{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q5IBQCFNJAFAYOC4KSNYO25O2P","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":"a36efb44852397ffa066f9cf8a83854e3930608a4c442a456b44321b3bec0ca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-20T11:18:40Z","title_canon_sha256":"018adddad6c21a15c1491518c8bc385f895cade4b674381fa60996572956aca5"},"schema_version":"1.0","source":{"id":"1408.4794","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4794","created_at":"2026-05-18T01:42:16Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4794v2","created_at":"2026-05-18T01:42:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4794","created_at":"2026-05-18T01:42:16Z"},{"alias_kind":"pith_short_12","alias_value":"Q5IBQCFNJAFA","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q5IBQCFNJAFAYOC4","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q5IBQCFN","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:0e0aaeb6e662c8491b20bca809d6e1044cf1731fec561e49e6de35e16f40cf3f","target":"graph","created_at":"2026-05-18T01:42:16Z","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 investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The system is given by a multi-phase flow model: the densities of the different cells are governed by a set of transport equations, the density of the nutrient and the density of the drug are governed by rather general diffusion equations, while the velocity of the tumor is given by Brinkman's equation. The domain occupied by the tumor in this setting is a growing co","authors_text":"Donatella Donatelli, Konstantina Trivisa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-20T11:18:40Z","title":"On a nonlinear model for tumor growth with drug application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4794","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:c47798682ed2790ee077cfc6ea5c7eec3cd69d85ff3a7360a1ded3c62b032930","target":"record","created_at":"2026-05-18T01:42:16Z","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":"a36efb44852397ffa066f9cf8a83854e3930608a4c442a456b44321b3bec0ca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-20T11:18:40Z","title_canon_sha256":"018adddad6c21a15c1491518c8bc385f895cade4b674381fa60996572956aca5"},"schema_version":"1.0","source":{"id":"1408.4794","kind":"arxiv","version":2}},"canonical_sha256":"87501808ad480a0c385c549b876baed3c535600c814365213db5b2b37759d9f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87501808ad480a0c385c549b876baed3c535600c814365213db5b2b37759d9f6","first_computed_at":"2026-05-18T01:42:16.559086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:16.559086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G7TbsyexRxAXWOR2p+2ZnkCNwzIY+P1YY1AC018RKoUrGursKE876Jh0GkuQDkEJr+BfnIPvTkSj1VNGpc5YDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:16.559639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4794","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c47798682ed2790ee077cfc6ea5c7eec3cd69d85ff3a7360a1ded3c62b032930","sha256:0e0aaeb6e662c8491b20bca809d6e1044cf1731fec561e49e6de35e16f40cf3f"],"state_sha256":"5b4bac186e78d172f20551e1bf0db786ec41dfd4d242cb7c0d4335dc9cd0e904"}