{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3CYKADHJ2MNZ4IPAWUL3TZJYT5","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":"6844d9a96b87e0ef9612d48faff2dfae8c6a032d7ca31b549c5c2df3329e1bb2","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-22T23:25:17Z","title_canon_sha256":"75d7242232215d4f03b8548fbea890d914d1bb39d8c21a84111665d0344bfa4d"},"schema_version":"1.0","source":{"id":"1810.09594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09594","created_at":"2026-05-18T00:02:39Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09594v1","created_at":"2026-05-18T00:02:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09594","created_at":"2026-05-18T00:02:39Z"},{"alias_kind":"pith_short_12","alias_value":"3CYKADHJ2MNZ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3CYKADHJ2MNZ4IPA","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3CYKADHJ","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:76889b593aeef14ed8b3733c26a86cc422db79643166c8ffb29a4dabe8474b37","target":"graph","created_at":"2026-05-18T00:02:39Z","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 paper we consider globally defined solutions of Camassa-Holm (CH) type equations outside the well-known nonzero speed, peakon region. These equations include the standard CH and Degasperis-Procesi (DP) equations, as well as nonintegrable generalizations such as the $b$-family, elastic rod and BBM equations. Having globally defined solutions for these models, we introduce the notion of \\emph{zero-speed and breather solutions}, i.e., solutions that do not decay to zero as $t\\to +\\infty$ on compact intervals of space. We prove that, under suitable decay assumptions, such solutions do not ","authors_text":"Chulkwang Kwak, Claudio Mu\\~noz, Manuel F. Cortez, Miguel A. Alejo","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-22T23:25:17Z","title":"On the dynamics of zero-speed solutions for Camassa-Holm type equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09594","kind":"arxiv","version":1},"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":"sha256:7c46eca95efb615ca6485276c87fce3dc013bb98b16e520c900deb1cf0590417","target":"record","created_at":"2026-05-18T00:02:39Z","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":"6844d9a96b87e0ef9612d48faff2dfae8c6a032d7ca31b549c5c2df3329e1bb2","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-22T23:25:17Z","title_canon_sha256":"75d7242232215d4f03b8548fbea890d914d1bb39d8c21a84111665d0344bfa4d"},"schema_version":"1.0","source":{"id":"1810.09594","kind":"arxiv","version":1}},"canonical_sha256":"d8b0a00ce9d31b9e21e0b517b9e5389f690af94d4796339f545753fd08be2d31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8b0a00ce9d31b9e21e0b517b9e5389f690af94d4796339f545753fd08be2d31","first_computed_at":"2026-05-18T00:02:39.099660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:39.099660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wIqIHDEkJPwBuaqaX/9GJTdaPz1FNVi3I3jQ0EyyTQVN3ZE/eo/O/RYJZ9ha2mBNxlH7bg7ZeG0PAh7lQS9hBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:39.100253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c46eca95efb615ca6485276c87fce3dc013bb98b16e520c900deb1cf0590417","sha256:76889b593aeef14ed8b3733c26a86cc422db79643166c8ffb29a4dabe8474b37"],"state_sha256":"eb3a4b22ded55d7a7b7a483dfe54e5f43b8695589bc0feeeed5cca0c53220132"}