{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2MIADCQBB55GRN3ME2XFFEW3JT","short_pith_number":"pith:2MIADCQB","schema_version":"1.0","canonical_sha256":"d310018a010f7a68b76c26ae5292db4ce2a791d02e7fcb6eb7f4b03d5d82e094","source":{"kind":"arxiv","id":"2605.14732","version":1},"attestation_state":"computed","paper":{"title":"Compact Embedding Theorem Associated with Classical Weight {Functions} in Two Variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B.J. Nkwamouo, J.L. Woukeng, M.K. Nangho","submitted_at":"2026-05-14T11:56:10Z","abstract_excerpt":"For a classical weight function $\\rho$ defined on a simply connected open subset $\\Omega$ of $\\mathbb{R}^2$ (either bounded or unbounded) with piecewise $C^1$ boundary, we prove density and compact embedding of a matrix-weighted Sobolev space in the weighted Lebesgue space $L^2(\\Omega,\\, \\rho)$. As an application, we investigate {via a variational} method, eigenvalue problem of a degenerate Helmholtz operator on triangle."},"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":"2605.14732","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-14T11:56:10Z","cross_cats_sorted":[],"title_canon_sha256":"2f154d20dc4625b91592d0eecf941932fecf1d4ba44d9ba8df9116ba114436f6","abstract_canon_sha256":"4eb856e73a4207023d1b5deed95dd96185cf977228431e7112ecea7f8ef2d65b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:38:59.014082Z","signature_b64":"bv/WlaC8GUXDfCIx2AQ5A8IzhAhNxVwG8zB+c+YuqLe/b1EOougpn9pvlINppOxTNXzByalS28er0PxVIXNLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d310018a010f7a68b76c26ae5292db4ce2a791d02e7fcb6eb7f4b03d5d82e094","last_reissued_at":"2026-05-17T23:38:59.013389Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:38:59.013389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compact Embedding Theorem Associated with Classical Weight {Functions} in Two Variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B.J. Nkwamouo, J.L. Woukeng, M.K. Nangho","submitted_at":"2026-05-14T11:56:10Z","abstract_excerpt":"For a classical weight function $\\rho$ defined on a simply connected open subset $\\Omega$ of $\\mathbb{R}^2$ (either bounded or unbounded) with piecewise $C^1$ boundary, we prove density and compact embedding of a matrix-weighted Sobolev space in the weighted Lebesgue space $L^2(\\Omega,\\, \\rho)$. As an application, we investigate {via a variational} method, eigenvalue problem of a degenerate Helmholtz operator on triangle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14732","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":"2605.14732","created_at":"2026-05-17T23:38:59.013506+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14732v1","created_at":"2026-05-17T23:38:59.013506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14732","created_at":"2026-05-17T23:38:59.013506+00:00"},{"alias_kind":"pith_short_12","alias_value":"2MIADCQBB55G","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"2MIADCQBB55GRN3M","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"2MIADCQB","created_at":"2026-05-18T12:33:37.589309+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/2MIADCQBB55GRN3ME2XFFEW3JT","json":"https://pith.science/pith/2MIADCQBB55GRN3ME2XFFEW3JT.json","graph_json":"https://pith.science/api/pith-number/2MIADCQBB55GRN3ME2XFFEW3JT/graph.json","events_json":"https://pith.science/api/pith-number/2MIADCQBB55GRN3ME2XFFEW3JT/events.json","paper":"https://pith.science/paper/2MIADCQB"},"agent_actions":{"view_html":"https://pith.science/pith/2MIADCQBB55GRN3ME2XFFEW3JT","download_json":"https://pith.science/pith/2MIADCQBB55GRN3ME2XFFEW3JT.json","view_paper":"https://pith.science/paper/2MIADCQB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14732&json=true","fetch_graph":"https://pith.science/api/pith-number/2MIADCQBB55GRN3ME2XFFEW3JT/graph.json","fetch_events":"https://pith.science/api/pith-number/2MIADCQBB55GRN3ME2XFFEW3JT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2MIADCQBB55GRN3ME2XFFEW3JT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2MIADCQBB55GRN3ME2XFFEW3JT/action/storage_attestation","attest_author":"https://pith.science/pith/2MIADCQBB55GRN3ME2XFFEW3JT/action/author_attestation","sign_citation":"https://pith.science/pith/2MIADCQBB55GRN3ME2XFFEW3JT/action/citation_signature","submit_replication":"https://pith.science/pith/2MIADCQBB55GRN3ME2XFFEW3JT/action/replication_record"}},"created_at":"2026-05-17T23:38:59.013506+00:00","updated_at":"2026-05-17T23:38:59.013506+00:00"}