{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:MJXQLM5BPLWGLKMBADDOFQWA7V","short_pith_number":"pith:MJXQLM5B","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"},"canonical_sha256":"626f05b3a17aec65a98100c6e2c2c0fd573cfdc9f214072de26d57abde1bd96c","source":{"kind":"arxiv","id":"nlin/0507029","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0507029","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0507029v2","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0507029","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"MJXQLM5BPLWG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MJXQLM5BPLWGLKMB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MJXQLM5B","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:MJXQLM5BPLWGLKMBADDOFQWA7V","target":"record","payload":{"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"},"canonical_sha256":"626f05b3a17aec65a98100c6e2c2c0fd573cfdc9f214072de26d57abde1bd96c","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"},"source_kind":"arxiv","source_id":"nlin/0507029","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dfv7FAYx+A5VoNMa52EwajDoOpTDLJaLuOZubCCMqY9B3PJnx5OD3VZ0yIQDI4TQZpJJb8giB4M0xLa6VCprCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:28:35.679400Z"},"content_sha256":"c487a38233e081ef863e76b04fc5f96fae002cb8d8adfa979c605b1e69651d66","schema_version":"1.0","event_id":"sha256:c487a38233e081ef863e76b04fc5f96fae002cb8d8adfa979c605b1e69651d66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:MJXQLM5BPLWGLKMBADDOFQWA7V","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8zzGr/zJFTwhhDD3moNmQxc0JZWA5TqrbpxFAlcLSWxFqnRN6PCnBC7RSCp0S5nlK/bfDOfz6OdV4qrR+OpqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:28:35.680099Z"},"content_sha256":"5dfa6b1a527872ab83e17d0652841059f8b9ecfcd467f576484d86f4ad3a843b","schema_version":"1.0","event_id":"sha256:5dfa6b1a527872ab83e17d0652841059f8b9ecfcd467f576484d86f4ad3a843b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/bundle.json","state_url":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T18:28:35Z","links":{"resolver":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V","bundle":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/bundle.json","state":"https://pith.science/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJXQLM5BPLWGLKMBADDOFQWA7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:MJXQLM5BPLWGLKMBADDOFQWA7V","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3a054851599021522ed920d29814da3f54d891ebc5a4b248bc1d560551ab7172","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2005-07-14T20:28:55Z","title_canon_sha256":"4c68ed0216a8c934e301e731d3475c1ab4fa20368d15037d62b35a20d76f3067"},"schema_version":"1.0","source":{"id":"nlin/0507029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0507029","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0507029v2","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0507029","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"MJXQLM5BPLWG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MJXQLM5BPLWGLKMB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MJXQLM5B","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:5dfa6b1a527872ab83e17d0652841059f8b9ecfcd467f576484d86f4ad3a843b","target":"graph","created_at":"2026-05-18T04:40:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"G.A. El, N.F. Smyth, R.H.J. Grimshaw","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.PS","submitted_at":"2005-07-14T20:28:55Z","title":"Unsteady undular bores in fully nonlinear shallow-water theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0507029","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c487a38233e081ef863e76b04fc5f96fae002cb8d8adfa979c605b1e69651d66","target":"record","created_at":"2026-05-18T04:40:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3a054851599021522ed920d29814da3f54d891ebc5a4b248bc1d560551ab7172","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2005-07-14T20:28:55Z","title_canon_sha256":"4c68ed0216a8c934e301e731d3475c1ab4fa20368d15037d62b35a20d76f3067"},"schema_version":"1.0","source":{"id":"nlin/0507029","kind":"arxiv","version":2}},"canonical_sha256":"626f05b3a17aec65a98100c6e2c2c0fd573cfdc9f214072de26d57abde1bd96c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"626f05b3a17aec65a98100c6e2c2c0fd573cfdc9f214072de26d57abde1bd96c","first_computed_at":"2026-05-18T04:40:54.876940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:54.876940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqpO9LusQQ0X0EMau+tOWCfnUePVXVtyohcJva+e848QCZSElWabc+gSfI/YHfIVBtUJVbJCKdbzOlrdSuRxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:54.877455Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0507029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c487a38233e081ef863e76b04fc5f96fae002cb8d8adfa979c605b1e69651d66","sha256:5dfa6b1a527872ab83e17d0652841059f8b9ecfcd467f576484d86f4ad3a843b"],"state_sha256":"88c844d9387224fae043b6f3e93efa9a995d81a92a4e6b333150ec8b453b7ac5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v/wyeCHIHCoE/uWzz/cAKGYP9rJXMlMriAFjrDicgLwSGKgaj1rRtFU5TH4usi3hy81JwAOcGSvIPoe1Stg9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:28:35.684238Z","bundle_sha256":"493fdf077f65dd8cfa6844728a3b855dbce92dba6d8d22b4dc28f4ee564a104e"}}