{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DCTT5IDJKJ576EKY25SL2EMTKE","short_pith_number":"pith:DCTT5IDJ","canonical_record":{"source":{"id":"1404.4769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-18T12:46:34Z","cross_cats_sorted":[],"title_canon_sha256":"f1a7dfc5342fc46d44b0809f0fb9dc65546e0b6607f9039746f8e4800ecc1a19","abstract_canon_sha256":"7b469a19c29e0f296277aeeb258af8622a374cbe89480778a6fd20c0a6972164"},"schema_version":"1.0"},"canonical_sha256":"18a73ea069527bff1158d764bd119351193f24bcbe672f22d5b21d91e8e54dc1","source":{"kind":"arxiv","id":"1404.4769","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4769","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4769v1","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4769","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"DCTT5IDJKJ57","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DCTT5IDJKJ576EKY","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DCTT5IDJ","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DCTT5IDJKJ576EKY25SL2EMTKE","target":"record","payload":{"canonical_record":{"source":{"id":"1404.4769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-18T12:46:34Z","cross_cats_sorted":[],"title_canon_sha256":"f1a7dfc5342fc46d44b0809f0fb9dc65546e0b6607f9039746f8e4800ecc1a19","abstract_canon_sha256":"7b469a19c29e0f296277aeeb258af8622a374cbe89480778a6fd20c0a6972164"},"schema_version":"1.0"},"canonical_sha256":"18a73ea069527bff1158d764bd119351193f24bcbe672f22d5b21d91e8e54dc1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:55.017250Z","signature_b64":"fOb6zFq9e4tH+Yos+5H8/HifIqxLBvGNXgtKrMQYhKWKT5S2Tq3vrlnJeFpTbA0DqREuEyBQ3JCw+//QnTEcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18a73ea069527bff1158d764bd119351193f24bcbe672f22d5b21d91e8e54dc1","last_reissued_at":"2026-05-18T02:53:55.016431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:55.016431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.4769","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":"2026-05-18T02:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Lm9bUSfPv44YRRRpGoLdJAybTsk1lpGvzHbuHqMJvm8Hr0p5LZ3k0FVXBWQzhf1O2hiLItGP/RYJBbiVRFYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:38:38.872602Z"},"content_sha256":"539ba0ec7d8898e9d0594f25b5bff47ff2f01ca0966d1f41bce4b780492a5ffd","schema_version":"1.0","event_id":"sha256:539ba0ec7d8898e9d0594f25b5bff47ff2f01ca0966d1f41bce4b780492a5ffd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DCTT5IDJKJ576EKY25SL2EMTKE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and diffusive limit of a two-species kinetic model of chemotaxis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Casimir Emako (LJLL), INRIA-Paris-Rocquencourt), Lu\\'is Almeida (LJLL, Nicolas Vauchelet (LJLL","submitted_at":"2014-04-18T12:46:34Z","abstract_excerpt":"In this paper, we propose a kinetic model describing the collective motion by chemotaxis of two species in interaction emitting the same chemoattractant. Such model can be seen as a generalisation to several species of the Othmer-Dunbar-Alt model which takes into account the run-and-tumble process of bacteria. Existence of weak solutions for this two-species kinetic model is studied and the convergence of its diffusive limit towards a macroscopic model of Keller-Segel type is analysed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4769","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":"2026-05-18T02:53:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KLsw2EmfZKYS3+/QkMkBu0c+Lz3dXYiUVJznRz3fpoKqKJYe2toHIzxBtOJwE2yP/G19ds077P0WEbm1ZP2LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:38:38.873265Z"},"content_sha256":"bbe8b3cc6d5fc0fbf96c9e13ce8bf942127dd53737055f56a90e485cd511a77c","schema_version":"1.0","event_id":"sha256:bbe8b3cc6d5fc0fbf96c9e13ce8bf942127dd53737055f56a90e485cd511a77c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DCTT5IDJKJ576EKY25SL2EMTKE/bundle.json","state_url":"https://pith.science/pith/DCTT5IDJKJ576EKY25SL2