{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7Q7G5D32QTRFWQQVGEXFH7AAQG","short_pith_number":"pith:7Q7G5D32","canonical_record":{"source":{"id":"1204.2755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-12T15:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"e2713806fba8c9933513372fa2ece940f5262c255d9ad1d8bf96e4f1786f615c","abstract_canon_sha256":"3c298f33fef55f68e3197fff2190c1a63bc6e2776c18f1a2e962337c2deacd55"},"schema_version":"1.0"},"canonical_sha256":"fc3e6e8f7a84e25b4215312e53fc0081adf2b5bb88566fe3876290d22706e79b","source":{"kind":"arxiv","id":"1204.2755","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2755","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2755v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2755","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"7Q7G5D32QTRF","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7Q7G5D32QTRFWQQV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7Q7G5D32","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7Q7G5D32QTRFWQQVGEXFH7AAQG","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-12T15:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"e2713806fba8c9933513372fa2ece940f5262c255d9ad1d8bf96e4f1786f615c","abstract_canon_sha256":"3c298f33fef55f68e3197fff2190c1a63bc6e2776c18f1a2e962337c2deacd55"},"schema_version":"1.0"},"canonical_sha256":"fc3e6e8f7a84e25b4215312e53fc0081adf2b5bb88566fe3876290d22706e79b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:03.622076Z","signature_b64":"+5j0lGjrUDdsZ41XQMp8aLnz4zybpcj6O9xgaLDwspv/70NVYgsNYnPFteaXvBPYWBEG2K5HLYVeOf3115m+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc3e6e8f7a84e25b4215312e53fc0081adf2b5bb88566fe3876290d22706e79b","last_reissued_at":"2026-05-18T03:58:03.621654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:03.621654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2755","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":"2026-05-18T03:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xBKl/5uBENk5HUeoB0j2QCCYrW7yyqKdpEKPCzayV/4Xuk8E9VDC8nznlMZaHSg7gCpMtcRTIOI+rPGlaRYwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:32:20.403125Z"},"content_sha256":"19d4ec089fbff9ee4ce4102132b816bc42f1445b69f602df335cbca7ee776def","schema_version":"1.0","event_id":"sha256:19d4ec089fbff9ee4ce4102132b816bc42f1445b69f602df335cbca7ee776def"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7Q7G5D32QTRFWQQVGEXFH7AAQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit theorems for continuous time branching flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hui He, Rugang Ma","submitted_at":"2012-04-12T15:22:50Z","abstract_excerpt":"We construct a flow of continuous time and discrete state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses over the positive half line studied in Li (2012)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2755","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":"2026-05-18T03:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OvoN8vfHCVBOVNRyoTBV+GicVf71Kt2Bzm3ojl8Hb37OFeCQW2ZW3LFI3HOo9kId8AshQ+oPTM2xcmLLn4SQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:32:20.403472Z"},"content_sha256":"4094278e1fe033d251e68dc12f8abcc8708fd845c8882026115d4e3e8efd57ad","schema_version":"1.0","event_id":"sha256:4094278e1fe033d251e68dc12f8abcc8708fd845c8882026115d4e3e8efd57ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Q7G5D32QTRFWQQVGEXFH7AAQG/bundle.json","state_url":"https://pith.science/pith/7Q7G5D32QTRFWQQVGEXFH7AAQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Q7G5D32QTRFWQQVGEXFH7AAQG/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":"2026-06-24T19:32:20Z","links":{"resolver":"https://pith.science/pith/7Q7G5D32QTRFWQQVGEXFH7AAQG","bundle":"https://pith.science/pith/7Q7G5D32QTRFWQQVGEXFH7AAQG/bundle.json","state":"https://pith.science/pith/7Q7G5D32QTRFWQQVGEXFH7AAQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Q7G5D32QTRFWQQVGEXFH7AAQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7Q7G5D32QTRFWQQVGEXFH7AAQG","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":"3c298f33fef55f68e3197fff2190c1a63bc6e2776c18f1a2e962337c2deacd55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-12T15:22:50Z","title_canon_sha256":"e2713806fba8c9933513372fa2ece940f5262c255d9ad1d8bf96e4f1786f615c"},"schema_version":"1.0","source":{"id":"1204.2755","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2755","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2755v1","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2755","created_at":"2026-05-18T03:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"7Q7G5D32QTRF","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7Q7G5D32QTRFWQQV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7Q7G5D32","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:4094278e1fe033d251e68dc12f8abcc8708fd845c8882026115d4e3e8efd57ad","target":"graph","created_at":"2026-05-18T03:58:03Z","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 flow of continuous time and discrete state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses over the positive half line studied in Li (2012).","authors_text":"Hui He, Rugang Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-12T15:22:50Z","title":"Limit theorems for continuous time branching flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2755","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":"sha256:19d4ec089fbff9ee4ce4102132b816bc42f1445b69f602df335cbca7ee776def","target":"record","created_at":"2026-05-18T03:58:03Z","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":"3c298f33fef55f68e3197fff2190c1a63bc6e2776c18f1a2e962337c2deacd55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-12T15:22:50Z","title_canon_sha256":"e2713806fba8c9933513372fa2ece940f5262c255d9ad1d8bf96e4f1786f615c"},"schema_version":"1.0","source":{"id":"1204.2755","kind":"arxiv","version":1}},"canonical_sha256":"fc3e6e8f7a84e25b4215312e53fc0081adf2b5bb88566fe3876290d22706e79b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc3e6e8f7a84e25b4215312e53fc0081adf2b5bb88566fe3876290d22706e79b","first_computed_at":"2026-05-18T03:58:03.621654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:03.621654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+5j0lGjrUDdsZ41XQMp8aLnz4zybpcj6O9xgaLDwspv/70NVYgsNYnPFteaXvBPYWBEG2K5HLYVeOf3115m+Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:03.622076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2755","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19d4ec089fbff9ee4ce4102132b816bc42f1445b69f602df335cbca7ee776def","sha256:4094278e1fe033d251e68dc12f8abcc8708fd845c8882026115d4e3e8efd57ad"],"state_sha256":"194595ef60765c45180e4ea7b5a0a0ee8ba51b4d743856eed680d07c151987ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MGYSbDwyJL45dTdfVKULarQ4nSF6wtyGLr9/YZ4VPywxuyut+IiWCuWiRr7ELX1/lM6dbFJldJGs36RN3X8gDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:32:20.405344Z","bundle_sha256":"29666ea990af09570b36bc2bf0f3c6fb37d41187c0b4961e1e2a9837f671a720"}}