{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MIWOJYJB53YUXTRV6YJGT5IW2I","short_pith_number":"pith:MIWOJYJB","canonical_record":{"source":{"id":"1503.02209","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-07T20:12:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b4b3923916c716e64162ffb540364366b78b5486dcf613ad93263517a717b3fb","abstract_canon_sha256":"98574742db3ad29346cb122c90b91df69c8c428d4058e598af65a73af8e2845d"},"schema_version":"1.0"},"canonical_sha256":"622ce4e121eef14bce35f61269f516d215ee96f6ab254c96d081691f3651f2a0","source":{"kind":"arxiv","id":"1503.02209","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02209","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02209v3","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02209","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"MIWOJYJB53YU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MIWOJYJB53YUXTRV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MIWOJYJB","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MIWOJYJB53YUXTRV6YJGT5IW2I","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02209","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-07T20:12:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b4b3923916c716e64162ffb540364366b78b5486dcf613ad93263517a717b3fb","abstract_canon_sha256":"98574742db3ad29346cb122c90b91df69c8c428d4058e598af65a73af8e2845d"},"schema_version":"1.0"},"canonical_sha256":"622ce4e121eef14bce35f61269f516d215ee96f6ab254c96d081691f3651f2a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:51.315328Z","signature_b64":"ipz5dRQBQOWZtdrXR+xv8wZtWpgWG2bcCDv1f8DrpSJZcTuV37ctldNj0ACfuJEe+Bnv7P88b+3FGTLiE8iSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"622ce4e121eef14bce35f61269f516d215ee96f6ab254c96d081691f3651f2a0","last_reissued_at":"2026-05-18T01:36:51.314703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:51.314703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02209","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D85ZLGXulOfx6qmJ3Ogatintxmv6T+1xxrqcIfiVjcWidWy89/yApftQ4y+2z6S27lUf9ozTHq3A4FidkRb6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:52:22.895489Z"},"content_sha256":"76d8b0ef729eb5c564306d9a3671fc30f83b0173be97705bea342a070c7d4f4f","schema_version":"1.0","event_id":"sha256:76d8b0ef729eb5c564306d9a3671fc30f83b0173be97705bea342a070c7d4f4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MIWOJYJB53YUXTRV6YJGT5IW2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Point and Potential Symmetries of the Fokker-Planck Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Bakary Manga, Faya Doumbo Kamano, Jo\\\"el Tossa","submitted_at":"2015-03-07T20:12:12Z","abstract_excerpt":"We determine the Lie point symmetries of the Fokker-Planck equation and provide examples of solutions of this equation. The Fokker-Planck equation admits a conserved form, hence there is an auxiliary system associated to this equation and whose point symmetries give rise to potential symmetries of the Fokker-Planck equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02209","kind":"arxiv","version":3},"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":"2026-05-18T01:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/IEp5jcT/Xsqpm9QySzjAbkEGQKi1cLYzv8Rax6ht3Ocf4G78bqLO76yryX/+/AtvgasEmy+vKcK1hXRCADDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:52:22.895874Z"},"content_sha256":"39faa55712b3f1ca66fcdf733fe238537c86b5b7c02ddaa5cf5d12ce73b70c66","schema_version":"1.0","event_id":"sha256:39faa55712b3f1ca66fcdf733fe238537c86b5b7c02ddaa5cf5d12ce73b70c66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIWOJYJB53YUXTRV6YJGT5IW2I/bundle.json","state_url":"https://pith.science/pith/MIWOJYJB53YUXTRV6YJGT5IW2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIWOJYJB53YUXTRV6YJGT5IW2I/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":"2026-06-25T16:52:22Z","links":{"resolver":"https://pith.science/pith/MIWOJYJB53YUXTRV6YJGT5IW2I","bundle":"https://pith.science/pith/MIWOJYJB53YUXTRV6YJGT5IW2I/bundle.json","state":"https://pith.science/pith/MIWOJYJB53YUXTRV6YJGT5IW2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIWOJYJB53YUXTRV6YJGT5IW2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MIWOJYJB53YUXTRV6YJGT5IW2I","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":"98574742db3ad29346cb122c90b91df69c8c428d4058e598af65a73af8e2845d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-07T20:12:12Z","title_canon_sha256":"b4b3923916c716e64162ffb540364366b78b5486dcf613ad93263517a717b3fb"},"schema_version":"1.0","source":{"id":"1503.02209","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02209","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02209v3","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02209","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"MIWOJYJB53YU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MIWOJYJB53YUXTRV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MIWOJYJB","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:39faa55712b3f1ca66fcdf733fe238537c86b5b7c02ddaa5cf5d12ce73b70c66","target":"graph","created_at":"2026-05-18T01:36:51Z","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 determine the Lie point symmetries of the Fokker-Planck equation and provide examples of solutions of this equation. The Fokker-Planck equation admits a conserved form, hence there is an auxiliary system associated to this equation and whose point symmetries give rise to potential symmetries of the Fokker-Planck equation.","authors_text":"Bakary Manga, Faya Doumbo Kamano, Jo\\\"el Tossa","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-07T20:12:12Z","title":"Point and Potential Symmetries of the Fokker-Planck Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02209","kind":"arxiv","version":3},"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":"sha256:76d8b0ef729eb5c564306d9a3671fc30f83b0173be97705bea342a070c7d4f4f","target":"record","created_at":"2026-05-18T01:36:51Z","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":"98574742db3ad29346cb122c90b91df69c8c428d4058e598af65a73af8e2845d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-07T20:12:12Z","title_canon_sha256":"b4b3923916c716e64162ffb540364366b78b5486dcf613ad93263517a717b3fb"},"schema_version":"1.0","source":{"id":"1503.02209","kind":"arxiv","version":3}},"canonical_sha256":"622ce4e121eef14bce35f61269f516d215ee96f6ab254c96d081691f3651f2a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"622ce4e121eef14bce35f61269f516d215ee96f6ab254c96d081691f3651f2a0","first_computed_at":"2026-05-18T01:36:51.314703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:51.314703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ipz5dRQBQOWZtdrXR+xv8wZtWpgWG2bcCDv1f8DrpSJZcTuV37ctldNj0ACfuJEe+Bnv7P88b+3FGTLiE8iSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:51.315328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02209","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76d8b0ef729eb5c564306d9a3671fc30f83b0173be97705bea342a070c7d4f4f","sha256:39faa55712b3f1ca66fcdf733fe238537c86b5b7c02ddaa5cf5d12ce73b70c66"],"state_sha256":"4b437d1ad0a44eb46821bc87f08a18da80f121752560a7d0686cfb6001839d28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HLonTyhgqtkb37NAdm2h8f3OsJUVKaHQZ3AsWcAtSlA8v/grq1Q0wE16M4ws6zJSP5RScqcGck/RjOMTjSGcDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T16:52:22.897893Z","bundle_sha256":"aceb4baaa4e4035504dacad3c0db1404d89c2365a8c9c9fb094990a357f09bea"}}