{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GODM2G4G3EXDRWWWTYACXVUYNG","short_pith_number":"pith:GODM2G4G","canonical_record":{"source":{"id":"1601.01656","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T20:19:30Z","cross_cats_sorted":[],"title_canon_sha256":"0d744934965fc13591ac8986d4478b3e8e66b01610a903b36a2f29718b587a16","abstract_canon_sha256":"40b2aee02117871060d2b720266edaab01227339cfd5ead1aba525e939cd1238"},"schema_version":"1.0"},"canonical_sha256":"3386cd1b86d92e38dad69e002bd69869bdad793da9189006dfd0da6af8f982f7","source":{"kind":"arxiv","id":"1601.01656","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01656","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01656v2","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01656","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"GODM2G4G3EXD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GODM2G4G3EXDRWWW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GODM2G4G","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GODM2G4G3EXDRWWWTYACXVUYNG","target":"record","payload":{"canonical_record":{"source":{"id":"1601.01656","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T20:19:30Z","cross_cats_sorted":[],"title_canon_sha256":"0d744934965fc13591ac8986d4478b3e8e66b01610a903b36a2f29718b587a16","abstract_canon_sha256":"40b2aee02117871060d2b720266edaab01227339cfd5ead1aba525e939cd1238"},"schema_version":"1.0"},"canonical_sha256":"3386cd1b86d92e38dad69e002bd69869bdad793da9189006dfd0da6af8f982f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:59.944108Z","signature_b64":"8Fgu32lFXqNfwaEqWRfZNq3FBbUgrLqNtzvGnEwReBdKDket/8xVyHqtPBa2mvCrdomqW2HvGwQ5xqTglzm3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3386cd1b86d92e38dad69e002bd69869bdad793da9189006dfd0da6af8f982f7","last_reissued_at":"2026-05-18T01:21:59.943684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:59.943684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.01656","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":"2026-05-18T01:21:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gsf/1F722mJug/S6pa5onZ6xyHJHQBmsVitzpkoVt9G6ZpahLZRJdGP2Dy/RCFIjlZsXD0R24pSgQ8Q33feyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:23:10.554578Z"},"content_sha256":"b1eeef513cd5b5e3cd8968731413a8b4ff2d958c7da2ea2297c56e25fd1fff57","schema_version":"1.0","event_id":"sha256:b1eeef513cd5b5e3cd8968731413a8b4ff2d958c7da2ea2297c56e25fd1fff57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GODM2G4G3EXDRWWWTYACXVUYNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Branching Random Walks, Stable Point Processes and Regular Variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ayan Bhattacharya, Parthanil Roy, Rajat Subhra Hazra","submitted_at":"2016-01-07T20:19:30Z","abstract_excerpt":"Using the language of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is then used to obtain an explicit representation of the weak limit of a sequence of point processes induced by a branching random walk with jointly regularly varying displacements. As a consequence, we extend the main result of Durrett (1983) and verify that two related predictions of Brunet and Derrida (2011) remain valid for this model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01656","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":"2026-05-18T01:21:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tbeCY90Tk0wy/jAjzCZW4b6tlx/nDNtCEWlqadXoCZ4KGmLjOm8mKPm5WpklVNW7m/2aO57oY3Lq2RdizjIjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:23:10.554960Z"},"content_sha256":"cb99f5853d3bda0c5b357060a53023edb34ea7f0e271a0d0a5db00fc9b39ed77","schema_version":"1.0","event_id":"sha256:cb99f5853d3bda0c5b357060a53023edb34ea7f0e271a0d0a5db00fc9b39ed77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GODM2G4G3EXDRWWWTYACXVUYNG/bundle.json","state_url":"https://pith.science/pith/GODM2G4G3EXDRWWWTYACXVUYNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GODM2G4G3EXDRWWWTYACXVUYNG/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":"2026-06-26T08:23:10Z","links":{"resolver":"https://pith.science/pith/GODM2G4G3EXDRWWWTYACXVUYNG","bundle":"https://pith.science/pith/GODM2G4G3EXDRWWWTYACXVUYNG/bundle.json","state":"https://pith.science/pith/GODM2G4G3EXDRWWWTYACXVUYNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GODM2G4G3EXDRWWWTYACXVUYNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GODM2G4G3EXDRWWWTYACXVUYNG","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":"40b2aee02117871060d2b720266edaab01227339cfd5ead1aba525e939cd1238","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T20:19:30Z","title_canon_sha256":"0d744934965fc13591ac8986d4478b3e8e66b01610a903b36a2f29718b587a16"},"schema_version":"1.0","source":{"id":"1601.01656","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.01656","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.01656v2","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01656","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"GODM2G4G3EXD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GODM2G4G3EXDRWWW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GODM2G4G","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:cb99f5853d3bda0c5b357060a53023edb34ea7f0e271a0d0a5db00fc9b39ed77","target":"graph","created_at":"2026-05-18T01:21:59Z","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":"Using the language of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is then used to obtain an explicit representation of the weak limit of a sequence of point processes induced by a branching random walk with jointly regularly varying displacements. As a consequence, we extend the main result of Durrett (1983) and verify that two related predictions of Brunet and Derrida (2011) remain valid for this model.","authors_text":"Ayan Bhattacharya, Parthanil Roy, Rajat Subhra Hazra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T20:19:30Z","title":"Branching Random Walks, Stable Point Processes and Regular Variation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01656","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:b1eeef513cd5b5e3cd8968731413a8b4ff2d958c7da2ea2297c56e25fd1fff57","target":"record","created_at":"2026-05-18T01:21:59Z","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":"40b2aee02117871060d2b720266edaab01227339cfd5ead1aba525e939cd1238","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-07T20:19:30Z","title_canon_sha256":"0d744934965fc13591ac8986d4478b3e8e66b01610a903b36a2f29718b587a16"},"schema_version":"1.0","source":{"id":"1601.01656","kind":"arxiv","version":2}},"canonical_sha256":"3386cd1b86d92e38dad69e002bd69869bdad793da9189006dfd0da6af8f982f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3386cd1b86d92e38dad69e002bd69869bdad793da9189006dfd0da6af8f982f7","first_computed_at":"2026-05-18T01:21:59.943684Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:59.943684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Fgu32lFXqNfwaEqWRfZNq3FBbUgrLqNtzvGnEwReBdKDket/8xVyHqtPBa2mvCrdomqW2HvGwQ5xqTglzm3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:59.944108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.01656","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1eeef513cd5b5e3cd8968731413a8b4ff2d958c7da2ea2297c56e25fd1fff57","sha256:cb99f5853d3bda0c5b357060a53023edb34ea7f0e271a0d0a5db00fc9b39ed77"],"state_sha256":"a68e8e6ce2387185f403695dc48c56fdf19efa7ba6a6dd3747fd084dab92376a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jbakHRYQc3XEHE46bL04/Qh2DzGOGDscOF6rBP4c0KUKw53ngNDoxABcEuaYb+f8urDjw7K713SocmPfBQkqCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:23:10.557131Z","bundle_sha256":"7ffd36611597f5d95117d8afadbb0fbd9d7837b06136e897869425394aaad0ab"}}