{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UMI6OWXFQACVKOYLBYC42GHDRW","short_pith_number":"pith:UMI6OWXF","schema_version":"1.0","canonical_sha256":"a311e75ae58005553b0b0e05cd18e38d845a3033b2c9e895e4566dacf724b64e","source":{"kind":"arxiv","id":"1808.03133","version":1},"attestation_state":"computed","paper":{"title":"Revisiting the Decoupling of Elastic Waves From a Weak Formulation Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Jingni Xiao, Junjiang Lai, Yifeng Xu","submitted_at":"2018-08-09T12:59:39Z","abstract_excerpt":"Elastic scattering governed by the Lame system associated with the third-type or fourth-type boundary condition is considered. It was shown in [8] by two of the authors that under suitable geometric conditions on the boundary surface of the elastic inclusion, the longitudinal and shear waves can be decoupled. The decoupling result in [8] was derived based on analyzing the local boundary behaviours of the elastic fields. In this article, we provide a different argument from a variational perspective in proving the decoupling result."},"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":"1808.03133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-09T12:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"6077c9607504af6f2b18dd0c5911e41cb964fcf74e5b6b1dc948de7bcf750219","abstract_canon_sha256":"4e1f5aefaca3e6833681a9a1e0ef47bd59114ecf6990bf1ef540340035af0c33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:09.561654Z","signature_b64":"p6Rbk57vx4+IHqrnh3D2QXq+eOYByY5wXBV0wUNPVU2R585OY5Vdq71ft5On/DamD+JVPYnIa/GTEMBKlsP1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a311e75ae58005553b0b0e05cd18e38d845a3033b2c9e895e4566dacf724b64e","last_reissued_at":"2026-05-17T23:46:09.560999Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:09.560999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revisiting the Decoupling of Elastic Waves From a Weak Formulation Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Jingni Xiao, Junjiang Lai, Yifeng Xu","submitted_at":"2018-08-09T12:59:39Z","abstract_excerpt":"Elastic scattering governed by the Lame system associated with the third-type or fourth-type boundary condition is considered. It was shown in [8] by two of the authors that under suitable geometric conditions on the boundary surface of the elastic inclusion, the longitudinal and shear waves can be decoupled. The decoupling result in [8] was derived based on analyzing the local boundary behaviours of the elastic fields. In this article, we provide a different argument from a variational perspective in proving the decoupling result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03133","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":"1808.03133","created_at":"2026-05-17T23:46:09.561097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.03133v1","created_at":"2026-05-17T23:46:09.561097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03133","created_at":"2026-05-17T23:46:09.561097+00:00"},{"alias_kind":"pith_short_12","alias_value":"UMI6OWXFQACV","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UMI6OWXFQACVKOYL","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UMI6OWXF","created_at":"2026-05-18T12:32:56.356000+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/UMI6OWXFQACVKOYLBYC42GHDRW","json":"https://pith.science/pith/UMI6OWXFQACVKOYLBYC42GHDRW.json","graph_json":"https://pith.science/api/pith-number/UMI6OWXFQACVKOYLBYC42GHDRW/graph.json","events_json":"https://pith.science/api/pith-number/UMI6OWXFQACVKOYLBYC42GHDRW/events.json","paper":"https://pith.science/paper/UMI6OWXF"},"agent_actions":{"view_html":"https://pith.science/pith/UMI6OWXFQACVKOYLBYC42GHDRW","download_json":"https://pith.science/pith/UMI6OWXFQACVKOYLBYC42GHDRW.json","view_paper":"https://pith.science/paper/UMI6OWXF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.03133&json=true","fetch_graph":"https://pith.science/api/pith-number/UMI6OWXFQACVKOYLBYC42GHDRW/graph.json","fetch_events":"https://pith.science/api/pith-number/UMI6OWXFQACVKOYLBYC42GHDRW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UMI6OWXFQACVKOYLBYC42GHDRW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UMI6OWXFQACVKOYLBYC42GHDRW/action/storage_attestation","attest_author":"https://pith.science/pith/UMI6OWXFQACVKOYLBYC42GHDRW/action/author_attestation","sign_citation":"https://pith.science/pith/UMI6OWXFQACVKOYLBYC42GHDRW/action/citation_signature","submit_replication":"https://pith.science/pith/UMI6OWXFQACVKOYLBYC42GHDRW/action/replication_record"}},"created_at":"2026-05-17T23:46:09.561097+00:00","updated_at":"2026-05-17T23:46:09.561097+00:00"}