{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XDFJFBDMFZYKUUNT2YZJMMW6YE","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":"6a2700345462aba57baf8d546a90dc6246727ed99b7bc8cdd3c2450721ce8cb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-07-05T19:42:31Z","title_canon_sha256":"65a18a4c3067f9e51cc9a123fb9685ce1c4864758fdc08ae47ff5cb6ff21b57b"},"schema_version":"1.0","source":{"id":"1107.0959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0959","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0959v1","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0959","created_at":"2026-05-18T04:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"XDFJFBDMFZYK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XDFJFBDMFZYKUUNT","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XDFJFBDM","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:74aa92d84bda66fe252239150e05b683f36f9e96642e62147462a7a315a9680a","target":"graph","created_at":"2026-05-18T04:18:46Z","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":"We consider a Langevin equation with variable drift and diffusion coefficients separable in time and space and its corresponding Fokker-Planck equation in the Stratonovich approach. From this Fokker-Planck equation we obtain a class of exact solutions with the same spatial drift and diffusion coefficients. Furthermore, we analyze some details of this system by using the spatial diffusion coefficient $D(x)=\\sqrt{D}|x| ^{-% \\frac{\\theta}{2}}$.","authors_text":"Kwok Sau Fa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-07-05T19:42:31Z","title":"Solution of Fokker-Planck equation for a broad class of drift and diffusion coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0959","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:f3a52e24597c3ebc1fc7a79a21f21ef0268615a73528c363fdbbbb7657185d7a","target":"record","created_at":"2026-05-18T04:18:46Z","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":"6a2700345462aba57baf8d546a90dc6246727ed99b7bc8cdd3c2450721ce8cb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-07-05T19:42:31Z","title_canon_sha256":"65a18a4c3067f9e51cc9a123fb9685ce1c4864758fdc08ae47ff5cb6ff21b57b"},"schema_version":"1.0","source":{"id":"1107.0959","kind":"arxiv","version":1}},"canonical_sha256":"b8ca92846c2e70aa51b3d6329632dec1015a775cfa784e2df46f6fc65012de09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8ca92846c2e70aa51b3d6329632dec1015a775cfa784e2df46f6fc65012de09","first_computed_at":"2026-05-18T04:18:46.440358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:46.440358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tr4ybelTwt5l4xJimJYtbsKSbSjUzJAokH/CJrOqdNRXOXHDBQGbofLOKYz7L4C9ZqgwXJL+lSqpIAjy1sg2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:46.440781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a52e24597c3ebc1fc7a79a21f21ef0268615a73528c363fdbbbb7657185d7a","sha256:74aa92d84bda66fe252239150e05b683f36f9e96642e62147462a7a315a9680a"],"state_sha256":"0a6e04ccf2e7829f11d34a03edc3f9eea7f498b8ee0ecdd7dd0d147a26fe5a1e"}