{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6HXACGCWHITH2OAKVBM3T7ZTJJ","short_pith_number":"pith:6HXACGCW","schema_version":"1.0","canonical_sha256":"f1ee0118563a267d380aa859b9ff334a4ba338dec04c3a3e0281f48b998453a2","source":{"kind":"arxiv","id":"1610.06303","version":2},"attestation_state":"computed","paper":{"title":"Weak Solution of a Doubly Degenerate Parabolic Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Di Kang, Jialun Zhang, Tharathep Sangsawang","submitted_at":"2016-10-20T07:08:31Z","abstract_excerpt":"This paper studies a fourth-order, nonlinear, doubly-degenerate parabolic equation derived from the thin film equation in spherical geometry. A regularization method is used to study the equation and several useful estimates are obtained. The main result of this paper is to prove the existence of a weak solution of the equation in a weighted Sobolev space."},"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":"1610.06303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T07:08:31Z","cross_cats_sorted":[],"title_canon_sha256":"8b337181e13797ab6ea238271d9dbb688ccdc519e8e4f6628a6375c9d0df992a","abstract_canon_sha256":"149a373493dd17ccf9d7f6078206ed968d82daffc7559c61d1778b833aabca56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:46.761235Z","signature_b64":"HD21T269iU+V6sfg2326U6z9Tdoby7mpC2SXIRvoia9QxYqaGtCnXoGSlDSTj0AhTlToGGmDfo0jSeKcDs42DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1ee0118563a267d380aa859b9ff334a4ba338dec04c3a3e0281f48b998453a2","last_reissued_at":"2026-05-18T00:49:46.760643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:46.760643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak Solution of a Doubly Degenerate Parabolic Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Di Kang, Jialun Zhang, Tharathep Sangsawang","submitted_at":"2016-10-20T07:08:31Z","abstract_excerpt":"This paper studies a fourth-order, nonlinear, doubly-degenerate parabolic equation derived from the thin film equation in spherical geometry. A regularization method is used to study the equation and several useful estimates are obtained. The main result of this paper is to prove the existence of a weak solution of the equation in a weighted Sobolev space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06303","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":"1610.06303","created_at":"2026-05-18T00:49:46.760721+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06303v2","created_at":"2026-05-18T00:49:46.760721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06303","created_at":"2026-05-18T00:49:46.760721+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HXACGCWHITH","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HXACGCWHITH2OAK","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HXACGCW","created_at":"2026-05-18T12:30:01.593930+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/6HXACGCWHITH2OAKVBM3T7ZTJJ","json":"https://pith.science/pith/6HXACGCWHITH2OAKVBM3T7ZTJJ.json","graph_json":"https://pith.science/api/pith-number/6HXACGCWHITH2OAKVBM3T7ZTJJ/graph.json","events_json":"https://pith.science/api/pith-number/6HXACGCWHITH2OAKVBM3T7ZTJJ/events.json","paper":"https://pith.science/paper/6HXACGCW"},"agent_actions":{"view_html":"https://pith.science/pith/6HXACGCWHITH2OAKVBM3T7ZTJJ","download_json":"https://pith.science/pith/6HXACGCWHITH2OAKVBM3T7ZTJJ.json","view_paper":"https://pith.science/paper/6HXACGCW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06303&json=true","fetch_graph":"https://pith.science/api/pith-number/6HXACGCWHITH2OAKVBM3T7ZTJJ/graph.json","fetch_events":"https://pith.science/api/pith-number/6HXACGCWHITH2OAKVBM3T7ZTJJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HXACGCWHITH2OAKVBM3T7ZTJJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HXACGCWHITH2OAKVBM3T7ZTJJ/action/storage_attestation","attest_author":"https://pith.science/pith/6HXACGCWHITH2OAKVBM3T7ZTJJ/action/author_attestation","sign_citation":"https://pith.science/pith/6HXACGCWHITH2OAKVBM3T7ZTJJ/action/citation_signature","submit_replication":"https://pith.science/pith/6HXACGCWHITH2OAKVBM3T7ZTJJ/action/replication_record"}},"created_at":"2026-05-18T00:49:46.760721+00:00","updated_at":"2026-05-18T00:49:46.760721+00:00"}