{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RB2UWO54FTUXWINPLUT3PVWRHM","short_pith_number":"pith:RB2UWO54","schema_version":"1.0","canonical_sha256":"88754b3bbc2ce97b21af5d27b7d6d13b03b129c8483f8fd2e7dde6108c7ad2e9","source":{"kind":"arxiv","id":"1102.1902","version":2},"attestation_state":"computed","paper":{"title":"Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angel Castro, Charles Fefferman, Diego Cordoba, Francisco Gancedo, Maria Lopez-Fernandez","submitted_at":"2011-02-09T16:45:06Z","abstract_excerpt":"The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning."},"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":"1102.1902","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-09T16:45:06Z","cross_cats_sorted":[],"title_canon_sha256":"dbb14d3b80567a29102fb3ed446cb4202c9869336332e77c38a1541c5545edd9","abstract_canon_sha256":"bd67a0e36239c9a8cfa46518b929c1942fce875741448a7147f789aa328aa0d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:12.882897Z","signature_b64":"nVh0XiDJ5tAo3S5FOusEYWV6IDgphu1CPsY6BWdVc5pXUKsABFlxd1Hz064kVfQR9uGyFVbGrHxq/FTkZAHsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88754b3bbc2ce97b21af5d27b7d6d13b03b129c8483f8fd2e7dde6108c7ad2e9","last_reissued_at":"2026-05-18T04:20:12.882429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:12.882429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angel Castro, Charles Fefferman, Diego Cordoba, Francisco Gancedo, Maria Lopez-Fernandez","submitted_at":"2011-02-09T16:45:06Z","abstract_excerpt":"The Muskat problem models the evolution of the interface given by two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach the linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1902","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":"1102.1902","created_at":"2026-05-18T04:20:12.882499+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.1902v2","created_at":"2026-05-18T04:20:12.882499+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1902","created_at":"2026-05-18T04:20:12.882499+00:00"},{"alias_kind":"pith_short_12","alias_value":"RB2UWO54FTUX","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RB2UWO54FTUXWINP","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RB2UWO54","created_at":"2026-05-18T12:26:41.206345+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/RB2UWO54FTUXWINPLUT3PVWRHM","json":"https://pith.science/pith/RB2UWO54FTUXWINPLUT3PVWRHM.json","graph_json":"https://pith.science/api/pith-number/RB2UWO54FTUXWINPLUT3PVWRHM/graph.json","events_json":"https://pith.science/api/pith-number/RB2UWO54FTUXWINPLUT3PVWRHM/events.json","paper":"https://pith.science/paper/RB2UWO54"},"agent_actions":{"view_html":"https://pith.science/pith/RB2UWO54FTUXWINPLUT3PVWRHM","download_json":"https://pith.science/pith/RB2UWO54FTUXWINPLUT3PVWRHM.json","view_paper":"https://pith.science/paper/RB2UWO54","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.1902&json=true","fetch_graph":"https://pith.science/api/pith-number/RB2UWO54FTUXWINPLUT3PVWRHM/graph.json","fetch_events":"https://pith.science/api/pith-number/RB2UWO54FTUXWINPLUT3PVWRHM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RB2UWO54FTUXWINPLUT3PVWRHM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RB2UWO54FTUXWINPLUT3PVWRHM/action/storage_attestation","attest_author":"https://pith.science/pith/RB2UWO54FTUXWINPLUT3PVWRHM/action/author_attestation","sign_citation":"https://pith.science/pith/RB2UWO54FTUXWINPLUT3PVWRHM/action/citation_signature","submit_replication":"https://pith.science/pith/RB2UWO54FTUXWINPLUT3PVWRHM/action/replication_record"}},"created_at":"2026-05-18T04:20:12.882499+00:00","updated_at":"2026-05-18T04:20:12.882499+00:00"}