{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ROXQEZGP6KYGF5FAFV4WBTELCX","short_pith_number":"pith:ROXQEZGP","schema_version":"1.0","canonical_sha256":"8baf0264cff2b062f4a02d7960cc8b15d4f0a35dcb8d328355851611c60db644","source":{"kind":"arxiv","id":"1509.06287","version":1},"attestation_state":"computed","paper":{"title":"Porous medium equation to Hele-Shaw flow with general initial density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Inwon Kim, Norbert Pozar","submitted_at":"2015-09-21T16:10:40Z","abstract_excerpt":"In this paper we study the \"stiff pressure limit\" of the porous medium equation, where the initial density is a bounded, integrable function with a sufficient decay at infinity. Our particular model, introduced by Perthame-Quiros-Vazquez, describes the growth of a tumor zone with a restriction on the maximal cell density. In a general context, this extends previous results of Caffarelli-Vazquez and Kim who restrict the initial data to be the characteristic function of a compact set. In the limit a Hele-Shaw type problem is obtained, where the interface motion law reflects the acceleration effe"},"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":"1509.06287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-21T16:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"2d7c167a8f50746040b46350ccf4ab2b6193403e06cb272eac41663be830c539","abstract_canon_sha256":"f55002ff4b226be250af75dd739c6f71c0fe52b0ec965c1dd0517fc6a5f31eaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:35.396364Z","signature_b64":"RwreeH0AAiNkj8uA+pcgKkWWGK9M9ut/b74arvnVknFbmztfu5Ad9tjdmSfh5mcCs85K34DOH9jvUuvWMFcyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8baf0264cff2b062f4a02d7960cc8b15d4f0a35dcb8d328355851611c60db644","last_reissued_at":"2026-05-18T01:32:35.395751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:35.395751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Porous medium equation to Hele-Shaw flow with general initial density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Inwon Kim, Norbert Pozar","submitted_at":"2015-09-21T16:10:40Z","abstract_excerpt":"In this paper we study the \"stiff pressure limit\" of the porous medium equation, where the initial density is a bounded, integrable function with a sufficient decay at infinity. Our particular model, introduced by Perthame-Quiros-Vazquez, describes the growth of a tumor zone with a restriction on the maximal cell density. In a general context, this extends previous results of Caffarelli-Vazquez and Kim who restrict the initial data to be the characteristic function of a compact set. In the limit a Hele-Shaw type problem is obtained, where the interface motion law reflects the acceleration effe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06287","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":"1509.06287","created_at":"2026-05-18T01:32:35.395851+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.06287v1","created_at":"2026-05-18T01:32:35.395851+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06287","created_at":"2026-05-18T01:32:35.395851+00:00"},{"alias_kind":"pith_short_12","alias_value":"ROXQEZGP6KYG","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"ROXQEZGP6KYGF5FA","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"ROXQEZGP","created_at":"2026-05-18T12:29:39.896362+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/ROXQEZGP6KYGF5FAFV4WBTELCX","json":"https://pith.science/pith/ROXQEZGP6KYGF5FAFV4WBTELCX.json","graph_json":"https://pith.science/api/pith-number/ROXQEZGP6KYGF5FAFV4WBTELCX/graph.json","events_json":"https://pith.science/api/pith-number/ROXQEZGP6KYGF5FAFV4WBTELCX/events.json","paper":"https://pith.science/paper/ROXQEZGP"},"agent_actions":{"view_html":"https://pith.science/pith/ROXQEZGP6KYGF5FAFV4WBTELCX","download_json":"https://pith.science/pith/ROXQEZGP6KYGF5FAFV4WBTELCX.json","view_paper":"https://pith.science/paper/ROXQEZGP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.06287&json=true","fetch_graph":"https://pith.science/api/pith-number/ROXQEZGP6KYGF5FAFV4WBTELCX/graph.json","fetch_events":"https://pith.science/api/pith-number/ROXQEZGP6KYGF5FAFV4WBTELCX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ROXQEZGP6KYGF5FAFV4WBTELCX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ROXQEZGP6KYGF5FAFV4WBTELCX/action/storage_attestation","attest_author":"https://pith.science/pith/ROXQEZGP6KYGF5FAFV4WBTELCX/action/author_attestation","sign_citation":"https://pith.science/pith/ROXQEZGP6KYGF5FAFV4WBTELCX/action/citation_signature","submit_replication":"https://pith.science/pith/ROXQEZGP6KYGF5FAFV4WBTELCX/action/replication_record"}},"created_at":"2026-05-18T01:32:35.395851+00:00","updated_at":"2026-05-18T01:32:35.395851+00:00"}