{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XGOHODYMI5DD2FVZPQ6PKRKPHO","short_pith_number":"pith:XGOHODYM","schema_version":"1.0","canonical_sha256":"b99c770f0c47463d16b97c3cf5454f3b83d7f384d5b7626f93302870e92e484b","source":{"kind":"arxiv","id":"2605.20773","version":1},"attestation_state":"computed","paper":{"title":"Peakon solutions and analytical properties for the Camassa-Holm type equations with quadratic nonlinearities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mingxuan Zhu, Yonghong Chen, Zhijun Qiao","submitted_at":"2026-05-20T06:15:25Z","abstract_excerpt":"In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local well-posedness of solutions in Besov spaces and then provide the blow-up criteria. Subsequently, we impose appropriate sufficient conditions on the initial data to guaranty that the corresponding solution either exists globally or blows up in a finite time. Finally, we prove the ill-posedness in the Besov space $B_{2,\\infty}^{3/2}$ by utilizing the non-traveling wave sol"},"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":"2605.20773","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-20T06:15:25Z","cross_cats_sorted":[],"title_canon_sha256":"0e8d9e02542043eb5195f877559f72a9e1625b97934bc11b7b7b5abba117358b","abstract_canon_sha256":"5da744a7ff6ca762200bfa3e0339a8705d5bdf03ebd14f6a197ade584a4d402d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:53.564328Z","signature_b64":"hb3Z+x8gffOvGF2/Do17PJPVY9ZsgeAXvbzeGkgIkR1JhhXPN6G3mTlIKONGvUJ8deApp1etMXdsEz8BJW8RCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b99c770f0c47463d16b97c3cf5454f3b83d7f384d5b7626f93302870e92e484b","last_reissued_at":"2026-05-21T01:04:53.563612Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:53.563612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Peakon solutions and analytical properties for the Camassa-Holm type equations with quadratic nonlinearities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mingxuan Zhu, Yonghong Chen, Zhijun Qiao","submitted_at":"2026-05-20T06:15:25Z","abstract_excerpt":"In this paper, we derive the multi-peakon dynamical system of a class of Camassa-Holm-type equations with quadratic nonlinearities. We also consider the analytical properties for the Cauchy problem. Firstly, we establish local well-posedness of solutions in Besov spaces and then provide the blow-up criteria. Subsequently, we impose appropriate sufficient conditions on the initial data to guaranty that the corresponding solution either exists globally or blows up in a finite time. Finally, we prove the ill-posedness in the Besov space $B_{2,\\infty}^{3/2}$ by utilizing the non-traveling wave sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20773","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20773/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.20773","created_at":"2026-05-21T01:04:53.563715+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20773v1","created_at":"2026-05-21T01:04:53.563715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20773","created_at":"2026-05-21T01:04:53.563715+00:00"},{"alias_kind":"pith_short_12","alias_value":"XGOHODYMI5DD","created_at":"2026-05-21T01:04:53.563715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XGOHODYMI5DD2FVZ","created_at":"2026-05-21T01:04:53.563715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XGOHODYM","created_at":"2026-05-21T01:04:53.563715+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/XGOHODYMI5DD2FVZPQ6PKRKPHO","json":"https://pith.science/pith/XGOHODYMI5DD2FVZPQ6PKRKPHO.json","graph_json":"https://pith.science/api/pith-number/XGOHODYMI5DD2FVZPQ6PKRKPHO/graph.json","events_json":"https://pith.science/api/pith-number/XGOHODYMI5DD2FVZPQ6PKRKPHO/events.json","paper":"https://pith.science/paper/XGOHODYM"},"agent_actions":{"view_html":"https://pith.science/pith/XGOHODYMI5DD2FVZPQ6PKRKPHO","download_json":"https://pith.science/pith/XGOHODYMI5DD2FVZPQ6PKRKPHO.json","view_paper":"https://pith.science/paper/XGOHODYM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20773&json=true","fetch_graph":"https://pith.science/api/pith-number/XGOHODYMI5DD2FVZPQ6PKRKPHO/graph.json","fetch_events":"https://pith.science/api/pith-number/XGOHODYMI5DD2FVZPQ6PKRKPHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XGOHODYMI5DD2FVZPQ6PKRKPHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XGOHODYMI5DD2FVZPQ6PKRKPHO/action/storage_attestation","attest_author":"https://pith.science/pith/XGOHODYMI5DD2FVZPQ6PKRKPHO/action/author_attestation","sign_citation":"https://pith.science/pith/XGOHODYMI5DD2FVZPQ6PKRKPHO/action/citation_signature","submit_replication":"https://pith.science/pith/XGOHODYMI5DD2FVZPQ6PKRKPHO/action/replication_record"}},"created_at":"2026-05-21T01:04:53.563715+00:00","updated_at":"2026-05-21T01:04:53.563715+00:00"}