EMTKE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DCTT5IDJKJ576EKY25SL2EMTKE/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":"2026-05-27T11:38:38Z","links":{"resolver":"https://pith.science/pith/DCTT5IDJKJ576EKY25SL2EMTKE","bundle":"https://pith.science/pith/DCTT5IDJKJ576EKY25SL2EMTKE/bundle.json","state":"https://pith.science/pith/DCTT5IDJKJ576EKY25SL2EMTKE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DCTT5IDJKJ576EKY25SL2EMTKE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DCTT5IDJKJ576EKY25SL2EMTKE","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":"7b469a19c29e0f296277aeeb258af8622a374cbe89480778a6fd20c0a6972164","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-18T12:46:34Z","title_canon_sha256":"f1a7dfc5342fc46d44b0809f0fb9dc65546e0b6607f9039746f8e4800ecc1a19"},"schema_version":"1.0","source":{"id":"1404.4769","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4769","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4769v1","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4769","created_at":"2026-05-18T02:53:55Z"},{"alias_kind":"pith_short_12","alias_value":"DCTT5IDJKJ57","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DCTT5IDJKJ576EKY","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DCTT5IDJ","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:bbe8b3cc6d5fc0fbf96c9e13ce8bf942127dd53737055f56a90e485cd511a77c","target":"graph","created_at":"2026-05-18T02:53:55Z","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":"In this paper, we propose a kinetic model describing the collective motion by chemotaxis of two species in interaction emitting the same chemoattractant. Such model can be seen as a generalisation to several species of the Othmer-Dunbar-Alt model which takes into account the run-and-tumble process of bacteria. Existence of weak solutions for this two-species kinetic model is studied and the convergence of its diffusive limit towards a macroscopic model of Keller-Segel type is analysed.","authors_text":"Casimir Emako (LJLL), INRIA-Paris-Rocquencourt), Lu\\'is Almeida (LJLL, Nicolas Vauchelet (LJLL","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-18T12:46:34Z","title":"Existence and diffusive limit of a two-species kinetic model of chemotaxis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4769","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":"sha256:539ba0ec7d8898e9d0594f25b5bff47ff2f01ca0966d1f41bce4b780492a5ffd","target":"record","created_at":"2026-05-18T02:53:55Z","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":"7b469a19c29e0f296277aeeb258af8622a374cbe89480778a6fd20c0a6972164","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-18T12:46:34Z","title_canon_sha256":"f1a7dfc5342fc46d44b0809f0fb9dc65546e0b6607f9039746f8e4800ecc1a19"},"schema_version":"1.0","source":{"id":"1404.4769","kind":"arxiv","version":1}},"canonical_sha256":"18a73ea069527bff1158d764bd119351193f24bcbe672f22d5b21d91e8e54dc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18a73ea069527bff1158d764bd119351193f24bcbe672f22d5b21d91e8e54dc1","first_computed_at":"2026-05-18T02:53:55.016431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:55.016431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fOb6zFq9e4tH+Yos+5H8/HifIqxLBvGNXgtKrMQYhKWKT5S2Tq3vrlnJeFpTbA0DqREuEyBQ3JCw+//QnTEcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:55.017250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4769","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:539ba0ec7d8898e9d0594f25b5bff47ff2f01ca0966d1f41bce4b780492a5ffd","sha256:bbe8b3cc6d5fc0fbf96c9e13ce8bf942127dd53737055f56a90e485cd511a77c"],"state_sha256":"2d97c95a185ed37144a69a35df2316d45ffd225040fc96be5f0820431f48fef0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJRxHwHidpsh/6+N5b/FaVIG8r4A518TMvEfsKgFqSJbTM3qSKMjk30X4hwRBEBMbuCxkze0+G5t5Al/FErmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:38:38.877293Z","bundle_sha256":"5b998470063af6c3667ac6b12c50db7f9767ca26c7035a57c5995a93b5145cd4"}}