{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5HRXLUMK4TV2LJJ24MSFBH3GYA","short_pith_number":"pith:5HRXLUMK","canonical_record":{"source":{"id":"1708.02751","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2017-08-09T08:08:50Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"3ab6c590c261d5ccb221f84077845749fd33eb25ec67aaa36e3c4a826f312d39","abstract_canon_sha256":"683f0993bf15967354c73b3aa52d57bca0b6125a473a4a6b342636bfec4180da"},"schema_version":"1.0"},"canonical_sha256":"e9e375d18ae4eba5a53ae324509f66c0122d484c8d383de46bbacf80957c4dce","source":{"kind":"arxiv","id":"1708.02751","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02751","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02751v2","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02751","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"5HRXLUMK4TV2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5HRXLUMK4TV2LJJ2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5HRXLUMK","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5HRXLUMK4TV2LJJ24MSFBH3GYA","target":"record","payload":{"canonical_record":{"source":{"id":"1708.02751","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2017-08-09T08:08:50Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"3ab6c590c261d5ccb221f84077845749fd33eb25ec67aaa36e3c4a826f312d39","abstract_canon_sha256":"683f0993bf15967354c73b3aa52d57bca0b6125a473a4a6b342636bfec4180da"},"schema_version":"1.0"},"canonical_sha256":"e9e375d18ae4eba5a53ae324509f66c0122d484c8d383de46bbacf80957c4dce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:46.333525Z","signature_b64":"f9KEymwThefqUGQcrmqPFF2SNFKFqGiCvpZlci+efxojncYmKt+a+1GNwMkSFRItMb9NB+qJlaLACGIKZI8CBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9e375d18ae4eba5a53ae324509f66c0122d484c8d383de46bbacf80957c4dce","last_reissued_at":"2026-05-18T00:18:46.332934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:46.332934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.02751","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qzb01IdcabkpQqUTGwhobpW/v23q0s/SnTGVRq+pc7xkCIY5UvBeJ+xhbykWR6T109XSQTUsSR4hOi3wFA6RDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:32:39.890371Z"},"content_sha256":"fa4ecd6545e10078e9b6cd8d0490a4816a372c1e5268456fa666c355be3d99e1","schema_version":"1.0","event_id":"sha256:fa4ecd6545e10078e9b6cd8d0490a4816a372c1e5268456fa666c355be3d99e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5HRXLUMK4TV2LJJ24MSFBH3GYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Patlak-Keller-Segel equations for chemotactic superdiffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"physics.bio-ph","authors_text":"Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J. Painter","submitted_at":"2017-08-09T08:08:50Z","abstract_excerpt":"The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Levy distribution. This article clarifies the form of biologically relevant model equations: We derive Patlak-Keller-Segel-like equations involving nonlocal, fractional Laplacians from a microscopic model for cell movement. Starting from a power-law distribution of run times, we derive a kinetic equation in which the collision term takes into account the long range behaviour of the individuals. A fractional chemotactic equation is obtained in a bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02751","kind":"arxiv","version":2},"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":"2026-05-18T00:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETRzvQglcD9TFPqlYOiduS0yTbs6LyGWetvY6Oc2pMKqXzwSkOjsa3OaQiuhY8ENtScrJvihMX8sosk9OQHxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:32:39.890880Z"},"content_sha256":"b1e8e15d6beccdfeb29a15ff564b11df95b1526fd4c85ddb953cc2d5230304a5","schema_version":"1.0","event_id":"sha256:b1e8e15d6beccdfeb29a15ff564b11df95b1526fd4c85ddb953cc2d5230304a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HRXLUMK4TV2LJJ24MSFBH3GYA/bundle.json","state_url":"https://pith.science/pith/5HRXLUMK4TV2LJJ24MSFBH3GYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HRXLUMK4TV2LJJ24MSFBH3GYA/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":"2026-05-30T15:32:39Z","links":{"resolver":"https://pith.science/pith/5HRXLUMK4TV2LJJ24MSFBH3GYA","bundle":"https://pith.science/pith/5HRXLUMK4TV2LJJ24MSFBH3GYA/bundle.json","state":"https://pith.science/pith/5HRXLUMK4TV2LJJ24MSFBH3GYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HRXLUMK4TV2LJJ24MSFBH3GYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5HRXLUMK4TV2LJJ24MSFBH3GYA","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":"683f0993bf15967354c73b3aa52d57bca0b6125a473a4a6b342636bfec4180da","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2017-08-09T08:08:50Z","title_canon_sha256":"3ab6c590c261d5ccb221f84077845749fd33eb25ec67aaa36e3c4a826f312d39"},"schema_version":"1.0","source":{"id":"1708.02751","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02751","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02751v2","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02751","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"5HRXLUMK4TV2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5HRXLUMK4TV2LJJ2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5HRXLUMK","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:b1e8e15d6beccdfeb29a15ff564b11df95b1526fd4c85ddb953cc2d5230304a5","target":"graph","created_at":"2026-05-18T00:18:46Z","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":"The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Levy distribution. This article clarifies the form of biologically relevant model equations: We derive Patlak-Keller-Segel-like equations involving nonlocal, fractional Laplacians from a microscopic model for cell movement. Starting from a power-law distribution of run times, we derive a kinetic equation in which the collision term takes into account the long range behaviour of the individuals. A fractional chemotactic equation is obtained in a bi","authors_text":"Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J. Painter","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2017-08-09T08:08:50Z","title":"Fractional Patlak-Keller-Segel equations for chemotactic superdiffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02751","kind":"arxiv","version":2},"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:fa4ecd6545e10078e9b6cd8d0490a4816a372c1e5268456fa666c355be3d99e1","target":"record","created_at":"2026-05-18T00:18:46Z","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":"683f0993bf15967354c73b3aa52d57bca0b6125a473a4a6b342636bfec4180da","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2017-08-09T08:08:50Z","title_canon_sha256":"3ab6c590c261d5ccb221f84077845749fd33eb25ec67aaa36e3c4a826f312d39"},"schema_version":"1.0","source":{"id":"1708.02751","kind":"arxiv","version":2}},"canonical_sha256":"e9e375d18ae4eba5a53ae324509f66c0122d484c8d383de46bbacf80957c4dce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9e375d18ae4eba5a53ae324509f66c0122d484c8d383de46bbacf80957c4dce","first_computed_at":"2026-05-18T00:18:46.332934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:46.332934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f9KEymwThefqUGQcrmqPFF2SNFKFqGiCvpZlci+efxojncYmKt+a+1GNwMkSFRItMb9NB+qJlaLACGIKZI8CBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:46.333525Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02751","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa4ecd6545e10078e9b6cd8d0490a4816a372c1e5268456fa666c355be3d99e1","sha256:b1e8e15d6beccdfeb29a15ff564b11df95b1526fd4c85ddb953cc2d5230304a5"],"state_sha256":"7eb1a0e97b877942656eddc4eefebe2a6ade420244a03e2c1fdc7ff2e7eb7d6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NN9QbYKlI8nC6NCaWcwaVWv4/KqFQUJRMjG8Uix1q7eqH6vWjJ+fUpzdtao8mcnqoG9cnJ3IblN9fnro/GcOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:32:39.893166Z","bundle_sha256":"ab1f20b60c21e9c19d9a379806e3d0126f73b32f44536dbdc0c393ab69b32e7f"}}