{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:6CL52W44EK6AKNEYQAA7477FNQ","short_pith_number":"pith:6CL52W44","schema_version":"1.0","canonical_sha256":"f097dd5b9c22bc0534988001fe7fe56c241235e1166f53563ac71bb45ac296ae","source":{"kind":"arxiv","id":"1011.3678","version":1},"attestation_state":"computed","paper":{"title":"Maximum Path Information and Fokker-Planck Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alain Le Mehaute, Alexandre Wang, Wei Li","submitted_at":"2010-11-16T12:48:24Z","abstract_excerpt":"We present in this paper a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy) and the time t."},"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":"1011.3678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-11-16T12:48:24Z","cross_cats_sorted":[],"title_canon_sha256":"c0fbbc236d5a605b1968b19d40bd7d4fad5c848f0642132b4eac8a6116e9a9e3","abstract_canon_sha256":"9d102038fea565e7d1dcf430e2d5036c0e169d3564ed34a4b808054b28808314"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:45.221458Z","signature_b64":"gvvprACzdbjvRLh7ePigeRbmBD/SHTByU2/CXpe/9GCxzwEsg8mpu3HEsd0lzqsGJ8vSiO6bxvNQL2rlwDCxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f097dd5b9c22bc0534988001fe7fe56c241235e1166f53563ac71bb45ac296ae","last_reissued_at":"2026-05-18T02:04:45.220656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:45.220656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum Path Information and Fokker-Planck Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Alain Le Mehaute, Alexandre Wang, Wei Li","submitted_at":"2010-11-16T12:48:24Z","abstract_excerpt":"We present in this paper a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy) and the time t."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3678","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.3678","created_at":"2026-05-18T02:04:45.220778+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3678v1","created_at":"2026-05-18T02:04:45.220778+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3678","created_at":"2026-05-18T02:04:45.220778+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CL52W44EK6A","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CL52W44EK6AKNEY","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CL52W44","created_at":"2026-05-18T12:26:04.259169+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/6CL52W44EK6AKNEYQAA7477FNQ","json":"https://pith.science/pith/6CL52W44EK6AKNEYQAA7477FNQ.json","graph_json":"https://pith.science/api/pith-number/6CL52W44EK6AKNEYQAA7477FNQ/graph.json","events_json":"https://pith.science/api/pith-number/6CL52W44EK6AKNEYQAA7477FNQ/events.json","paper":"https://pith.science/paper/6CL52W44"},"agent_actions":{"view_html":"https://pith.science/pith/6CL52W44EK6AKNEYQAA7477FNQ","download_json":"https://pith.science/pith/6CL52W44EK6AKNEYQAA7477FNQ.json","view_paper":"https://pith.science/paper/6CL52W44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3678&json=true","fetch_graph":"https://pith.science/api/pith-number/6CL52W44EK6AKNEYQAA7477FNQ/graph.json","fetch_events":"https://pith.science/api/pith-number/6CL52W44EK6AKNEYQAA7477FNQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CL52W44EK6AKNEYQAA7477FNQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CL52W44EK6AKNEYQAA7477FNQ/action/storage_attestation","attest_author":"https://pith.science/pith/6CL52W44EK6AKNEYQAA7477FNQ/action/author_attestation","sign_citation":"https://pith.science/pith/6CL52W44EK6AKNEYQAA7477FNQ/action/citation_signature","submit_replication":"https://pith.science/pith/6CL52W44EK6AKNEYQAA7477FNQ/action/replication_record"}},"created_at":"2026-05-18T02:04:45.220778+00:00","updated_at":"2026-05-18T02:04:45.220778+00:00"}