in $\\RR^d$ are considered. They arise in the spatio-temporal construction process of such a tessellation as intersections of $(d-1)$-dimensional maximal polytopes. A precise description of the joint distribution of their birth-times is obtained. This in turn is used to determine the probabilities that the typical or the length-weighted typical maximal segment of the tessellation contains a fixed number of internal vertices.","authors_text":"Christoph Thaele, Nguyen Ngoc Linh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-03T18:07:55Z","title":"Birth-time distributions of weighted polytopes in STIT tessellations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0423","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":"sha256:18193a70d6148703f01d609caa800bce712806f766d645496c2acb9b2b5cac2c","target":"record","created_at":"2026-05-18T03:46:29Z","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":"9b7db59fd71c8d0b8c43f67b75bdfe86d23e1e5e6e524d7fa618264857fee8ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-03T18:07:55Z","title_canon_sha256":"470bdad2a590bb5fc5eee6c93ef6567af3f58c38c722a387b410a4d23d22b0ae"},"schema_version":"1.0","source":{"id":"1209.0423","kind":"arxiv","version":1}},"canonical_sha256":"e8c5e679f42f6b774e53f2a2b8e02f4847e91e32519e59a12965596ea7cd3e9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c5e679f42f6b774e53f2a2b8e02f4847e91e32519e59a12965596ea7cd3e9e","first_computed_at":"2026-05-18T03:46:29.004215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:29.004215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Av+iVkt3XzQ65MyarGmrXSN3baIFFnnj/V/2fSe3rylUDy8ZKJH0X70NyEhLNJfRQWrFaHNQf81J4+N0KB97Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:29.005125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18193a70d6148703f01d609caa800bce712806f766d645496c2acb9b2b5cac2c","sha256:600bda86c4df40567e522ee8ab9a0a71628339ef32003e6f775ed7aa05dc568b"],"state_sha256":"a978c1f0f7446250f2f65f3df13c12a5d8cf99270fb2b54718378013aeb01a4c"}