{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:L66MPEYJSB3KN7OKP7Y2QG3MML","short_pith_number":"pith:L66MPEYJ","schema_version":"1.0","canonical_sha256":"5fbcc793099076a6fdca7ff1a81b6c62f4be8d227108188c1cc1cec977805781","source":{"kind":"arxiv","id":"1011.2114","version":2},"attestation_state":"computed","paper":{"title":"Spatial coagulation with bounded coagulation rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Ismael Bailleul","submitted_at":"2010-11-09T15:19:46Z","abstract_excerpt":"We prove that the spatial coagulation equation with bounded coagulation rate is well-posed for all times in a given class of kernels if the convection term of the underlying particle dynamics has divergence bounded below by a positive constant. Multiple coagulations, fragmentation and scattering are also considered."},"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":"1011.2114","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-11-09T15:19:46Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"fd24bd1a84ff4bb00892d606e7504cb37832006a4f814c7e1a798f604922b463","abstract_canon_sha256":"beb7e86213e4c983eaa8fbdc58d4b4a23f4cf529703955b02df0fc9ff82298d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:21.464006Z","signature_b64":"T+L8gAiM21nSqBi7lkI5NpeV+d50nI2wL5n8H0fA9HWIWqHJUdx+Bpg6Kc7Quv/E5HHZdm9wKQ3/LD5UYq+FAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fbcc793099076a6fdca7ff1a81b6c62f4be8d227108188c1cc1cec977805781","last_reissued_at":"2026-05-18T04:28:21.463443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:21.463443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spatial coagulation with bounded coagulation rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Ismael Bailleul","submitted_at":"2010-11-09T15:19:46Z","abstract_excerpt":"We prove that the spatial coagulation equation with bounded coagulation rate is well-posed for all times in a given class of kernels if the convection term of the underlying particle dynamics has divergence bounded below by a positive constant. Multiple coagulations, fragmentation and scattering are also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2114","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.2114","created_at":"2026-05-18T04:28:21.463569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.2114v2","created_at":"2026-05-18T04:28:21.463569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2114","created_at":"2026-05-18T04:28:21.463569+00:00"},{"alias_kind":"pith_short_12","alias_value":"L66MPEYJSB3K","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"L66MPEYJSB3KN7OK","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"L66MPEYJ","created_at":"2026-05-18T12:26:10.704358+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/L66MPEYJSB3KN7OKP7Y2QG3MML","json":"https://pith.science/pith/L66MPEYJSB3KN7OKP7Y2QG3MML.json","graph_json":"https://pith.science/api/pith-number/L66MPEYJSB3KN7OKP7Y2QG3MML/graph.json","events_json":"https://pith.science/api/pith-number/L66MPEYJSB3KN7OKP7Y2QG3MML/events.json","paper":"https://pith.science/paper/L66MPEYJ"},"agent_actions":{"view_html":"https://pith.science/pith/L66MPEYJSB3KN7OKP7Y2QG3MML","download_json":"https://pith.science/pith/L66MPEYJSB3KN7OKP7Y2QG3MML.json","view_paper":"https://pith.science/paper/L66MPEYJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.2114&json=true","fetch_graph":"https://pith.science/api/pith-number/L66MPEYJSB3KN7OKP7Y2QG3MML/graph.json","fetch_events":"https://pith.science/api/pith-number/L66MPEYJSB3KN7OKP7Y2QG3MML/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L66MPEYJSB3KN7OKP7Y2QG3MML/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L66MPEYJSB3KN7OKP7Y2QG3MML/action/storage_attestation","attest_author":"https://pith.science/pith/L66MPEYJSB3KN7OKP7Y2QG3MML/action/author_attestation","sign_citation":"https://pith.science/pith/L66MPEYJSB3KN7OKP7Y2QG3MML/action/citation_signature","submit_replication":"https://pith.science/pith/L66MPEYJSB3KN7OKP7Y2QG3MML/action/replication_record"}},"created_at":"2026-05-18T04:28:21.463569+00:00","updated_at":"2026-05-18T04:28:21.463569+00:00"}