{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HUD65FMLGHWJWQQV6RW2PLUW4Q","short_pith_number":"pith:HUD65FML","canonical_record":{"source":{"id":"1302.2665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-02-11T23:03:38Z","cross_cats_sorted":["math.AP","q-bio.PE"],"title_canon_sha256":"569aaae9e03aa94c4891a1b0bf7f85358197bf00f566b28d9334a7d923b59f07","abstract_canon_sha256":"504993f3d91debc3c4ffe3f6aaf126b7dab2cc8b0d879a8fbdfbbe9e4cca4315"},"schema_version":"1.0"},"canonical_sha256":"3d07ee958b31ec9b4215f46da7ae96e439638507051677f832524571d7131739","source":{"kind":"arxiv","id":"1302.2665","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2665","created_at":"2026-05-18T03:33:51Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2665v1","created_at":"2026-05-18T03:33:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2665","created_at":"2026-05-18T03:33:51Z"},{"alias_kind":"pith_short_12","alias_value":"HUD65FMLGHWJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HUD65FMLGHWJWQQV","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HUD65FML","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HUD65FMLGHWJWQQV6RW2PLUW4Q","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-02-11T23:03:38Z","cross_cats_sorted":["math.AP","q-bio.PE"],"title_canon_sha256":"569aaae9e03aa94c4891a1b0bf7f85358197bf00f566b28d9334a7d923b59f07","abstract_canon_sha256":"504993f3d91debc3c4ffe3f6aaf126b7dab2cc8b0d879a8fbdfbbe9e4cca4315"},"schema_version":"1.0"},"canonical_sha256":"3d07ee958b31ec9b4215f46da7ae96e439638507051677f832524571d7131739","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:51.269756Z","signature_b64":"l+lxdAb1MG7rlBEHmgPCvjMg/NHnqfPIb9fu5aTy53KrGt5rcQZZtqBUYFX/Lwd/HYpS2T+tyYiPSHRcsqivCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d07ee958b31ec9b4215f46da7ae96e439638507051677f832524571d7131739","last_reissued_at":"2026-05-18T03:33:51.265379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:51.265379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2665","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":"2026-05-18T03:33:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JmkfkfsFgCrwPUYsDPe6xct/qXZkHmRXnO7XPpuw/Ep7zHQsJyDBLhOXUmR0wsfgANNYnrG5h51kAfGAOAzEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:04:08.488339Z"},"content_sha256":"3b2af7ea7ee237c405b3d80f8fa8f1725ea96b342993961ed9dd774182f07931","schema_version":"1.0","event_id":"sha256:3b2af7ea7ee237c405b3d80f8fa8f1725ea96b342993961ed9dd774182f07931"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HUD65FMLGHWJWQQV6RW2PLUW4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Travelling waves in hybrid chemotaxis models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","q-bio.PE"],"primary_cat":"physics.bio-ph","authors_text":"Benjamin Franz, Chuan Xue, Kevin J. Painter, Radek Erban","submitted_at":"2013-02-11T23:03:38Z","abstract_excerpt":"Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant) which is modelled using a partial diff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2665","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":"2026-05-18T03:33:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0HlAtbTrAVJpWwMMLavlvQWhKVnkcQtr6k7up9vt3IsSAm/k9HU6NfNwdyefv4SMgez3PCnHX6NzIfbVPmJRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:04:08.488989Z"},"content_sha256":"230048765da8ae3fa38cd733196c96e2243fa19265bf65a0b28d53850d474c71","schema_version":"1.0","event_id":"sha256:230048765da8ae3fa38cd733196c96e2243fa19265bf65a0b28d53850d474c71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUD65FMLGHWJWQQV6RW2PLUW4Q/bundle.json","state_url":"https://pith.science/pith/HUD65FMLGHWJWQQV6RW2PLUW4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUD65FMLGHWJWQQV6RW2PLUW4Q/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":"2026-05-27T05:04:08Z","links":{"resolver":"https://pith.science/pith/HUD65FMLGHWJWQQV6RW2PLUW4Q","bundle":"https://pith.science/pith/HUD65FMLGHWJWQQV6RW2PLUW4Q/bundle.json","state":"https://pith.science/pith/HUD65FMLGHWJWQQV6RW2PLUW4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUD65FMLGHWJWQQV6RW2PLUW4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HUD65FMLGHWJWQQV6RW2PLUW4Q","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":"504993f3d91debc3c4ffe3f6aaf126b7dab2cc8b0d879a8fbdfbbe9e4cca4315","cross_cats_sorted":["math.AP","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-02-11T23:03:38Z","title_canon_sha256":"569aaae9e03aa94c4891a1b0bf7f85358197bf00f566b28d9334a7d923b59f07"},"schema_version":"1.0","source":{"id":"1302.2665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2665","created_at":"2026-05-18T03:33:51Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2665v1","created_at":"2026-05-18T03:33:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2665","created_at":"2026-05-18T03:33:51Z"},{"alias_kind":"pith_short_12","alias_value":"HUD65FMLGHWJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HUD65FMLGHWJWQQV","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HUD65FML","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:230048765da8ae3fa38cd733196c96e2243fa19265bf65a0b28d53850d474c71","target":"graph","created_at":"2026-05-18T03:33:51Z","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":"Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant) which is modelled using a partial diff","authors_text":"Benjamin Franz, Chuan Xue, Kevin J. Painter, Radek Erban","cross_cats":["math.AP","q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-02-11T23:03:38Z","title":"Travelling waves in hybrid chemotaxis models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2665","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":"sha256:3b2af7ea7ee237c405b3d80f8fa8f1725ea96b342993961ed9dd774182f07931","target":"record","created_at":"2026-05-18T03:33:51Z","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":"504993f3d91debc3c4ffe3f6aaf126b7dab2cc8b0d879a8fbdfbbe9e4cca4315","cross_cats_sorted":["math.AP","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2013-02-11T23:03:38Z","title_canon_sha256":"569aaae9e03aa94c4891a1b0bf7f85358197bf00f566b28d9334a7d923b59f07"},"schema_version":"1.0","source":{"id":"1302.2665","kind":"arxiv","version":1}},"canonical_sha256":"3d07ee958b31ec9b4215f46da7ae96e439638507051677f832524571d7131739","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d07ee958b31ec9b4215f46da7ae96e439638507051677f832524571d7131739","first_computed_at":"2026-05-18T03:33:51.265379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:51.265379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l+lxdAb1MG7rlBEHmgPCvjMg/NHnqfPIb9fu5aTy53KrGt5rcQZZtqBUYFX/Lwd/HYpS2T+tyYiPSHRcsqivCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:51.269756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b2af7ea7ee237c405b3d80f8fa8f1725ea96b342993961ed9dd774182f07931","sha256:230048765da8ae3fa38cd733196c96e2243fa19265bf65a0b28d53850d474c71"],"state_sha256":"e24f7bdcb32f25f50f95650b05f9dfe69f0c996915268f0f37eacb2e6869de5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HJ231nOu0gkJ2A7KEV3eiE/7lFzcOZ+0QLqyOEy3RFsemIO373crC5qbZih7YULgrE5XC/9jHA9+MyggmOL3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:04:08.492559Z","bundle_sha256":"5c3144a2c4f572d4a2f3b7854cdb01b600f1de810432f87278f7598901ea98d3"}}