{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:SZFVJNMAKGZPJXA2P3GSIJ7C5Y","short_pith_number":"pith:SZFVJNMA","canonical_record":{"source":{"id":"math/0606615","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-06-24T11:49:59Z","cross_cats_sorted":[],"title_canon_sha256":"528f2aa43cfd782cc56cab1dc844f1d4d8663ae66ec47a51dd909f53e276e2d0","abstract_canon_sha256":"cea0cef0b3b1d573333de4ec3bf907892bc28d9a0450d3ea0337bf34b32ba967"},"schema_version":"1.0"},"canonical_sha256":"964b54b58051b2f4dc1a7ecd2427e2ee2f5204ffbec8f5785a8eaaaf4f5ad285","source":{"kind":"arxiv","id":"math/0606615","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606615","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606615v1","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606615","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"SZFVJNMAKGZP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"SZFVJNMAKGZPJXA2","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"SZFVJNMA","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:SZFVJNMAKGZPJXA2P3GSIJ7C5Y","target":"record","payload":{"canonical_record":{"source":{"id":"math/0606615","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-06-24T11:49:59Z","cross_cats_sorted":[],"title_canon_sha256":"528f2aa43cfd782cc56cab1dc844f1d4d8663ae66ec47a51dd909f53e276e2d0","abstract_canon_sha256":"cea0cef0b3b1d573333de4ec3bf907892bc28d9a0450d3ea0337bf34b32ba967"},"schema_version":"1.0"},"canonical_sha256":"964b54b58051b2f4dc1a7ecd2427e2ee2f5204ffbec8f5785a8eaaaf4f5ad285","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:28.094007Z","signature_b64":"PSyKWSe9dIZCWOhFtsSif/XlniNllR138VOrCDMwR6QXkGXagiA0ywn5xXh7Y6bglJKz+HAkM2sAPClg3ZDYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"964b54b58051b2f4dc1a7ecd2427e2ee2f5204ffbec8f5785a8eaaaf4f5ad285","last_reissued_at":"2026-05-18T04:28:28.093519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:28.093519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0606615","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":"2026-05-18T04:28:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RosciNVqtzQaFKfq+LmYC8OhKl7Ued/3sYQ/T0mKJclln0HUWHDZ7D4sXVshR8fcHD7p4uhgEnKbLKTPdPpqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:28:39.154825Z"},"content_sha256":"3be641c2953e9bcf61037daeccf5d4bf74a0fdb989ae17a1c13b05cf4263ac96","schema_version":"1.0","event_id":"sha256:3be641c2953e9bcf61037daeccf5d4bf74a0fdb989ae17a1c13b05cf4263ac96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:SZFVJNMAKGZPJXA2P3GSIJ7C5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Superprocesses with Dependent Spatial Motion and General Branching Densities","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Donald A. Dawson, Hao Wang, Zenghu Li","submitted_at":"2006-06-24T11:49:59Z","abstract_excerpt":"We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitrary bounded non-negative Borel function, and the superprocess is characterized by a martingale problem as a diffusion process with state space $M(\\IR)$, improving and extending considerably the construction of Wang (1997, 1998). It is then proved in a special case that a suitable rescaled process of the superprocess converges to the u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606615","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":"2026-05-18T04:28:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XqvjH7TrQCOpvP7lv7jxdnNvS1ItPkHido8R7cuWve8O3b38a4FuxRKT6WlrdNAUZSarF/k814yRYDAWsLzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:28:39.155177Z"},"content_sha256":"0f00a7a8149adad2dd2c834fe24166009a87ffdd39fd312b4da4ced355a2b40a","schema_version":"1.0","event_id":"sha256:0f00a7a8149adad2dd2c834fe24166009a87ffdd39fd312b4da4ced355a2b40a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SZFVJNMAKGZPJXA2P3GSIJ7C5Y/bundle.json","state_url":"https://pith.science/pith/SZFVJNMAKGZPJXA2P3GSIJ7C5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SZFVJNMAKGZPJXA2P3GSIJ7C5Y/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":"2026-05-28T06:28:39Z","links":{"resolver":"https://pith.science/pith/SZFVJNMAKGZPJXA2P3GSIJ7C5Y","bundle":"https://pith.science/pith/SZFVJNMAKGZPJXA2P3GSIJ7C5Y/bundle.json","state":"https://pith.science/pith/SZFVJNMAKGZPJXA2P3GSIJ7C5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SZFVJNMAKGZPJXA2P3GSIJ7C5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:SZFVJNMAKGZPJXA2P3GSIJ7C5Y","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":"cea0cef0b3b1d573333de4ec3bf907892bc28d9a0450d3ea0337bf34b32ba967","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-06-24T11:49:59Z","title_canon_sha256":"528f2aa43cfd782cc56cab1dc844f1d4d8663ae66ec47a51dd909f53e276e2d0"},"schema_version":"1.0","source":{"id":"math/0606615","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606615","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606615v1","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606615","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"SZFVJNMAKGZP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"SZFVJNMAKGZPJXA2","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"SZFVJNMA","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:0f00a7a8149adad2dd2c834fe24166009a87ffdd39fd312b4da4ced355a2b40a","target":"graph","created_at":"2026-05-18T04:28:28Z","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":"We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitrary bounded non-negative Borel function, and the superprocess is characterized by a martingale problem as a diffusion process with state space $M(\\IR)$, improving and extending considerably the construction of Wang (1997, 1998). It is then proved in a special case that a suitable rescaled process of the superprocess converges to the u","authors_text":"Donald A. Dawson, Hao Wang, Zenghu Li","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-06-24T11:49:59Z","title":"Superprocesses with Dependent Spatial Motion and General Branching Densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606615","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":"sha256:3be641c2953e9bcf61037daeccf5d4bf74a0fdb989ae17a1c13b05cf4263ac96","target":"record","created_at":"2026-05-18T04:28:28Z","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":"cea0cef0b3b1d573333de4ec3bf907892bc28d9a0450d3ea0337bf34b32ba967","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-06-24T11:49:59Z","title_canon_sha256":"528f2aa43cfd782cc56cab1dc844f1d4d8663ae66ec47a51dd909f53e276e2d0"},"schema_version":"1.0","source":{"id":"math/0606615","kind":"arxiv","version":1}},"canonical_sha256":"964b54b58051b2f4dc1a7ecd2427e2ee2f5204ffbec8f5785a8eaaaf4f5ad285","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"964b54b58051b2f4dc1a7ecd2427e2ee2f5204ffbec8f5785a8eaaaf4f5ad285","first_computed_at":"2026-05-18T04:28:28.093519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:28.093519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PSyKWSe9dIZCWOhFtsSif/XlniNllR138VOrCDMwR6QXkGXagiA0ywn5xXh7Y6bglJKz+HAkM2sAPClg3ZDYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:28.094007Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606615","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3be641c2953e9bcf61037daeccf5d4bf74a0fdb989ae17a1c13b05cf4263ac96","sha256:0f00a7a8149adad2dd2c834fe24166009a87ffdd39fd312b4da4ced355a2b40a"],"state_sha256":"7ebe3cf3a07160cf2117fac9121b0425684366d060dcb25d95fac4c7cd71aa0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vn7nqEN+Z5Qt9M0qdJLWdotZstRjXwSHHbNfiRKmuvVDbfhMUWu61FA6QkzMT0v7IRzJCYurLe40/U0y2eR1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:28:39.157563Z","bundle_sha256":"5b4722516e4f3d99a38d70a6edefa5130fa597918f79f7ba4df4ea59f9b2e125"}}