{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:3X73MRONHYFMADTT57KIUL4KQG","short_pith_number":"pith:3X73MRON","schema_version":"1.0","canonical_sha256":"ddffb645cd3e0ac00e73efd48a2f8a81ae4a581941bf9cc78daf3a6397b73162","source":{"kind":"arxiv","id":"2403.19540","version":2},"attestation_state":"computed","paper":{"title":"A third-order trigonometric integrator with low regularity for the semilinear Klein-Gordon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bin Wang, Yaolin Jiang","submitted_at":"2024-03-28T16:20:30Z","abstract_excerpt":"In this paper, we propose and analyse a novel third-order low-regularity trigonometric integrator for the semilinear Klein-Gordon equation with non-smooth solution in the $d$-dimensional space, where $d=1,2,3$. The integrator is constructed based on the full use of Duhamel's formula and the employment of a twisted function tailored for trigonometric integrals. Robust error analysis is conducted, demonstrating that the proposed scheme achieves third-order accuracy in the energy space under a weak regularity requirement in $H^{1+\\max(\\mu,1)}(\\mathbb{T}^d)\\times H^{\\max(\\mu,1)}(\\mathbb{T}^d)$ wit"},"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":"2403.19540","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-03-28T16:20:30Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b013e394fd7e44a66d419117efe87006903f65b1a0428766f9fa22d25fce4dbf","abstract_canon_sha256":"dddf1db4f12836eda0d7b376419bb74653d6aa382f264262a62ab49abaa629df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:53.850427Z","signature_b64":"I9HhiWWBx8GkfWcBnY9SMh7yclC94t/fn+WxWYaXTgvJyCEwipn3O2RbqMHhHnH4V+b9EYIdi9OIkwcSfwCHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddffb645cd3e0ac00e73efd48a2f8a81ae4a581941bf9cc78daf3a6397b73162","last_reissued_at":"2026-07-05T09:39:53.849922Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:53.849922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A third-order trigonometric integrator with low regularity for the semilinear Klein-Gordon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bin Wang, Yaolin Jiang","submitted_at":"2024-03-28T16:20:30Z","abstract_excerpt":"In this paper, we propose and analyse a novel third-order low-regularity trigonometric integrator for the semilinear Klein-Gordon equation with non-smooth solution in the $d$-dimensional space, where $d=1,2,3$. The integrator is constructed based on the full use of Duhamel's formula and the employment of a twisted function tailored for trigonometric integrals. Robust error analysis is conducted, demonstrating that the proposed scheme achieves third-order accuracy in the energy space under a weak regularity requirement in $H^{1+\\max(\\mu,1)}(\\mathbb{T}^d)\\times H^{\\max(\\mu,1)}(\\mathbb{T}^d)$ wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.19540","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.19540/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":"2403.19540","created_at":"2026-07-05T09:39:53.849979+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.19540v2","created_at":"2026-07-05T09:39:53.849979+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.19540","created_at":"2026-07-05T09:39:53.849979+00:00"},{"alias_kind":"pith_short_12","alias_value":"3X73MRONHYFM","created_at":"2026-07-05T09:39:53.849979+00:00"},{"alias_kind":"pith_short_16","alias_value":"3X73MRONHYFMADTT","created_at":"2026-07-05T09:39:53.849979+00:00"},{"alias_kind":"pith_short_8","alias_value":"3X73MRON","created_at":"2026-07-05T09:39:53.849979+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/3X73MRONHYFMADTT57KIUL4KQG","json":"https://pith.science/pith/3X73MRONHYFMADTT57KIUL4KQG.json","graph_json":"https://pith.science/api/pith-number/3X73MRONHYFMADTT57KIUL4KQG/graph.json","events_json":"https://pith.science/api/pith-number/3X73MRONHYFMADTT57KIUL4KQG/events.json","paper":"https://pith.science/paper/3X73MRON"},"agent_actions":{"view_html":"https://pith.science/pith/3X73MRONHYFMADTT57KIUL4KQG","download_json":"https://pith.science/pith/3X73MRONHYFMADTT57KIUL4KQG.json","view_paper":"https://pith.science/paper/3X73MRON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.19540&json=true","fetch_graph":"https://pith.science/api/pith-number/3X73MRONHYFMADTT57KIUL4KQG/graph.json","fetch_events":"https://pith.science/api/pith-number/3X73MRONHYFMADTT57KIUL4KQG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3X73MRONHYFMADTT57KIUL4KQG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3X73MRONHYFMADTT57KIUL4KQG/action/storage_attestation","attest_author":"https://pith.science/pith/3X73MRONHYFMADTT57KIUL4KQG/action/author_attestation","sign_citation":"https://pith.science/pith/3X73MRONHYFMADTT57KIUL4KQG/action/citation_signature","submit_replication":"https://pith.science/pith/3X73MRONHYFMADTT57KIUL4KQG/action/replication_record"}},"created_at":"2026-07-05T09:39:53.849979+00:00","updated_at":"2026-07-05T09:39:53.849979+00:00"}