{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:VM7OM5RQOQWXQ6PW7FKEU7GFWB","short_pith_number":"pith:VM7OM5RQ","schema_version":"1.0","canonical_sha256":"ab3ee67630742d7879f6f9544a7cc5b06142ed82c55fdea5e90c4215180c72b0","source":{"kind":"arxiv","id":"2605.19599","version":1},"attestation_state":"computed","paper":{"title":"Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Bao-Zhu Guo, Dong-Hui Yang","submitted_at":"2026-05-19T09:41:03Z","abstract_excerpt":"In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem, which acts as a framework for approximating the degenerate parabolic equation through a series of uniformly parabolic equations. Finally, as a tangible application of this shape design approach, we deduce a boundary observability inequality associated with the degenerate parabolic equation."},"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":"2605.19599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-19T09:41:03Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"28542cc80829b31e147c711f0419af0b2706794ede7fd8e8b2437b116ead9bdb","abstract_canon_sha256":"d54caed1a22dcc0d2799d44300a68eb494d0d18d625df845d7af27f9c1dc9cab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:53.676006Z","signature_b64":"ZcvS17pd1aj3MEwRU0jlhIgX+SKUBxgMLMvrKfRDvWHGOJzaJN55mhd0nhg4y6k0+g7CCQ/STnNKjXgcFV3eBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab3ee67630742d7879f6f9544a7cc5b06142ed82c55fdea5e90c4215180c72b0","last_reissued_at":"2026-05-20T01:05:53.675304Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:53.675304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Bao-Zhu Guo, Dong-Hui Yang","submitted_at":"2026-05-19T09:41:03Z","abstract_excerpt":"In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem, which acts as a framework for approximating the degenerate parabolic equation through a series of uniformly parabolic equations. Finally, as a tangible application of this shape design approach, we deduce a boundary observability inequality associated with the degenerate parabolic equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19599","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19599/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.19599","created_at":"2026-05-20T01:05:53.675428+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.19599v1","created_at":"2026-05-20T01:05:53.675428+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19599","created_at":"2026-05-20T01:05:53.675428+00:00"},{"alias_kind":"pith_short_12","alias_value":"VM7OM5RQOQWX","created_at":"2026-05-20T01:05:53.675428+00:00"},{"alias_kind":"pith_short_16","alias_value":"VM7OM5RQOQWXQ6PW","created_at":"2026-05-20T01:05:53.675428+00:00"},{"alias_kind":"pith_short_8","alias_value":"VM7OM5RQ","created_at":"2026-05-20T01:05:53.675428+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/VM7OM5RQOQWXQ6PW7FKEU7GFWB","json":"https://pith.science/pith/VM7OM5RQOQWXQ6PW7FKEU7GFWB.json","graph_json":"https://pith.science/api/pith-number/VM7OM5RQOQWXQ6PW7FKEU7GFWB/graph.json","events_json":"https://pith.science/api/pith-number/VM7OM5RQOQWXQ6PW7FKEU7GFWB/events.json","paper":"https://pith.science/paper/VM7OM5RQ"},"agent_actions":{"view_html":"https://pith.science/pith/VM7OM5RQOQWXQ6PW7FKEU7GFWB","download_json":"https://pith.science/pith/VM7OM5RQOQWXQ6PW7FKEU7GFWB.json","view_paper":"https://pith.science/paper/VM7OM5RQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.19599&json=true","fetch_graph":"https://pith.science/api/pith-number/VM7OM5RQOQWXQ6PW7FKEU7GFWB/graph.json","fetch_events":"https://pith.science/api/pith-number/VM7OM5RQOQWXQ6PW7FKEU7GFWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VM7OM5RQOQWXQ6PW7FKEU7GFWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VM7OM5RQOQWXQ6PW7FKEU7GFWB/action/storage_attestation","attest_author":"https://pith.science/pith/VM7OM5RQOQWXQ6PW7FKEU7GFWB/action/author_attestation","sign_citation":"https://pith.science/pith/VM7OM5RQOQWXQ6PW7FKEU7GFWB/action/citation_signature","submit_replication":"https://pith.science/pith/VM7OM5RQOQWXQ6PW7FKEU7GFWB/action/replication_record"}},"created_at":"2026-05-20T01:05:53.675428+00:00","updated_at":"2026-05-20T01:05:53.675428+00:00"}