{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ALK2DUFDOUUSCXY4JCXUU6IDXD","short_pith_number":"pith:ALK2DUFD","canonical_record":{"source":{"id":"1310.5410","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T03:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"772eb573a54e1266a1869aad92331c7e45ffac486049c1ae32f652db1490eb48","abstract_canon_sha256":"19598d629ce616b180c37850a409a09d781520e45b50aaf6719464b2ba56cb54"},"schema_version":"1.0"},"canonical_sha256":"02d5a1d0a37529215f1c48af4a7903b8fde4670ef51f4be55ae36094491a92c5","source":{"kind":"arxiv","id":"1310.5410","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5410","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5410v2","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5410","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"ALK2DUFDOUUS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ALK2DUFDOUUSCXY4","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ALK2DUFD","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ALK2DUFDOUUSCXY4JCXUU6IDXD","target":"record","payload":{"canonical_record":{"source":{"id":"1310.5410","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T03:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"772eb573a54e1266a1869aad92331c7e45ffac486049c1ae32f652db1490eb48","abstract_canon_sha256":"19598d629ce616b180c37850a409a09d781520e45b50aaf6719464b2ba56cb54"},"schema_version":"1.0"},"canonical_sha256":"02d5a1d0a37529215f1c48af4a7903b8fde4670ef51f4be55ae36094491a92c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:28.676990Z","signature_b64":"ptieCyGKkHCxN06KgFN4Y15yd1WlcosXT4Lpr6ccOLqf82wDB0K6RpK8kMX+squ3Mg1zBegXUz0weBQKCMH5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02d5a1d0a37529215f1c48af4a7903b8fde4670ef51f4be55ae36094491a92c5","last_reissued_at":"2026-05-18T02:42:28.675918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:28.675918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.5410","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"37sAi3hITriSw1Wzck12ZgBsWSB4Hd5VG+6DS6rcRWVXG2PLaCBY6t9HF9/26c4qchexH8ohop5z6Dr02k4MDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:23:26.773646Z"},"content_sha256":"109b4c66228becc7806f3cd61b63c59ba2ae8206a471d8dea60a90a9c49a4f64","schema_version":"1.0","event_id":"sha256:109b4c66228becc7806f3cd61b63c59ba2ae8206a471d8dea60a90a9c49a4f64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ALK2DUFDOUUSCXY4JCXUU6IDXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central Limit Theorems for Supercritical Superprocesses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Renming Song, Rui Zhang, Yan-Xia Ren","submitted_at":"2013-10-21T03:29:42Z","abstract_excerpt":"In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and unifies all the central limit theorems obtained recently in Mi{\\l}o\\'{s} (2012, arXiv:1203:6661) and Ren, Song and Zhang (2013, to appear in Acta Appl. Math., DOI 10.1007/s10440-013-9837-0) for supercritical super Ornstein-Uhlenbeck processes. The advantage of this central limit theorem is that it allows us to characterize the limit Gaussian field. In the case "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5410","kind":"arxiv","version":2},"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":"2026-05-18T02:42:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YN+BbiDSzhkHORaND6IGkyJH0dwGff7jX7zNidR4qoyHc4VvD/NTWGh32b501GGT2lA3ClWuUyQay+hH3kvjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:23:26.774292Z"},"content_sha256":"260eb6625cb1f606c83dd9c16d5d6eed0af6e38db3d4631e506777ed3dc28bae","schema_version":"1.0","event_id":"sha256:260eb6625cb1f606c83dd9c16d5d6eed0af6e38db3d4631e506777ed3dc28bae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ALK2DUFDOUUSCXY4JCXUU6IDXD/bundle.json","state_url":"https://pith.science/pith/ALK2DUFDOUUSCXY4JCXUU6IDXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ALK2DUFDOUUSCXY4JCXUU6IDXD/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":"2026-06-09T04:23:26Z","links":{"resolver":"https://pith.science/pith/ALK2DUFDOUUSCXY4JCXUU6IDXD","bundle":"https://pith.science/pith/ALK2DUFDOUUSCXY4JCXUU6IDXD/bundle.json","state":"https://pith.science/pith/ALK2DUFDOUUSCXY4JCXUU6IDXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ALK2DUFDOUUSCXY4JCXUU6IDXD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ALK2DUFDOUUSCXY4JCXUU6IDXD","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":"19598d629ce616b180c37850a409a09d781520e45b50aaf6719464b2ba56cb54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T03:29:42Z","title_canon_sha256":"772eb573a54e1266a1869aad92331c7e45ffac486049c1ae32f652db1490eb48"},"schema_version":"1.0","source":{"id":"1310.5410","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5410","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5410v2","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5410","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"ALK2DUFDOUUS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ALK2DUFDOUUSCXY4","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ALK2DUFD","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:260eb6625cb1f606c83dd9c16d5d6eed0af6e38db3d4631e506777ed3dc28bae","target":"graph","created_at":"2026-05-18T02:42:28Z","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":"In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem generalizes and unifies all the central limit theorems obtained recently in Mi{\\l}o\\'{s} (2012, arXiv:1203:6661) and Ren, Song and Zhang (2013, to appear in Acta Appl. Math., DOI 10.1007/s10440-013-9837-0) for supercritical super Ornstein-Uhlenbeck processes. The advantage of this central limit theorem is that it allows us to characterize the limit Gaussian field. In the case ","authors_text":"Renming Song, Rui Zhang, Yan-Xia Ren","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T03:29:42Z","title":"Central Limit Theorems for Supercritical Superprocesses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5410","kind":"arxiv","version":2},"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":"sha256:109b4c66228becc7806f3cd61b63c59ba2ae8206a471d8dea60a90a9c49a4f64","target":"record","created_at":"2026-05-18T02:42:28Z","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":"19598d629ce616b180c37850a409a09d781520e45b50aaf6719464b2ba56cb54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T03:29:42Z","title_canon_sha256":"772eb573a54e1266a1869aad92331c7e45ffac486049c1ae32f652db1490eb48"},"schema_version":"1.0","source":{"id":"1310.5410","kind":"arxiv","version":2}},"canonical_sha256":"02d5a1d0a37529215f1c48af4a7903b8fde4670ef51f4be55ae36094491a92c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02d5a1d0a37529215f1c48af4a7903b8fde4670ef51f4be55ae36094491a92c5","first_computed_at":"2026-05-18T02:42:28.675918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:28.675918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptieCyGKkHCxN06KgFN4Y15yd1WlcosXT4Lpr6ccOLqf82wDB0K6RpK8kMX+squ3Mg1zBegXUz0weBQKCMH5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:28.676990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5410","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:109b4c66228becc7806f3cd61b63c59ba2ae8206a471d8dea60a90a9c49a4f64","sha256:260eb6625cb1f606c83dd9c16d5d6eed0af6e38db3d4631e506777ed3dc28bae"],"state_sha256":"2d248c7af326861b898fe734f3965b05ccd0d3791d5ff193bfec59497d35f4f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h35Jq3ynXDZflDfD9gtNKc7IyWcZe0u90hFbqU6Gkna6ODHNcPEJLEqHKQCryqQ1ws/bStN7q9wZcRAdPin2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:23:26.778923Z","bundle_sha256":"17a43790df4a7374c3d6882d6f6436f41e8ae42c67d483f22e1b06672b0d714f"}}