{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:M7V5U77URHFGP5AIS3BNV6BMJT","short_pith_number":"pith:M7V5U77U","schema_version":"1.0","canonical_sha256":"67ebda7ff489ca67f40896c2daf82c4cd871db7bb71ed151020041876d8d56da","source":{"kind":"arxiv","id":"1208.6410","version":1},"attestation_state":"computed","paper":{"title":"Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Helge Holden, Nils Henrik Risebro, Ujjwal Koley","submitted_at":"2012-08-31T07:26:10Z","abstract_excerpt":"We prove convergence of a fully discrete finite difference scheme for the Korteweg--de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0}=u_0$ is of high regularity, $u_0\\in H^3(\\R)$, the scheme is shown to converge to a classical solution, and if the regularity of the initial data is smaller, $u_0\\in L^2(\\R)$, then the scheme converges strongly in $L^2(0,T;L^2_{\\mathrm{loc}}(\\R))$ to a weak solution."},"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":"1208.6410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-31T07:26:10Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"34a6a77078aa182298267dfd339a502cd9ff9a8d1b30a2f3ec9becd4f585d6cf","abstract_canon_sha256":"a6f8dbbdf4578cd1e7a0f69ed596e2780360467af60c6fecd83744563f73545f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:33.227106Z","signature_b64":"1DxGZMfGUgFjoc6pCbmXMfUuiRvKJbwwcyIGTxL0LfWHG1M29hPrHheqXR6attIEx5IKxDXu+YnDIUdD68MnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ebda7ff489ca67f40896c2daf82c4cd871db7bb71ed151020041876d8d56da","last_reissued_at":"2026-05-18T03:46:33.226072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:33.226072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Helge Holden, Nils Henrik Risebro, Ujjwal Koley","submitted_at":"2012-08-31T07:26:10Z","abstract_excerpt":"We prove convergence of a fully discrete finite difference scheme for the Korteweg--de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0}=u_0$ is of high regularity, $u_0\\in H^3(\\R)$, the scheme is shown to converge to a classical solution, and if the regularity of the initial data is smaller, $u_0\\in L^2(\\R)$, then the scheme converges strongly in $L^2(0,T;L^2_{\\mathrm{loc}}(\\R))$ to a weak solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6410","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":"1208.6410","created_at":"2026-05-18T03:46:33.226288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.6410v1","created_at":"2026-05-18T03:46:33.226288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6410","created_at":"2026-05-18T03:46:33.226288+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7V5U77URHFG","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7V5U77URHFGP5AI","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7V5U77U","created_at":"2026-05-18T12:27:14.488303+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/M7V5U77URHFGP5AIS3BNV6BMJT","json":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT.json","graph_json":"https://pith.science/api/pith-number/M7V5U77URHFGP5AIS3BNV6BMJT/graph.json","events_json":"https://pith.science/api/pith-number/M7V5U77URHFGP5AIS3BNV6BMJT/events.json","paper":"https://pith.science/paper/M7V5U77U"},"agent_actions":{"view_html":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT","download_json":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT.json","view_paper":"https://pith.science/paper/M7V5U77U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.6410&json=true","fetch_graph":"https://pith.science/api/pith-number/M7V5U77URHFGP5AIS3BNV6BMJT/graph.json","fetch_events":"https://pith.science/api/pith-number/M7V5U77URHFGP5AIS3BNV6BMJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/action/storage_attestation","attest_author":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/action/author_attestation","sign_citation":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/action/citation_signature","submit_replication":"https://pith.science/pith/M7V5U77URHFGP5AIS3BNV6BMJT/action/replication_record"}},"created_at":"2026-05-18T03:46:33.226288+00:00","updated_at":"2026-05-18T03:46:33.226288+00:00"}