{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WRJDFR4YE7VNI3EL3AVEGYKVAR","short_pith_number":"pith:WRJDFR4Y","canonical_record":{"source":{"id":"1105.1274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-06T12:50:02Z","cross_cats_sorted":["math.MP","nlin.CD","physics.data-an","physics.soc-ph"],"title_canon_sha256":"b3fc85434a6f0c06e4506f4e1667f46aa80176569aa15fbd3bf181a26eeddddd","abstract_canon_sha256":"44b18164c196b17b1ec18c75c1e08f45b207fe4a4e7bc4832d16bec388ccf89b"},"schema_version":"1.0"},"canonical_sha256":"b45232c79827ead46c8bd82a4361550444fd1e644961fcb4534ee83859a13c23","source":{"kind":"arxiv","id":"1105.1274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1274","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1274v1","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1274","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"WRJDFR4YE7VN","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WRJDFR4YE7VNI3EL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WRJDFR4Y","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WRJDFR4YE7VNI3EL3AVEGYKVAR","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-06T12:50:02Z","cross_cats_sorted":["math.MP","nlin.CD","physics.data-an","physics.soc-ph"],"title_canon_sha256":"b3fc85434a6f0c06e4506f4e1667f46aa80176569aa15fbd3bf181a26eeddddd","abstract_canon_sha256":"44b18164c196b17b1ec18c75c1e08f45b207fe4a4e7bc4832d16bec388ccf89b"},"schema_version":"1.0"},"canonical_sha256":"b45232c79827ead46c8bd82a4361550444fd1e644961fcb4534ee83859a13c23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:40.744450Z","signature_b64":"H+Jln2G84cm2/kgmtDxARJX9dIvjB+nhD7L9GiNhmMK+Uy2yhoC6a1D86dIrH+RFxQJOr1wmnzrBo+EAhoUDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b45232c79827ead46c8bd82a4361550444fd1e644961fcb4534ee83859a13c23","last_reissued_at":"2026-05-18T04:22:40.744038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:40.744038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1274","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":"2026-05-18T04:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g63c9MfEuffI6zjfjbRtYsnnj99ccFx8qLoCRPL2WVte7HB5JiNR72rhOUgc3Jz3p6bAeqlDwo1DCvv5cN9jDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:11:41.467995Z"},"content_sha256":"caa61699c2860928deca6af0092a2c5ac6dedd2c6686dd5a77e0c701873b3afb","schema_version":"1.0","event_id":"sha256:caa61699c2860928deca6af0092a2c5ac6dedd2c6686dd5a77e0c701873b3afb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WRJDFR4YE7VNI3EL3AVEGYKVAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy-tailed Distributions In Stochastic Dynamical Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.CD","physics.data-an","physics.soc-ph"],"primary_cat":"math-ph","authors_text":"D. Volchenkov, Ph. Blanchard, T. Krueger","submitted_at":"2011-05-06T12:50:02Z","abstract_excerpt":"Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the Degree-Mass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavy-tailed distributions appear in them as the emergent phenomena sensit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1274","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":"2026-05-18T04:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3DT0wKTJb6LXZhjMXfFtFYfLdgF8Okb9As0G4TF/gJ1xVf6VVvLwehbQE4ad8BlrVdXb9coO0dNHLdZ5shCNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:11:41.468354Z"},"content_sha256":"eed314da841713d0f398da454d3f8643de2862074a75783ed168b3c0145ba3f1","schema_version":"1.0","event_id":"sha256:eed314da841713d0f398da454d3f8643de2862074a75783ed168b3c0145ba3f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WRJDFR4YE7VNI3EL3AVEGYKVAR/bundle.json","state_url":"https://pith.science/pith/WRJDFR4YE7VNI3EL3AVEGYKVAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WRJDFR4YE7VNI3EL3AVEGYKVAR/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":"2026-06-02T11:11:41Z","links":{"resolver":"https://pith.science/pith/WRJDFR4YE7VNI3EL3AVEGYKVAR","bundle":"https://pith.science/pith/WRJDFR4YE7VNI3EL3AVEGYKVAR/bundle.json","state":"https://pith.science/pith/WRJDFR4YE7VNI3EL3AVEGYKVAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WRJDFR4YE7VNI3EL3AVEGYKVAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WRJDFR4YE7VNI3EL3AVEGYKVAR","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":"44b18164c196b17b1ec18c75c1e08f45b207fe4a4e7bc4832d16bec388ccf89b","cross_cats_sorted":["math.MP","nlin.CD","physics.data-an","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-06T12:50:02Z","title_canon_sha256":"b3fc85434a6f0c06e4506f4e1667f46aa80176569aa15fbd3bf181a26eeddddd"},"schema_version":"1.0","source":{"id":"1105.1274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1274","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1274v1","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1274","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"WRJDFR4YE7VN","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WRJDFR4YE7VNI3EL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WRJDFR4Y","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:eed314da841713d0f398da454d3f8643de2862074a75783ed168b3c0145ba3f1","target":"graph","created_at":"2026-05-18T04:22:40Z","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":"Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the Degree-Mass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavy-tailed distributions appear in them as the emergent phenomena sensit","authors_text":"D. Volchenkov, Ph. Blanchard, T. Krueger","cross_cats":["math.MP","nlin.CD","physics.data-an","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-06T12:50:02Z","title":"Heavy-tailed Distributions In Stochastic Dynamical Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1274","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:caa61699c2860928deca6af0092a2c5ac6dedd2c6686dd5a77e0c701873b3afb","target":"record","created_at":"2026-05-18T04:22:40Z","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":"44b18164c196b17b1ec18c75c1e08f45b207fe4a4e7bc4832d16bec388ccf89b","cross_cats_sorted":["math.MP","nlin.CD","physics.data-an","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-06T12:50:02Z","title_canon_sha256":"b3fc85434a6f0c06e4506f4e1667f46aa80176569aa15fbd3bf181a26eeddddd"},"schema_version":"1.0","source":{"id":"1105.1274","kind":"arxiv","version":1}},"canonical_sha256":"b45232c79827ead46c8bd82a4361550444fd1e644961fcb4534ee83859a13c23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b45232c79827ead46c8bd82a4361550444fd1e644961fcb4534ee83859a13c23","first_computed_at":"2026-05-18T04:22:40.744038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:40.744038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H+Jln2G84cm2/kgmtDxARJX9dIvjB+nhD7L9GiNhmMK+Uy2yhoC6a1D86dIrH+RFxQJOr1wmnzrBo+EAhoUDDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:40.744450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa61699c2860928deca6af0092a2c5ac6dedd2c6686dd5a77e0c701873b3afb","sha256:eed314da841713d0f398da454d3f8643de2862074a75783ed168b3c0145ba3f1"],"state_sha256":"2cb1b1c040af08f6598bb8b47027d82e5256dabfbae258dc7f5253ff76be4731"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6rzbSzlumksFpjSORzmOXzFS1mPezosWpQEseJ+THlNmXMEn3U8zS5c+zFIA4b7uNugYK3P7nBYKbH5SXzDgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:11:41.470257Z","bundle_sha256":"86ac64bce3c9209b52266cf4906bf9230436da61b545f822bc4b050ceed148b1"}}