{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OYG4CKCSFJDDN7DJRCEHIDWUXW","short_pith_number":"pith:OYG4CKCS","canonical_record":{"source":{"id":"1003.1548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-08T03:33:38Z","cross_cats_sorted":["cond-mat.stat-mech","q-bio.OT"],"title_canon_sha256":"db169d547518555bde22079b793ab11a2a717fcd1b47d99f572f409353970bb2","abstract_canon_sha256":"ff8e5f2ab387ad989ba81c7b152cf469aa8817bbf6daaa58b2ef5a03f8b0a3fc"},"schema_version":"1.0"},"canonical_sha256":"760dc128522a4636fc698888740ed4bd9c420c79a80e494ed87176dba989b4d1","source":{"kind":"arxiv","id":"1003.1548","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1548","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1548v1","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1548","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"OYG4CKCSFJDD","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OYG4CKCSFJDDN7DJ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OYG4CKCS","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OYG4CKCSFJDDN7DJRCEHIDWUXW","target":"record","payload":{"canonical_record":{"source":{"id":"1003.1548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-08T03:33:38Z","cross_cats_sorted":["cond-mat.stat-mech","q-bio.OT"],"title_canon_sha256":"db169d547518555bde22079b793ab11a2a717fcd1b47d99f572f409353970bb2","abstract_canon_sha256":"ff8e5f2ab387ad989ba81c7b152cf469aa8817bbf6daaa58b2ef5a03f8b0a3fc"},"schema_version":"1.0"},"canonical_sha256":"760dc128522a4636fc698888740ed4bd9c420c79a80e494ed87176dba989b4d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:42.288103Z","signature_b64":"KmSl1VEUOA9Q+40gvSF/kL3eJc1J++prw2C51h6rc/GfRUz1nM2Y3lPz8lNnpGpg0jQZo10qRrKc0LJ66r4VBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"760dc128522a4636fc698888740ed4bd9c420c79a80e494ed87176dba989b4d1","last_reissued_at":"2026-05-18T03:39:42.287223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:42.287223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.1548","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":"2026-05-18T03:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lszN96feGTvocQI0La40H9TJr1d7OqRcOsm+Z8iSINud2z3RhVK3TgvFbeUBtePgFtURHKDmvC5PHNcgQymBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:51:51.162214Z"},"content_sha256":"a73d3767709f96bbe3027b56d9eb30b5830be81ab84498ad4a555baacc97d34a","schema_version":"1.0","event_id":"sha256:a73d3767709f96bbe3027b56d9eb30b5830be81ab84498ad4a555baacc97d34a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OYG4CKCSFJDDN7DJRCEHIDWUXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Chemotaxis Diffusion Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","q-bio.OT"],"primary_cat":"math.DS","authors_text":"B.I. Henry, T.A.M. Langlands","submitted_at":"2010-03-08T03:33:38Z","abstract_excerpt":"We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion  for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding.  The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with  fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to  include linear reaction dynamics are also d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1548","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":"2026-05-18T03:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WkLkhJMNY5ABJ3ZpguwezWqm3N7Hl/7lW78sKOjqMs5fXlOtIGdDejjSNUcuegJhnQCi85SjLGnMd9OjyemtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:51:51.162573Z"},"content_sha256":"9e526736e156e450948449e0adea405179d67b5c4f5699a1a59e39eb6037430b","schema_version":"1.0","event_id":"sha256:9e526736e156e450948449e0adea405179d67b5c4f5699a1a59e39eb6037430b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYG4CKCSFJDDN7DJRCEHIDWUXW/bundle.json","state_url":"https://pith.science/pith/OYG4CKCSFJDDN7DJRCEHIDWUXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYG4CKCSFJDDN7DJRCEHIDWUXW/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":"2026-06-27T03:51:51Z","links":{"resolver":"https://pith.science/pith/OYG4CKCSFJDDN7DJRCEHIDWUXW","bundle":"https://pith.science/pith/OYG4CKCSFJDDN7DJRCEHIDWUXW/bundle.json","state":"https://pith.science/pith/OYG4CKCSFJDDN7DJRCEHIDWUXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYG4CKCSFJDDN7DJRCEHIDWUXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OYG4CKCSFJDDN7DJRCEHIDWUXW","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":"ff8e5f2ab387ad989ba81c7b152cf469aa8817bbf6daaa58b2ef5a03f8b0a3fc","cross_cats_sorted":["cond-mat.stat-mech","q-bio.OT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-08T03:33:38Z","title_canon_sha256":"db169d547518555bde22079b793ab11a2a717fcd1b47d99f572f409353970bb2"},"schema_version":"1.0","source":{"id":"1003.1548","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1548","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1548v1","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1548","created_at":"2026-05-18T03:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"OYG4CKCSFJDD","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OYG4CKCSFJDDN7DJ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OYG4CKCS","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:9e526736e156e450948449e0adea405179d67b5c4f5699a1a59e39eb6037430b","target":"graph","created_at":"2026-05-18T03:39:42Z","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 introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion  for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding.  The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with  fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to  include linear reaction dynamics are also d","authors_text":"B.I. Henry, T.A.M. Langlands","cross_cats":["cond-mat.stat-mech","q-bio.OT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-08T03:33:38Z","title":"Fractional Chemotaxis Diffusion Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1548","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:a73d3767709f96bbe3027b56d9eb30b5830be81ab84498ad4a555baacc97d34a","target":"record","created_at":"2026-05-18T03:39:42Z","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":"ff8e5f2ab387ad989ba81c7b152cf469aa8817bbf6daaa58b2ef5a03f8b0a3fc","cross_cats_sorted":["cond-mat.stat-mech","q-bio.OT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-08T03:33:38Z","title_canon_sha256":"db169d547518555bde22079b793ab11a2a717fcd1b47d99f572f409353970bb2"},"schema_version":"1.0","source":{"id":"1003.1548","kind":"arxiv","version":1}},"canonical_sha256":"760dc128522a4636fc698888740ed4bd9c420c79a80e494ed87176dba989b4d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"760dc128522a4636fc698888740ed4bd9c420c79a80e494ed87176dba989b4d1","first_computed_at":"2026-05-18T03:39:42.287223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:42.287223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KmSl1VEUOA9Q+40gvSF/kL3eJc1J++prw2C51h6rc/GfRUz1nM2Y3lPz8lNnpGpg0jQZo10qRrKc0LJ66r4VBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:42.288103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1548","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a73d3767709f96bbe3027b56d9eb30b5830be81ab84498ad4a555baacc97d34a","sha256:9e526736e156e450948449e0adea405179d67b5c4f5699a1a59e39eb6037430b"],"state_sha256":"c903f9682ab520c93a20f4401e1f69d9f46f94e98f359d9e97e95838bbf9d607"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/cQk/9p6CzWsDCcADAzmoV/C2/9pN6V43pxzLI6mgoQbydB4wzfLYvIuL/71FyRfh80FIxfxMY0N+Quwr+uyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:51:51.164422Z","bundle_sha256":"4d55ebf43433288221e109f4bba789e0685756e6fd1a55801c7259ac97b01199"}}