{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ABCTG66HR5WGSRKFRZ5F2TTOHJ","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":"bf085a995f81ef38f31f56fddc3027e4d6969ffcc9c496f250c8069f0feb6a80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-08T12:33:41Z","title_canon_sha256":"02b0d4a729b6a7ec0dbf7838b02ac2f4099ed1073c9ba678222133ad3af78125"},"schema_version":"1.0","source":{"id":"1810.03405","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03405","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03405v2","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03405","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"ABCTG66HR5WG","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ABCTG66HR5WGSRKF","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ABCTG66H","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:e372c4f890c66365166ebe8abf252a28804869317f4f55b6a1cbb6a68e27ed18","target":"graph","created_at":"2026-05-17T23:48:06Z","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":"In this note we study solitary wave solutions of a class of Whitham-Boussinesq systems which includes the bi-directional Whitham system as a special example. The travelling wave version of the evolution system can be reduced to a single evolution equation, similar to a class of equations studied by Ehrnstr\\\"om, Groves and Wahl\\'en. In that paper the authors prove the existence of solitary wave solutions using a constrained minimization argument adapted to noncoercive functionals, developed by Buffoni, Groves and Wahl\\'en, together with the concentration-compactness principle.","authors_text":"Dag Nilsson, Yuexun Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-08T12:33:41Z","title":"Solitary wave solutions to a class of Whitham-Boussinesq systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03405","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:fa3e0b00926c642126688ce2a0c2d9ed297db5eaca1fd10d59cc6d7eeab8adc8","target":"record","created_at":"2026-05-17T23:48:06Z","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":"bf085a995f81ef38f31f56fddc3027e4d6969ffcc9c496f250c8069f0feb6a80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-08T12:33:41Z","title_canon_sha256":"02b0d4a729b6a7ec0dbf7838b02ac2f4099ed1073c9ba678222133ad3af78125"},"schema_version":"1.0","source":{"id":"1810.03405","kind":"arxiv","version":2}},"canonical_sha256":"0045337bc78f6c6945458e7a5d4e6e3a6b27c2a7b81de0870a753fb086f48a45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0045337bc78f6c6945458e7a5d4e6e3a6b27c2a7b81de0870a753fb086f48a45","first_computed_at":"2026-05-17T23:48:06.503739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:06.503739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WR9WmZFMTh8pSVCrQCjZ9NK9y6N0PMXuP8yswggTZLdP5TTuLh1zRag+4SPFMqrWoWs54Wgo/pO06aO3jSP5Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:06.504103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03405","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa3e0b00926c642126688ce2a0c2d9ed297db5eaca1fd10d59cc6d7eeab8adc8","sha256:e372c4f890c66365166ebe8abf252a28804869317f4f55b6a1cbb6a68e27ed18"],"state_sha256":"8371047e2da528f1cba736de7f7a59d59e91e5e54174a20b112ff222561d7c76"}