{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:W6RM4OW7JWWC7DOQPNQYHIP26V","short_pith_number":"pith:W6RM4OW7","schema_version":"1.0","canonical_sha256":"b7a2ce3adf4dac2f8dd07b6183a1faf564df062c9390e7dd883239b0105bf9ce","source":{"kind":"arxiv","id":"1101.5973","version":1},"attestation_state":"computed","paper":{"title":"Shape-Driven Nested Markov Tessellations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Tomasz Schreiber","submitted_at":"2011-01-31T14:03:15Z","abstract_excerpt":"A new and rather broad class of stationary (i.e. stochastically translation invariant) random tessellations of the $d$-dimensional Euclidean space is introduced, which are called shape-driven nested Markov tessellations. Locally, these tessellations are constructed by means of a spatio-temporal random recursive split dynamics governed by a family of Markovian split kernel, generalizing thereby the -- by now classical -- construction of iteration stable random tessellations. By providing an explicit global construction of the tessellations, it is shown that under suitable assumptions on the spl"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.5973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-31T14:03:15Z","cross_cats_sorted":[],"title_canon_sha256":"632c365eecfee3c4ad550bfc284ab02045490194d6ecc477b667c704bc2d799b","abstract_canon_sha256":"a41a86ba2d99b60726369f5d3820806a2cc12ad93ec844ac5737cd26d6722aa8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:32.299798Z","signature_b64":"E6p3KBPgHIK3/UBeQbFFdru/O4C6bDrzMNE8k2IEGbPvPR9b09FoG5ZTyX7DyWhFlkIGFj5o9GmUQmLwNGHRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7a2ce3adf4dac2f8dd07b6183a1faf564df062c9390e7dd883239b0105bf9ce","last_reissued_at":"2026-05-18T03:13:32.299121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:32.299121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shape-Driven Nested Markov Tessellations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Tomasz Schreiber","submitted_at":"2011-01-31T14:03:15Z","abstract_excerpt":"A new and rather broad class of stationary (i.e. stochastically translation invariant) random tessellations of the $d$-dimensional Euclidean space is introduced, which are called shape-driven nested Markov tessellations. Locally, these tessellations are constructed by means of a spatio-temporal random recursive split dynamics governed by a family of Markovian split kernel, generalizing thereby the -- by now classical -- construction of iteration stable random tessellations. By providing an explicit global construction of the tessellations, it is shown that under suitable assumptions on the spl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5973","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.5973","created_at":"2026-05-18T03:13:32.299209+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.5973v1","created_at":"2026-05-18T03:13:32.299209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5973","created_at":"2026-05-18T03:13:32.299209+00:00"},{"alias_kind":"pith_short_12","alias_value":"W6RM4OW7JWWC","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"W6RM4OW7JWWC7DOQ","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"W6RM4OW7","created_at":"2026-05-18T12:26:44.992195+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V","json":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V.json","graph_json":"https://pith.science/api/pith-number/W6RM4OW7JWWC7DOQPNQYHIP26V/graph.json","events_json":"https://pith.science/api/pith-number/W6RM4OW7JWWC7DOQPNQYHIP26V/events.json","paper":"https://pith.science/paper/W6RM4OW7"},"agent_actions":{"view_html":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V","download_json":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V.json","view_paper":"https://pith.science/paper/W6RM4OW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.5973&json=true","fetch_graph":"https://pith.science/api/pith-number/W6RM4OW7JWWC7DOQPNQYHIP26V/graph.json","fetch_events":"https://pith.science/api/pith-number/W6RM4OW7JWWC7DOQPNQYHIP26V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V/action/storage_attestation","attest_author":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V/action/author_attestation","sign_citation":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V/action/citation_signature","submit_replication":"https://pith.science/pith/W6RM4OW7JWWC7DOQPNQYHIP26V/action/replication_record"}},"created_at":"2026-05-18T03:13:32.299209+00:00","updated_at":"2026-05-18T03:13:32.299209+00:00"}