{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AHJEM7P4FHGN6PXIS33KYMT45D","short_pith_number":"pith:AHJEM7P4","canonical_record":{"source":{"id":"1802.02412","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-02-07T13:29:17Z","cross_cats_sorted":["physics.data-an"],"title_canon_sha256":"cc0af4b51714fce1b3cbdb2d4d9d23eac2936e185737e07402ea4c671d3844e4","abstract_canon_sha256":"e86f280d5262de237f286918abe1f00ef2b757965644451734c0b88bfa1110f5"},"schema_version":"1.0"},"canonical_sha256":"01d2467dfc29ccdf3ee896f6ac327ce8d07c34cb1951c550b78734b131eab555","source":{"kind":"arxiv","id":"1802.02412","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02412","created_at":"2026-05-18T00:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02412v1","created_at":"2026-05-18T00:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02412","created_at":"2026-05-18T00:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"AHJEM7P4FHGN","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AHJEM7P4FHGN6PXI","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AHJEM7P4","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AHJEM7P4FHGN6PXIS33KYMT45D","target":"record","payload":{"canonical_record":{"source":{"id":"1802.02412","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-02-07T13:29:17Z","cross_cats_sorted":["physics.data-an"],"title_canon_sha256":"cc0af4b51714fce1b3cbdb2d4d9d23eac2936e185737e07402ea4c671d3844e4","abstract_canon_sha256":"e86f280d5262de237f286918abe1f00ef2b757965644451734c0b88bfa1110f5"},"schema_version":"1.0"},"canonical_sha256":"01d2467dfc29ccdf3ee896f6ac327ce8d07c34cb1951c550b78734b131eab555","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:01.281070Z","signature_b64":"l85FiU7PXlHRv8Cka+hwWFlPCdCLsMAZ0p1eMEv55C5RqyxHuyeuxH9rmxlXM6JEeg7paQEH/KlytI4KkJY1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01d2467dfc29ccdf3ee896f6ac327ce8d07c34cb1951c550b78734b131eab555","last_reissued_at":"2026-05-18T00:17:01.280377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:01.280377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.02412","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":"2026-05-18T00:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvKwBWfDnDqUqTQo1wUzCp6Xw5LKZnhuF8qx7tuCw7XQKkNl3d9bcyvIWEG+J+oQD0vY0BbZZEx1zWxin9+zAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:48:40.625307Z"},"content_sha256":"bc197abee190c01269499eb187162c2b9792e6a84c6189a10e33a4084ba275d3","schema_version":"1.0","event_id":"sha256:bc197abee190c01269499eb187162c2b9792e6a84c6189a10e33a4084ba275d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AHJEM7P4FHGN6PXIS33KYMT45D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of stochastic bifurcations with phase portraits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"cond-mat.stat-mech","authors_text":"Barbara Drossel, Johannes Falk, Marc Mendler","submitted_at":"2018-02-07T13:29:17Z","abstract_excerpt":"We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective field correspond to maxima and minima of the stationary probability distribution if the probability current vanishes at these points. Stochastic phase portraits, which are vector plots of the convective field, therefore indicate the extrema of the stationary distribution and can be used to identify stochastic bifurcations that change the number and stabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02412","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":"2026-05-18T00:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zukkGxr+AoeDVO/LF2oAg5/dhIoQIsRrU3sZuFxPcyBhY3Ta7w1DW0Z1mJjxEDDpwzu7+L/O58EuQh1y24cGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:48:40.625950Z"},"content_sha256":"10fe44b3760a0bca7edec1d637aae662353d06627f2fbcb279d4d06a5f871401","schema_version":"1.0","event_id":"sha256:10fe44b3760a0bca7edec1d637aae662353d06627f2fbcb279d4d06a5f871401"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHJEM7P4FHGN6PXIS33KYMT45D/bundle.json","state_url":"https://pith.science/pith/AHJEM7P4FHGN6PXIS33KYMT45D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHJEM7P4FHGN6PXIS33KYMT45D/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":"2026-05-30T17:48:40Z","links":{"resolver":"https://pith.science/pith/AHJEM7P4FHGN6PXIS33KYMT45D","bundle":"https://pith.science/pith/AHJEM7P4FHGN6PXIS33KYMT45D/bundle.json","state":"https://pith.science/pith/AHJEM7P4FHGN6PXIS33KYMT45D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHJEM7P4FHGN6PXIS33KYMT45D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AHJEM7P4FHGN6PXIS33KYMT45D","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":"e86f280d5262de237f286918abe1f00ef2b757965644451734c0b88bfa1110f5","cross_cats_sorted":["physics.data-an"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-02-07T13:29:17Z","title_canon_sha256":"cc0af4b51714fce1b3cbdb2d4d9d23eac2936e185737e07402ea4c671d3844e4"},"schema_version":"1.0","source":{"id":"1802.02412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02412","created_at":"2026-05-18T00:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02412v1","created_at":"2026-05-18T00:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02412","created_at":"2026-05-18T00:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"AHJEM7P4FHGN","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AHJEM7P4FHGN6PXI","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AHJEM7P4","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:10fe44b3760a0bca7edec1d637aae662353d06627f2fbcb279d4d06a5f871401","target":"graph","created_at":"2026-05-18T00:17:01Z","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 propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective field correspond to maxima and minima of the stationary probability distribution if the probability current vanishes at these points. Stochastic phase portraits, which are vector plots of the convective field, therefore indicate the extrema of the stationary distribution and can be used to identify stochastic bifurcations that change the number and stabilit","authors_text":"Barbara Drossel, Johannes Falk, Marc Mendler","cross_cats":["physics.data-an"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-02-07T13:29:17Z","title":"Analysis of stochastic bifurcations with phase portraits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02412","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:bc197abee190c01269499eb187162c2b9792e6a84c6189a10e33a4084ba275d3","target":"record","created_at":"2026-05-18T00:17:01Z","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":"e86f280d5262de237f286918abe1f00ef2b757965644451734c0b88bfa1110f5","cross_cats_sorted":["physics.data-an"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-02-07T13:29:17Z","title_canon_sha256":"cc0af4b51714fce1b3cbdb2d4d9d23eac2936e185737e07402ea4c671d3844e4"},"schema_version":"1.0","source":{"id":"1802.02412","kind":"arxiv","version":1}},"canonical_sha256":"01d2467dfc29ccdf3ee896f6ac327ce8d07c34cb1951c550b78734b131eab555","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01d2467dfc29ccdf3ee896f6ac327ce8d07c34cb1951c550b78734b131eab555","first_computed_at":"2026-05-18T00:17:01.280377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:01.280377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l85FiU7PXlHRv8Cka+hwWFlPCdCLsMAZ0p1eMEv55C5RqyxHuyeuxH9rmxlXM6JEeg7paQEH/KlytI4KkJY1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:01.281070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc197abee190c01269499eb187162c2b9792e6a84c6189a10e33a4084ba275d3","sha256:10fe44b3760a0bca7edec1d637aae662353d06627f2fbcb279d4d06a5f871401"],"state_sha256":"793c99a9bd57f659699934a1075aa91b1a5c51d7c74934815177750c57f4a901"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"euui2b1YFtoqZu3YCXA0pPq8OFF28cknJduvLSemW1etGtv2fZ1Zj21fp7MFKhZ66I/hW/j+N+7xEFre5fibAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T17:48:40.629828Z","bundle_sha256":"73c69afb620a8c021294429bb8e39b0072d3c8628201ee25f9ae156ffb6a4124"}}