{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IGXZUUUAEWHJVYA2A46OVTKKXP","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":"43581ed1132205f490d279c96f1f694f5e8c3f763c856d3b88932c414c3ef886","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-02T13:28:49Z","title_canon_sha256":"dceb7b9ffc6a40d101e097d792166ebbdf3d8cfb072f89a707a2ec57734d7fc9"},"schema_version":"1.0","source":{"id":"1111.0488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0488","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0488v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0488","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"IGXZUUUAEWHJ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IGXZUUUAEWHJVYA2","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IGXZUUUA","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:af15e465a6add57fc83417f7d23c1e0cc6897216f10bc0fbde96abf1d579151c","target":"graph","created_at":"2026-05-18T03:12:58Z","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":"Spatially homogeneous random tessellations that are stable under iteration (nesting) in the 3-dimensional Euclidean space are considered, so-called STIT tessellations. They arise as outcome of a spatio-temporal process of subsequent cell division and consequently they are not facet-to-facet. The intent of this paper is to develop a detailed analysis of the combinatorial structure of such tessellations and to determine a number of new geometric mean values, for example for the neighborhood of the typical vertex. The heart of the results is a fine classification of tessellation edges based on th","authors_text":"Christoph Thaele, Viola Weiss","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-02T13:28:49Z","title":"The combinatorial structure of spatial STIT tessellations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0488","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":"sha256:372d089c21e9a3ccfe33edf9cc8748337fd753e13a0280fcdd89a75d21411433","target":"record","created_at":"2026-05-18T03:12:58Z","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":"43581ed1132205f490d279c96f1f694f5e8c3f763c856d3b88932c414c3ef886","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-02T13:28:49Z","title_canon_sha256":"dceb7b9ffc6a40d101e097d792166ebbdf3d8cfb072f89a707a2ec57734d7fc9"},"schema_version":"1.0","source":{"id":"1111.0488","kind":"arxiv","version":1}},"canonical_sha256":"41af9a5280258e9ae01a073ceacd4abbc2ab782eca50d9e94540ad65c5ab7ae3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41af9a5280258e9ae01a073ceacd4abbc2ab782eca50d9e94540ad65c5ab7ae3","first_computed_at":"2026-05-18T03:12:58.120094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:58.120094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9RuC2EjU8RTk0ewLeJf/IaShwNZWP385aZvtZQUMMD4ykPhsH1E3D8LvsR0jv6jOkm2utI0xehJ7eKPQI8k6Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:58.120831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:372d089c21e9a3ccfe33edf9cc8748337fd753e13a0280fcdd89a75d21411433","sha256:af15e465a6add57fc83417f7d23c1e0cc6897216f10bc0fbde96abf1d579151c"],"state_sha256":"9a4d716461fd19438e449c8cd5afdf533e7f8c27f7778e07eafd36b52751ba15"}