{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:HHFFXZ6F7O4DZRVHQUQQGPWUFO","short_pith_number":"pith:HHFFXZ6F","canonical_record":{"source":{"id":"0908.1730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-12T15:19:42Z","cross_cats_sorted":[],"title_canon_sha256":"fdf082af112248dfcf2a1b7efd9d11b5f22fa95eaec2ff48d6a148d15ae6f385","abstract_canon_sha256":"1de8e39b58efdfe64fdb6435e0bf7a64601a35351156e5e1030789429b30fb0c"},"schema_version":"1.0"},"canonical_sha256":"39ca5be7c5fbb83cc6a78521033ed42b9103c47ce989c5e057a11e6508a6d5e5","source":{"kind":"arxiv","id":"0908.1730","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1730","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1730v1","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1730","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"HHFFXZ6F7O4D","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HHFFXZ6F7O4DZRVH","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HHFFXZ6F","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:HHFFXZ6F7O4DZRVHQUQQGPWUFO","target":"record","payload":{"canonical_record":{"source":{"id":"0908.1730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-12T15:19:42Z","cross_cats_sorted":[],"title_canon_sha256":"fdf082af112248dfcf2a1b7efd9d11b5f22fa95eaec2ff48d6a148d15ae6f385","abstract_canon_sha256":"1de8e39b58efdfe64fdb6435e0bf7a64601a35351156e5e1030789429b30fb0c"},"schema_version":"1.0"},"canonical_sha256":"39ca5be7c5fbb83cc6a78521033ed42b9103c47ce989c5e057a11e6508a6d5e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:44.385515Z","signature_b64":"45Y3T6pE1QO4NiRa/bJkd1A6gOcBCuqcpVC9gGQCEQwRQMmNXezBpqE04GbTpODAuLw2GwLHncloTthKx86qAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39ca5be7c5fbb83cc6a78521033ed42b9103c47ce989c5e057a11e6508a6d5e5","last_reissued_at":"2026-05-18T00:06:44.385168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:44.385168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.1730","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqXV/RmwGhfj/h3otx7zus48/gNH2t1aAy79QM6jRG7EupJnwPJ25Rqy9hvxcMBqCb/a4Y5wXg5hhWwSNMkdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:24:08.763849Z"},"content_sha256":"e0027df6e5dbc61c52d3f03d3d0ccdc1631a82e0f61317ded1fc848e24373b31","schema_version":"1.0","event_id":"sha256:e0027df6e5dbc61c52d3f03d3d0ccdc1631a82e0f61317ded1fc848e24373b31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:HHFFXZ6F7O4DZRVHQUQQGPWUFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rate description of Fokker-Planck processes with time-periodic parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Changho Kim, Eok Kyun Lee, Peter Hanggi, Peter Talkner","submitted_at":"2009-08-12T15:19:42Z","abstract_excerpt":"The large time dynamics of a periodically driven Fokker-Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete Markovian process characterized by time dependent rates. Apart from the occupation probabilities, so-called specific probability densities and localizing functions can be associated to each metastable state. Together, these three sets of functions uniquely characterize the large time dynamics of the conditional probability density of the original process. Exact equa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1730","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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vEPPutqlnfOZKmcDlEK8AqAHf+f+rKF340fe/F6LAiQctPN/JXJeTwEIBGZDAys0/JUWS2kT2YqO3C6/vlRQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:24:08.764712Z"},"content_sha256":"d8b9e2c48babef384def310625315af91faa3f42e4961c981f8b1411beec5d38","schema_version":"1.0","event_id":"sha256:d8b9e2c48babef384def310625315af91faa3f42e4961c981f8b1411beec5d38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HHFFXZ6F7O4DZRVHQUQQGPWUFO/bundle.json","state_url":"https://pith.science/pith/HHFFXZ6F7O4DZRVHQUQQGPWUFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HHFFXZ6F7O4DZRVHQUQQGPWUFO/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":"2026-05-31T18:24:08Z","links":{"resolver":"https://pith.science/pith/HHFFXZ6F7O4DZRVHQUQQGPWUFO","bundle":"https://pith.science/pith/HHFFXZ6F7O4DZRVHQUQQGPWUFO/bundle.json","state":"https://pith.science/pith/HHFFXZ6F7O4DZRVHQUQQGPWUFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HHFFXZ6F7O4DZRVHQUQQGPWUFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:HHFFXZ6F7O4DZRVHQUQQGPWUFO","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":"1de8e39b58efdfe64fdb6435e0bf7a64601a35351156e5e1030789429b30fb0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-12T15:19:42Z","title_canon_sha256":"fdf082af112248dfcf2a1b7efd9d11b5f22fa95eaec2ff48d6a148d15ae6f385"},"schema_version":"1.0","source":{"id":"0908.1730","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1730","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1730v1","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1730","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"HHFFXZ6F7O4D","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HHFFXZ6F7O4DZRVH","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HHFFXZ6F","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:d8b9e2c48babef384def310625315af91faa3f42e4961c981f8b1411beec5d38","target":"graph","created_at":"2026-05-18T00:06:44Z","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":"The large time dynamics of a periodically driven Fokker-Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete Markovian process characterized by time dependent rates. Apart from the occupation probabilities, so-called specific probability densities and localizing functions can be associated to each metastable state. Together, these three sets of functions uniquely characterize the large time dynamics of the conditional probability density of the original process. Exact equa","authors_text":"Changho Kim, Eok Kyun Lee, Peter Hanggi, Peter Talkner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-12T15:19:42Z","title":"Rate description of Fokker-Planck processes with time-periodic parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1730","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:e0027df6e5dbc61c52d3f03d3d0ccdc1631a82e0f61317ded1fc848e24373b31","target":"record","created_at":"2026-05-18T00:06:44Z","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":"1de8e39b58efdfe64fdb6435e0bf7a64601a35351156e5e1030789429b30fb0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-12T15:19:42Z","title_canon_sha256":"fdf082af112248dfcf2a1b7efd9d11b5f22fa95eaec2ff48d6a148d15ae6f385"},"schema_version":"1.0","source":{"id":"0908.1730","kind":"arxiv","version":1}},"canonical_sha256":"39ca5be7c5fbb83cc6a78521033ed42b9103c47ce989c5e057a11e6508a6d5e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39ca5be7c5fbb83cc6a78521033ed42b9103c47ce989c5e057a11e6508a6d5e5","first_computed_at":"2026-05-18T00:06:44.385168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:44.385168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"45Y3T6pE1QO4NiRa/bJkd1A6gOcBCuqcpVC9gGQCEQwRQMmNXezBpqE04GbTpODAuLw2GwLHncloTthKx86qAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:44.385515Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1730","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0027df6e5dbc61c52d3f03d3d0ccdc1631a82e0f61317ded1fc848e24373b31","sha256:d8b9e2c48babef384def310625315af91faa3f42e4961c981f8b1411beec5d38"],"state_sha256":"b09c2a0fd5d6645da2cdab1688f5bb09bfd4a16c24b80de9352b36e574ac714a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+6MxdBptRJb4KRhH1RsW9qYd7oBLON5ZVzHuV8HWc/Cb4bqZZ66masGCPgWQCoOQ6l2izhbRjWzRXAa+D88AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:24:08.769121Z","bundle_sha256":"d1de33e95bc7b92237ff0bc56dde88d60dee4d5b6db276fcea2ef199a137e3c0"}}