{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:PLUSB5U6CHD5COKA37I75VQBMR","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":"42989596451525c425b360826bb8e2aaed7f5aa482fab200df3daa59d4ae5672","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2007-10-17T19:46:52Z","title_canon_sha256":"1d7d2a8d6294f90e77c3ddf78f2063b81dc5a33c6f1a52dcc354a0eee5c3d216"},"schema_version":"1.0","source":{"id":"0710.3379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3379","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3379v2","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3379","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"PLUSB5U6CHD5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"PLUSB5U6CHD5COKA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"PLUSB5U6","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:9dc9aa755a4cf98371803f0d0371af19cd163e2401615b0c1e0c1e943d47633d","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 derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su-Gardner (or one-dimensional Green-Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate \"undular bore\" stage of the evolution. The resulting formula represents a \"non-integrable\" analogue of the well-known semi-classical distribution for the Korteweg-de Vries equation, which is usually obtained thro","authors_text":"G.A. El, N.F. Smyth, R.H.J. Grimshaw","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.PS","submitted_at":"2007-10-17T19:46:52Z","title":"Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3379","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":"sha256:019b7282c167fb134db5e32dea89ccdc417ba6b8a309ae6cc62550922fcbc526","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":"42989596451525c425b360826bb8e2aaed7f5aa482fab200df3daa59d4ae5672","cross_cats_sorted":[],"license":"","primary_cat":"nlin.PS","submitted_at":"2007-10-17T19:46:52Z","title_canon_sha256":"1d7d2a8d6294f90e77c3ddf78f2063b81dc5a33c6f1a52dcc354a0eee5c3d216"},"schema_version":"1.0","source":{"id":"0710.3379","kind":"arxiv","version":2}},"canonical_sha256":"7ae920f69e11c7d13940dfd1fed60164781aa905c039618b7b7406d9036074b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ae920f69e11c7d13940dfd1fed60164781aa905c039618b7b7406d9036074b4","first_computed_at":"2026-05-18T04:40:54.986052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:54.986052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t5KFCMMgFiBlwkJViizx8f4YSvA2zDSO86ioxWgekm1FauOOXgYThdvKPnWG2oU8+cMcH69+ytZ+WQaKQ2DeDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:54.986458Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:019b7282c167fb134db5e32dea89ccdc417ba6b8a309ae6cc62550922fcbc526","sha256:9dc9aa755a4cf98371803f0d0371af19cd163e2401615b0c1e0c1e943d47633d"],"state_sha256":"a90fc3d59be276de88df3f16bbbceb95bb0194ceed889a1415d2b4d6b40196eb"}