{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JLYLAWXRSWU525K5CDZPUISM3D","short_pith_number":"pith:JLYLAWXR","schema_version":"1.0","canonical_sha256":"4af0b05af195a9dd755d10f2fa224cd8e2ba312d079983b00b0a9e2b5ebeb568","source":{"kind":"arxiv","id":"1103.1184","version":2},"attestation_state":"computed","paper":{"title":"Stochastic dynamical theory of power-law distributions induced by multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Jiulin Du","submitted_at":"2011-03-07T02:27:51Z","abstract_excerpt":"The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of stationary power-law distributions through the multiplicative noise. The power-law distributions induced by this inhomogeneous noise are proved to be a result of that the relation of diffusion to friction depends on the energy. We understand the conditions under which the power-law distributions are produced and how they are produced in systems away from equilibrium"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1103.1184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-03-07T02:27:51Z","cross_cats_sorted":[],"title_canon_sha256":"a0459553b3258fb82a934216bb44e2d6cdd8c906e9564766eee1c192f94df614","abstract_canon_sha256":"1e2f2fb3c857d173f2666e136ddb1cef9a2ca119322e2f686eb5880dd7706975"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:42.318894Z","signature_b64":"iZ96BExyCH6Fu9BqPBW4lgsjsqwUcvDC5rNA3XaiNjEoYiui60jAsNvKfYs/VTkKLu3BNDTbw8YHL/gBf/c8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4af0b05af195a9dd755d10f2fa224cd8e2ba312d079983b00b0a9e2b5ebeb568","last_reissued_at":"2026-05-18T01:35:42.318501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:42.318501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic dynamical theory of power-law distributions induced by multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Jiulin Du","submitted_at":"2011-03-07T02:27:51Z","abstract_excerpt":"The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of stationary power-law distributions through the multiplicative noise. The power-law distributions induced by this inhomogeneous noise are proved to be a result of that the relation of diffusion to friction depends on the energy. We understand the conditions under which the power-law distributions are produced and how they are produced in systems away from equilibrium"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1184","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.1184","created_at":"2026-05-18T01:35:42.318562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1184v2","created_at":"2026-05-18T01:35:42.318562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1184","created_at":"2026-05-18T01:35:42.318562+00:00"},{"alias_kind":"pith_short_12","alias_value":"JLYLAWXRSWU5","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JLYLAWXRSWU525K5","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JLYLAWXR","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D","json":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D.json","graph_json":"https://pith.science/api/pith-number/JLYLAWXRSWU525K5CDZPUISM3D/graph.json","events_json":"https://pith.science/api/pith-number/JLYLAWXRSWU525K5CDZPUISM3D/events.json","paper":"https://pith.science/paper/JLYLAWXR"},"agent_actions":{"view_html":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D","download_json":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D.json","view_paper":"https://pith.science/paper/JLYLAWXR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1184&json=true","fetch_graph":"https://pith.science/api/pith-number/JLYLAWXRSWU525K5CDZPUISM3D/graph.json","fetch_events":"https://pith.science/api/pith-number/JLYLAWXRSWU525K5CDZPUISM3D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D/action/storage_attestation","attest_author":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D/action/author_attestation","sign_citation":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D/action/citation_signature","submit_replication":"https://pith.science/pith/JLYLAWXRSWU525K5CDZPUISM3D/action/replication_record"}},"created_at":"2026-05-18T01:35:42.318562+00:00","updated_at":"2026-05-18T01:35:42.318562+00:00"}