{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:PCMEPY7YFVSS7VXAAPYG7PJ4DZ","short_pith_number":"pith:PCMEPY7Y","schema_version":"1.0","canonical_sha256":"789847e3f82d652fd6e003f06fbd3c1e758cdc3285c8196838d285df36d02e66","source":{"kind":"arxiv","id":"1001.0410","version":2},"attestation_state":"computed","paper":{"title":"Nonlinear porous medium flow with fractional potential pressure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan L. Vazquez, Luis A. Caffarelli","submitted_at":"2010-01-03T21:08:28Z","abstract_excerpt":"We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove existence of a weak and bounded solution that propagates with finite speed, a property that is nor shared by other fractional diffusion models."},"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":"1001.0410","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-03T21:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"7f1937cfc1d596eb6e78eb28ead19fd087bef0c35f80a0fd70f76269ee438972","abstract_canon_sha256":"e2d5971e3a57e52c752a692f9d671d173d386abc9f380fcd762ac3cc86eb10f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:05.556988Z","signature_b64":"hY4kFIQlrALS94Oyp5JiTpsh9IYVSCqu5ovhJcuFHzABQqIeOQ8psPBfW7BNg/Qcs3YkJm9DnfAx90l7NtBFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"789847e3f82d652fd6e003f06fbd3c1e758cdc3285c8196838d285df36d02e66","last_reissued_at":"2026-05-18T02:10:05.556157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:05.556157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear porous medium flow with fractional potential pressure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan L. Vazquez, Luis A. Caffarelli","submitted_at":"2010-01-03T21:08:28Z","abstract_excerpt":"We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove existence of a weak and bounded solution that propagates with finite speed, a property that is nor shared by other fractional diffusion models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0410","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":"1001.0410","created_at":"2026-05-18T02:10:05.556288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.0410v2","created_at":"2026-05-18T02:10:05.556288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0410","created_at":"2026-05-18T02:10:05.556288+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCMEPY7YFVSS","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCMEPY7YFVSS7VXA","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCMEPY7Y","created_at":"2026-05-18T12:26:12.377268+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/PCMEPY7YFVSS7VXAAPYG7PJ4DZ","json":"https://pith.science/pith/PCMEPY7YFVSS7VXAAPYG7PJ4DZ.json","graph_json":"https://pith.science/api/pith-number/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/graph.json","events_json":"https://pith.science/api/pith-number/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/events.json","paper":"https://pith.science/paper/PCMEPY7Y"},"agent_actions":{"view_html":"https://pith.science/pith/PCMEPY7YFVSS7VXAAPYG7PJ4DZ","download_json":"https://pith.science/pith/PCMEPY7YFVSS7VXAAPYG7PJ4DZ.json","view_paper":"https://pith.science/paper/PCMEPY7Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.0410&json=true","fetch_graph":"https://pith.science/api/pith-number/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/action/storage_attestation","attest_author":"https://pith.science/pith/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/action/author_attestation","sign_citation":"https://pith.science/pith/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/action/citation_signature","submit_replication":"https://pith.science/pith/PCMEPY7YFVSS7VXAAPYG7PJ4DZ/action/replication_record"}},"created_at":"2026-05-18T02:10:05.556288+00:00","updated_at":"2026-05-18T02:10:05.556288+00:00"}