{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7EIE5MKLCS3OZMV66SYVKDNRZF","short_pith_number":"pith:7EIE5MKL","schema_version":"1.0","canonical_sha256":"f9104eb14b14b6ecb2bef4b1550db1c97df42a74c2d76253a391844e4853a4f9","source":{"kind":"arxiv","id":"1810.06909","version":1},"attestation_state":"computed","paper":{"title":"Global bounded and unbounded solutions to a chemotaxis system with indirect signal production","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Philippe Lauren\\c{c}ot (IMT)","submitted_at":"2018-10-16T10:06:05Z","abstract_excerpt":"The well-posedness of a chemotaxis system with indirect signal production in a two-dimensional domain is shown, all solutions being global unlike the classical Keller-Segel chemotaxis system. Nevertheless, there is a threshold value $M_c$ of the mass of the first component which separates two different behaviours: solutions are bounded when the mass is below $M_c$ while there are unbounded solutions starting from initial conditions having a mass exceeding $M_c$. This result extends to arbitrary two-dimensional domains a previous result of Tao \\& Winkler (2017) obtained for radially symmetric s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.06909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-16T10:06:05Z","cross_cats_sorted":[],"title_canon_sha256":"21edb18f94a7a8f4070dfa5ff1045768f42fc5c720d835b44e075a717ab15289","abstract_canon_sha256":"5dd3cbb70230f38de08524bafb046992947e0096593fac022d196cf578d12cec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:11.134044Z","signature_b64":"GfBbmBMTqsjSJ1kXhva0mIwr3BphbQ2yCzRXasZjgDvPNxRfUegALBlbIamCUw9nCKX8lctjeJRfqZgb44EUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9104eb14b14b6ecb2bef4b1550db1c97df42a74c2d76253a391844e4853a4f9","last_reissued_at":"2026-05-18T00:03:11.133377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:11.133377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global bounded and unbounded solutions to a chemotaxis system with indirect signal production","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Philippe Lauren\\c{c}ot (IMT)","submitted_at":"2018-10-16T10:06:05Z","abstract_excerpt":"The well-posedness of a chemotaxis system with indirect signal production in a two-dimensional domain is shown, all solutions being global unlike the classical Keller-Segel chemotaxis system. Nevertheless, there is a threshold value $M_c$ of the mass of the first component which separates two different behaviours: solutions are bounded when the mass is below $M_c$ while there are unbounded solutions starting from initial conditions having a mass exceeding $M_c$. This result extends to arbitrary two-dimensional domains a previous result of Tao \\& Winkler (2017) obtained for radially symmetric s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06909","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.06909","created_at":"2026-05-18T00:03:11.133485+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.06909v1","created_at":"2026-05-18T00:03:11.133485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06909","created_at":"2026-05-18T00:03:11.133485+00:00"},{"alias_kind":"pith_short_12","alias_value":"7EIE5MKLCS3O","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7EIE5MKLCS3OZMV6","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7EIE5MKL","created_at":"2026-05-18T12:32:11.075285+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF","json":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF.json","graph_json":"https://pith.science/api/pith-number/7EIE5MKLCS3OZMV66SYVKDNRZF/graph.json","events_json":"https://pith.science/api/pith-number/7EIE5MKLCS3OZMV66SYVKDNRZF/events.json","paper":"https://pith.science/paper/7EIE5MKL"},"agent_actions":{"view_html":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF","download_json":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF.json","view_paper":"https://pith.science/paper/7EIE5MKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.06909&json=true","fetch_graph":"https://pith.science/api/pith-number/7EIE5MKLCS3OZMV66SYVKDNRZF/graph.json","fetch_events":"https://pith.science/api/pith-number/7EIE5MKLCS3OZMV66SYVKDNRZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF/action/storage_attestation","attest_author":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF/action/author_attestation","sign_citation":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF/action/citation_signature","submit_replication":"https://pith.science/pith/7EIE5MKLCS3OZMV66SYVKDNRZF/action/replication_record"}},"created_at":"2026-05-18T00:03:11.133485+00:00","updated_at":"2026-05-18T00:03:11.133485+00:00"}