{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BKP35AGIEU4DWGGYO5IOBHQBT4","short_pith_number":"pith:BKP35AGI","schema_version":"1.0","canonical_sha256":"0a9fbe80c825383b18d87750e09e019f36ef21f0834e925729ca6756f6d90cf9","source":{"kind":"arxiv","id":"2605.14770","version":1},"attestation_state":"computed","paper":{"title":"A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Convection--Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chunmei Wang, Shangyou Zhang","submitted_at":"2026-05-14T12:36:24Z","abstract_excerpt":"We introduce and rigorously analyze a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem of convection--diffusion equations. The proposed framework utilizes weak derivatives defined on a class of discontinuous weak functions, enabling the natural treatment of complex boundary conditions and internal interfaces. A key advantage of the least-squares formulation is that it transforms the underlying non-self-adjoint operator into a discrete linear system that is inherently symmetric and positive definite (SPD). We demonstrate the geometric flexibili"},"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":"2605.14770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-05-14T12:36:24Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"f92870f3d9a8e3e0081f638d97193b56986e12baa3c83ae29795725278ed2778","abstract_canon_sha256":"392c453c80b658e955afc2ea0a8168ce7504e835aac8cb9a306fd5dfb4609743"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:38:58.664375Z","signature_b64":"YdQiJNJHPULQN6jb+3TaaZrhvkFZcz/HaKtdaIs1kKaKa10bDjUzMdVIo810ZNXWVpCjEB6BT5y/F21y92p5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a9fbe80c825383b18d87750e09e019f36ef21f0834e925729ca6756f6d90cf9","last_reissued_at":"2026-05-17T23:38:58.663680Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:38:58.663680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Convection--Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chunmei Wang, Shangyou Zhang","submitted_at":"2026-05-14T12:36:24Z","abstract_excerpt":"We introduce and rigorously analyze a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem of convection--diffusion equations. The proposed framework utilizes weak derivatives defined on a class of discontinuous weak functions, enabling the natural treatment of complex boundary conditions and internal interfaces. A key advantage of the least-squares formulation is that it transforms the underlying non-self-adjoint operator into a discrete linear system that is inherently symmetric and positive definite (SPD). We demonstrate the geometric flexibili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14770","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":"2605.14770","created_at":"2026-05-17T23:38:58.663791+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14770v1","created_at":"2026-05-17T23:38:58.663791+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14770","created_at":"2026-05-17T23:38:58.663791+00:00"},{"alias_kind":"pith_short_12","alias_value":"BKP35AGIEU4D","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"BKP35AGIEU4DWGGY","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"BKP35AGI","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.21162","citing_title":"A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Helmholtz","ref_index":50,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4","json":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4.json","graph_json":"https://pith.science/api/pith-number/BKP35AGIEU4DWGGYO5IOBHQBT4/graph.json","events_json":"https://pith.science/api/pith-number/BKP35AGIEU4DWGGYO5IOBHQBT4/events.json","paper":"https://pith.science/paper/BKP35AGI"},"agent_actions":{"view_html":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4","download_json":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4.json","view_paper":"https://pith.science/paper/BKP35AGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14770&json=true","fetch_graph":"https://pith.science/api/pith-number/BKP35AGIEU4DWGGYO5IOBHQBT4/graph.json","fetch_events":"https://pith.science/api/pith-number/BKP35AGIEU4DWGGYO5IOBHQBT4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4/action/storage_attestation","attest_author":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4/action/author_attestation","sign_citation":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4/action/citation_signature","submit_replication":"https://pith.science/pith/BKP35AGIEU4DWGGYO5IOBHQBT4/action/replication_record"}},"created_at":"2026-05-17T23:38:58.663791+00:00","updated_at":"2026-05-17T23:38:58.663791+00:00"}