{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HM5W4JASBLRDAHV644423H6B5H","short_pith_number":"pith:HM5W4JAS","schema_version":"1.0","canonical_sha256":"3b3b6e24120ae2301ebee739ad9fc1e9ec88a2d036ccc75e6c4432e343c9e7f4","source":{"kind":"arxiv","id":"1408.4606","version":2},"attestation_state":"computed","paper":{"title":"On a nonlinear model for tumor growth in a cellular medium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Donatella Donatelli, Konstantina Trivisa","submitted_at":"2014-08-20T11:13:19Z","abstract_excerpt":"We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the \"tumor\" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a collection of cells accounting for the \"waste\" and/or dead cells in the presence of a nutrient. Here, the tumor is thought of as a growing continuum $\\Omega$ with boundary $\\partial \\Omega$ both of which evolve in time. The key characteristic of the present model is that the total density of cancerous cells is allowed to vary, which is often the case within cell"},"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":"1408.4606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-20T11:13:19Z","cross_cats_sorted":[],"title_canon_sha256":"17bba49c46103c1fb55d41e749699b7437aa712692c4c26724657f195d8d060f","abstract_canon_sha256":"a42570af37262962f23cea4736589d8b54238c30417113e819bf3f59cf178330"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:10.179829Z","signature_b64":"wmnfDUvWDyCMHW08HeJr67Utbbno3Ppfbbi9nOEL/IKPxHo8w2HgfrJWLA8TWlqKnODgfePs0aGH6d7ri4QaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b3b6e24120ae2301ebee739ad9fc1e9ec88a2d036ccc75e6c4432e343c9e7f4","last_reissued_at":"2026-05-18T02:20:10.179207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:10.179207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a nonlinear model for tumor growth in a cellular medium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Donatella Donatelli, Konstantina Trivisa","submitted_at":"2014-08-20T11:13:19Z","abstract_excerpt":"We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the \"tumor\" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a collection of cells accounting for the \"waste\" and/or dead cells in the presence of a nutrient. Here, the tumor is thought of as a growing continuum $\\Omega$ with boundary $\\partial \\Omega$ both of which evolve in time. The key characteristic of the present model is that the total density of cancerous cells is allowed to vary, which is often the case within cell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4606","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":"1408.4606","created_at":"2026-05-18T02:20:10.179309+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.4606v2","created_at":"2026-05-18T02:20:10.179309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4606","created_at":"2026-05-18T02:20:10.179309+00:00"},{"alias_kind":"pith_short_12","alias_value":"HM5W4JASBLRD","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HM5W4JASBLRDAHV6","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HM5W4JAS","created_at":"2026-05-18T12:28:30.664211+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/HM5W4JASBLRDAHV644423H6B5H","json":"https://pith.science/pith/HM5W4JASBLRDAHV644423H6B5H.json","graph_json":"https://pith.science/api/pith-number/HM5W4JASBLRDAHV644423H6B5H/graph.json","events_json":"https://pith.science/api/pith-number/HM5W4JASBLRDAHV644423H6B5H/events.json","paper":"https://pith.science/paper/HM5W4JAS"},"agent_actions":{"view_html":"https://pith.science/pith/HM5W4JASBLRDAHV644423H6B5H","download_json":"https://pith.science/pith/HM5W4JASBLRDAHV644423H6B5H.json","view_paper":"https://pith.science/paper/HM5W4JAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.4606&json=true","fetch_graph":"https://pith.science/api/pith-number/HM5W4JASBLRDAHV644423H6B5H/graph.json","fetch_events":"https://pith.science/api/pith-number/HM5W4JASBLRDAHV644423H6B5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HM5W4JASBLRDAHV644423H6B5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HM5W4JASBLRDAHV644423H6B5H/action/storage_attestation","attest_author":"https://pith.science/pith/HM5W4JASBLRDAHV644423H6B5H/action/author_attestation","sign_citation":"https://pith.science/pith/HM5W4JASBLRDAHV644423H6B5H/action/citation_signature","submit_replication":"https://pith.science/pith/HM5W4JASBLRDAHV644423H6B5H/action/replication_record"}},"created_at":"2026-05-18T02:20:10.179309+00:00","updated_at":"2026-05-18T02:20:10.179309+00:00"}