{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5JNIQJJKRL7SFOHHDTOLL5ZK7B","short_pith_number":"pith:5JNIQJJK","canonical_record":{"source":{"id":"1204.2999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-13T14:09:16Z","cross_cats_sorted":[],"title_canon_sha256":"0defde3e618787fcb37ef6d0f17e9491a289424f814df6f7cf3721534cfbbffa","abstract_canon_sha256":"49a998f219eae70423275f86de669a512325d3345b3e39c4bdeac03406bbc5df"},"schema_version":"1.0"},"canonical_sha256":"ea5a88252a8aff22b8e71cdcb5f72af8799922dda62f64b956b0e78106c5df97","source":{"kind":"arxiv","id":"1204.2999","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2999","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2999v1","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2999","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"5JNIQJJKRL7S","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5JNIQJJKRL7SFOHH","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5JNIQJJK","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5JNIQJJKRL7SFOHHDTOLL5ZK7B","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-13T14:09:16Z","cross_cats_sorted":[],"title_canon_sha256":"0defde3e618787fcb37ef6d0f17e9491a289424f814df6f7cf3721534cfbbffa","abstract_canon_sha256":"49a998f219eae70423275f86de669a512325d3345b3e39c4bdeac03406bbc5df"},"schema_version":"1.0"},"canonical_sha256":"ea5a88252a8aff22b8e71cdcb5f72af8799922dda62f64b956b0e78106c5df97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:54.239294Z","signature_b64":"kYPrpEugKqX4d/onp/DfhSE8dGpSJxaeXGDZHbxqjzVYWZnQ4Cy0Yo8WHkV2j+TZ9HiWQupAi0VB+pJ0kDfEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea5a88252a8aff22b8e71cdcb5f72af8799922dda62f64b956b0e78106c5df97","last_reissued_at":"2026-05-18T03:57:54.238522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:54.238522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2999","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipHXcVkuq20c+1o3ML33uHtIfo2P8IghinifIWIi59PBM5abtCxkU2eRsCUOqJteE0Tgbv3yj0z8rrHrmS2fBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:47:47.123674Z"},"content_sha256":"2d907519d87a5c5494af438e0a609e7173fd3f2256fe161103cedc61c63a8130","schema_version":"1.0","event_id":"sha256:2d907519d87a5c5494af438e0a609e7173fd3f2256fe161103cedc61c63a8130"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5JNIQJJKRL7SFOHHDTOLL5ZK7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Poisson Rain Tessellation Under Spatial Expansion and Temporal Transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eike Biehler","submitted_at":"2012-04-13T14:09:16Z","abstract_excerpt":"For cell-division processes in a window, Cowan introduced four selection rules and two division rules each of which stands for one cell-division model. One of these is the area-weighted in-cell model. In this model, each cell is selected for division with a probability that corresponds to the ratio between its area and the area of the whole window. This selected cell is then divided by throwing a (uniformly distributed) point into the cell and drawing a line segment through the point under a random angle with the segment ending at the cell's boundary. For the STIT model which uses both a diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2999","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CqcxN7vY1ztBXPKuPsqJxdIMeGYxM/wms7weZIPdeX8aRS8oKfrydRWL9Hvwqg+b4ByMZCaAuRCnUrMVoHTRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:47:47.124022Z"},"content_sha256":"2c013900f15226aa8864f2296e366083693ac2cf0737c8829ca996a510e4465a","schema_version":"1.0","event_id":"sha256:2c013900f15226aa8864f2296e366083693ac2cf0737c8829ca996a510e4465a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JNIQJJKRL7SFOHHDTOLL5ZK7B/bundle.json","state_url":"https://pith.science/pith/5JNIQJJKRL7SFOHHDTOLL5ZK7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JNIQJJKRL7SFOHHDTOLL5ZK7B/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":"2026-06-25T18:47:47Z","links":{"resolver":"https://pith.science/pith/5JNIQJJKRL7SFOHHDTOLL5ZK7B","bundle":"https://pith.science/pith/5JNIQJJKRL7SFOHHDTOLL5ZK7B/bundle.json","state":"https://pith.science/pith/5JNIQJJKRL7SFOHHDTOLL5ZK7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JNIQJJKRL7SFOHHDTOLL5ZK7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5JNIQJJKRL7SFOHHDTOLL5ZK7B","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":"49a998f219eae70423275f86de669a512325d3345b3e39c4bdeac03406bbc5df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-13T14:09:16Z","title_canon_sha256":"0defde3e618787fcb37ef6d0f17e9491a289424f814df6f7cf3721534cfbbffa"},"schema_version":"1.0","source":{"id":"1204.2999","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2999","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2999v1","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2999","created_at":"2026-05-18T03:57:54Z"},{"alias_kind":"pith_short_12","alias_value":"5JNIQJJKRL7S","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5JNIQJJKRL7SFOHH","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5JNIQJJK","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:2c013900f15226aa8864f2296e366083693ac2cf0737c8829ca996a510e4465a","target":"graph","created_at":"2026-05-18T03:57:54Z","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":"For cell-division processes in a window, Cowan introduced four selection rules and two division rules each of which stands for one cell-division model. One of these is the area-weighted in-cell model. In this model, each cell is selected for division with a probability that corresponds to the ratio between its area and the area of the whole window. This selected cell is then divided by throwing a (uniformly distributed) point into the cell and drawing a line segment through the point under a random angle with the segment ending at the cell's boundary. For the STIT model which uses both a diffe","authors_text":"Eike Biehler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-13T14:09:16Z","title":"The Poisson Rain Tessellation Under Spatial Expansion and Temporal Transformation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2999","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":"sha256:2d907519d87a5c5494af438e0a609e7173fd3f2256fe161103cedc61c63a8130","target":"record","created_at":"2026-05-18T03:57:54Z","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":"49a998f219eae70423275f86de669a512325d3345b3e39c4bdeac03406bbc5df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-13T14:09:16Z","title_canon_sha256":"0defde3e618787fcb37ef6d0f17e9491a289424f814df6f7cf3721534cfbbffa"},"schema_version":"1.0","source":{"id":"1204.2999","kind":"arxiv","version":1}},"canonical_sha256":"ea5a88252a8aff22b8e71cdcb5f72af8799922dda62f64b956b0e78106c5df97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea5a88252a8aff22b8e71cdcb5f72af8799922dda62f64b956b0e78106c5df97","first_computed_at":"2026-05-18T03:57:54.238522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:54.238522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kYPrpEugKqX4d/onp/DfhSE8dGpSJxaeXGDZHbxqjzVYWZnQ4Cy0Yo8WHkV2j+TZ9HiWQupAi0VB+pJ0kDfEAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:54.239294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2999","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d907519d87a5c5494af438e0a609e7173fd3f2256fe161103cedc61c63a8130","sha256:2c013900f15226aa8864f2296e366083693ac2cf0737c8829ca996a510e4465a"],"state_sha256":"d97ed206a8bc7106b1126b744fc5645f0694eeb7b8a1fe5023eff3702f0b2dba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+WluIr9ic6ZvBClIGSC+mQASY7UJvaZ0uaLyLoDPqXlmTiR4e0pUEJMQ8mrh2wuham0Aqj001vEt2EtmbogmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:47:47.126106Z","bundle_sha256":"721d6b58cf9caeeda6849afa017f836a76fde3a37b7dd7f2209fc3b535378639"}}