{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:MJXQLM5BPLWGLKMBADDOFQWA7V","short_pith_number":"pith:MJXQLM5B","schema_version":"1.0","canonical_sha256":"626f05b3a17aec65a98100c6e2c2c0fd573cfdc9f214072de26d57abde1bd96c","source":{"kind":"arxiv","id":"nlin/0507029","version":2},"attestation_state":"computed","paper":{"title":"Unsteady undular bores in fully nonlinear shallow-water theory","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"G.A. El, N.F. Smyth, R.H.J. Grimshaw","submitted_at":"2005-07-14T20:28:55Z","abstract_excerpt":"We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using a standard long-wave asymptotic expansion.\n  In this context the system was first derived by Su and Gardner. It coincides with the one-dimensional flat-bottom reduction of the Green-Naghdi system and, a"},"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":"nlin/0507029","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.PS","submitted_at":"2005-07-14T20:28:55Z","cross_cats_sorted":[],"title_canon_sha256":"4c68ed0216a8c934e301e731d3475c1ab4fa20368d15037d62b35a20d76f3067","abstract_canon_sha256":"3a054851599021522ed920d29814da3f54d891ebc5a4b248bc1d560551ab7172"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:54.877455Z","signature_b64":"rqpO9LusQQ0X0EMau+tOWCfnUePVXVtyohcJva+e848QCZSElWabc+gSfI/YHfIVBtUJVbJCKdbzOlrdSuRxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"626f05b3a17aec65a98100c6e2c2c0fd573cfdc9f214072de26d57abde1bd96c","last_reissued_at":"2026-05-18T04:40:54.876940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:54.876940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unsteady undular bores in fully nonlinear shallow-water theory","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"G.A. El, N.F. Smyth, R.H.J. Grimshaw","submitted_at":"2005-07-14T20:28:55Z","abstract_excerpt":"We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using a standard long-wave asymptotic expansion.\n  In this context the system was first derived by Su and Gardner. It coincides with the one-dimensional flat-bottom reduction of the Green-Naghdi system and, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0507029","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":""},"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":"nlin/0507029","created_at":"2026-05-18T04:40:54.877021+00:00"},{"alias_kind":"arxiv_version","alias_value":"nlin/0507029v2","created_at":"2026-05-18T04:40:54.877021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0507029","created_at":"2026-05-18T04:40:54.877021+00:00"},{"alias_kind":"pith_short_12","alias_value":"MJXQLM5BPLWG","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"MJXQLM5BPLWGLKMB","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"MJXQLM5B","created_at":"2026-05-18T12:25:53.335082+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/MJXQLM5BPLWGLKMBADDOFQWA7V","json":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V.json","graph_json":"https://pith.science/api/pith-number/MJXQLM5BPLWGLKMBADDOFQWA7V/graph.json","events_json":"https://pith.science/api/pith-number/MJXQLM5BPLWGLKMBADDOFQWA7V/events.json","paper":"https://pith.science/paper/MJXQLM5B"},"agent_actions":{"view_html":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V","download_json":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V.json","view_paper":"https://pith.science/paper/MJXQLM5B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nlin/0507029&json=true","fetch_graph":"https://pith.science/api/pith-number/MJXQLM5BPLWGLKMBADDOFQWA7V/graph.json","fetch_events":"https://pith.science/api/pith-number/MJXQLM5BPLWGLKMBADDOFQWA7V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/action/storage_attestation","attest_author":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/action/author_attestation","sign_citation":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/action/citation_signature","submit_replication":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/action/replication_record"}},"created_at":"2026-05-18T04:40:54.877021+00:00","updated_at":"2026-05-18T04:40:54.877021+00:00"}