{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:F2RL4HZISUURXYZ3YAKMTQ3D5P","short_pith_number":"pith:F2RL4HZI","canonical_record":{"source":{"id":"1012.0786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-12-03T16:49:21Z","cross_cats_sorted":["math-ph","math.MP","physics.bio-ph","q-bio.QM"],"title_canon_sha256":"98481a10cfe98cf22967112adf8257bbf5f477d8ed7f8042f12d99d0cb0f769e","abstract_canon_sha256":"6939e391d15839ea76c8e893406a2e85cdbc2582fede7c6324b30a7a213c50fa"},"schema_version":"1.0"},"canonical_sha256":"2ea2be1f2895291be33bc014c9c363ebf0041cb1ec1413047281167394e019a0","source":{"kind":"arxiv","id":"1012.0786","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0786","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0786v2","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0786","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"F2RL4HZISUUR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F2RL4HZISUURXYZ3","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F2RL4HZI","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:F2RL4HZISUURXYZ3YAKMTQ3D5P","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-12-03T16:49:21Z","cross_cats_sorted":["math-ph","math.MP","physics.bio-ph","q-bio.QM"],"title_canon_sha256":"98481a10cfe98cf22967112adf8257bbf5f477d8ed7f8042f12d99d0cb0f769e","abstract_canon_sha256":"6939e391d15839ea76c8e893406a2e85cdbc2582fede7c6324b30a7a213c50fa"},"schema_version":"1.0"},"canonical_sha256":"2ea2be1f2895291be33bc014c9c363ebf0041cb1ec1413047281167394e019a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:16.143402Z","signature_b64":"0WxmcqYryqKsbYEak0arLbfvuRfXOEhMgibYSoeis3Al2uLOTFX5yy5m79tr5hfxkxCdk/x34oFe+fp53tSNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ea2be1f2895291be33bc014c9c363ebf0041cb1ec1413047281167394e019a0","last_reissued_at":"2026-05-18T02:23:16.142856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:16.142856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0786","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":"2026-05-18T02:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jT90yAdLAsSTVT9GTwLBkeYtfCJQgpeD9Yj/rI5p82rXmNfhitsYLNgVdjkYA/ClrZK/5hYHGdtJV4XlO57fAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T14:59:03.197491Z"},"content_sha256":"18fba37b23cacc0e03093b7ebe03e54aa82595a8bcce65757e16850d4e3f3f6c","schema_version":"1.0","event_id":"sha256:18fba37b23cacc0e03093b7ebe03e54aa82595a8bcce65757e16850d4e3f3f6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:F2RL4HZISUURXYZ3YAKMTQ3D5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattice Models of Nonequilibrium Bacterial Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.bio-ph","q-bio.QM"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. G. Thompson, J. Tailleur, M. E. Cates, R. A. Blythe","submitted_at":"2010-12-03T16:49:21Z","abstract_excerpt":"We study a model of self propelled particles exhibiting run and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run and tumble dynamics. We solve the externally driven non-interacting and zero-rang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0786","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":"2026-05-18T02:23:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vg7Rvd6hFHZkeZrDMNF5C77NiqL+jOzhBdoiaYKOJQXxoguNGpKmjSLeZujvjIJcuzxV2NYyf0u7NDDZs/o/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T14:59:03.197836Z"},"content_sha256":"0494a3fe811fa68dace64c1a5ce434734e71c79bf40bf41076a8e2e075574883","schema_version":"1.0","event_id":"sha256:0494a3fe811fa68dace64c1a5ce434734e71c79bf40bf41076a8e2e075574883"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2RL4HZISUURXYZ3YAKMTQ3D5P/bundle.json","state_url":"https://pith.science/pith/F2RL4HZISUURXYZ3YAKMTQ3D5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2RL4HZISUURXYZ3YAKMTQ3D5P/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":"2026-06-25T14:59:03Z","links":{"resolver":"https://pith.science/pith/F2RL4HZISUURXYZ3YAKMTQ3D5P","bundle":"https://pith.science/pith/F2RL4HZISUURXYZ3YAKMTQ3D5P/bundle.json","state":"https://pith.science/pith/F2RL4HZISUURXYZ3YAKMTQ3D5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2RL4HZISUURXYZ3YAKMTQ3D5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:F2RL4HZISUURXYZ3YAKMTQ3D5P","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":"6939e391d15839ea76c8e893406a2e85cdbc2582fede7c6324b30a7a213c50fa","cross_cats_sorted":["math-ph","math.MP","physics.bio-ph","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-12-03T16:49:21Z","title_canon_sha256":"98481a10cfe98cf22967112adf8257bbf5f477d8ed7f8042f12d99d0cb0f769e"},"schema_version":"1.0","source":{"id":"1012.0786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0786","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0786v2","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0786","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"F2RL4HZISUUR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F2RL4HZISUURXYZ3","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F2RL4HZI","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:0494a3fe811fa68dace64c1a5ce434734e71c79bf40bf41076a8e2e075574883","target":"graph","created_at":"2026-05-18T02:23:16Z","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 study a model of self propelled particles exhibiting run and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run and tumble dynamics. We solve the externally driven non-interacting and zero-rang","authors_text":"A. G. Thompson, J. Tailleur, M. E. Cates, R. A. Blythe","cross_cats":["math-ph","math.MP","physics.bio-ph","q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-12-03T16:49:21Z","title":"Lattice Models of Nonequilibrium Bacterial Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0786","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":"sha256:18fba37b23cacc0e03093b7ebe03e54aa82595a8bcce65757e16850d4e3f3f6c","target":"record","created_at":"2026-05-18T02:23:16Z","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":"6939e391d15839ea76c8e893406a2e85cdbc2582fede7c6324b30a7a213c50fa","cross_cats_sorted":["math-ph","math.MP","physics.bio-ph","q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-12-03T16:49:21Z","title_canon_sha256":"98481a10cfe98cf22967112adf8257bbf5f477d8ed7f8042f12d99d0cb0f769e"},"schema_version":"1.0","source":{"id":"1012.0786","kind":"arxiv","version":2}},"canonical_sha256":"2ea2be1f2895291be33bc014c9c363ebf0041cb1ec1413047281167394e019a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ea2be1f2895291be33bc014c9c363ebf0041cb1ec1413047281167394e019a0","first_computed_at":"2026-05-18T02:23:16.142856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:16.142856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0WxmcqYryqKsbYEak0arLbfvuRfXOEhMgibYSoeis3Al2uLOTFX5yy5m79tr5hfxkxCdk/x34oFe+fp53tSNBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:16.143402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18fba37b23cacc0e03093b7ebe03e54aa82595a8bcce65757e16850d4e3f3f6c","sha256:0494a3fe811fa68dace64c1a5ce434734e71c79bf40bf41076a8e2e075574883"],"state_sha256":"b88cea9fbeb6989226a8fbe193e2fda6159d005c6dfa4a2114298ce1917db88e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ZYmkAShCtH0pgCM47IiKDUtNE9aSV+eibwA4cu+hEEQWiMtqNkHgBtk+zr3tt5na8fSkJCHifzc6I9YsIx2Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T14:59:03.199769Z","bundle_sha256":"037466b393fceeb37299ea94a8c8e54ade83b916345c59a14e7d49685b06df4b"}}