{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ESWHZVQLMI4FLEKRED7VAKCKR2","short_pith_number":"pith:ESWHZVQL","schema_version":"1.0","canonical_sha256":"24ac7cd60b623855915120ff50284a8e9315d6abe093d9bab67d2f0b9b345cfb","source":{"kind":"arxiv","id":"1305.5642","version":1},"attestation_state":"computed","paper":{"title":"Blow-up solutions and peakons to a generalized $\\mu$-Camassa-Holm integrable equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changzheng Qu, Ying Fu, Yue Liu","submitted_at":"2013-05-24T07:58:58Z","abstract_excerpt":"Consideration here is a generalized $\\mu$-type integrable equation, which can be regarded as a generalization to both the $\\mu$-Camassa-Holm and modified $\\mu$-Camassa-Holm equations. It is shown that the proposed equation is formally integrable with the Lax-pair and the bi-Hamiltonian structure and its scale limit is an integrable model of hydrodynamical systems describing short capillary-gravity waves. Local well-posedness of the Cauchy problem in the suitable Sobolev space is established by the viscosity method. Existence of peaked traveling-wave solutions and formation of singularities of "},"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":"1305.5642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-24T07:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"7b38b62e4ff936e1ef6a48da8df1144bac3eec2d549127fdfb0bfeb7f2a7c288","abstract_canon_sha256":"1cb8255ee7c271eb8bf6bfc7105b4860cf71369a37de41eee32d59942aa1c730"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:47.004519Z","signature_b64":"TpJKtmixwFnkHXjLIpVsmr09AWfAU8bowfhTULVCBk/PSHDoL6E9gltzngmqh/3h8RyYKKU3BS0oxsiYYuu8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24ac7cd60b623855915120ff50284a8e9315d6abe093d9bab67d2f0b9b345cfb","last_reissued_at":"2026-05-18T01:49:47.004075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:47.004075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blow-up solutions and peakons to a generalized $\\mu$-Camassa-Holm integrable equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changzheng Qu, Ying Fu, Yue Liu","submitted_at":"2013-05-24T07:58:58Z","abstract_excerpt":"Consideration here is a generalized $\\mu$-type integrable equation, which can be regarded as a generalization to both the $\\mu$-Camassa-Holm and modified $\\mu$-Camassa-Holm equations. It is shown that the proposed equation is formally integrable with the Lax-pair and the bi-Hamiltonian structure and its scale limit is an integrable model of hydrodynamical systems describing short capillary-gravity waves. Local well-posedness of the Cauchy problem in the suitable Sobolev space is established by the viscosity method. Existence of peaked traveling-wave solutions and formation of singularities of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5642","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":""},"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":"1305.5642","created_at":"2026-05-18T01:49:47.004144+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5642v1","created_at":"2026-05-18T01:49:47.004144+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5642","created_at":"2026-05-18T01:49:47.004144+00:00"},{"alias_kind":"pith_short_12","alias_value":"ESWHZVQLMI4F","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"ESWHZVQLMI4FLEKR","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"ESWHZVQL","created_at":"2026-05-18T12:27:43.054852+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/ESWHZVQLMI4FLEKRED7VAKCKR2","json":"https://pith.science/pith/ESWHZVQLMI4FLEKRED7VAKCKR2.json","graph_json":"https://pith.science/api/pith-number/ESWHZVQLMI4FLEKRED7VAKCKR2/graph.json","events_json":"https://pith.science/api/pith-number/ESWHZVQLMI4FLEKRED7VAKCKR2/events.json","paper":"https://pith.science/paper/ESWHZVQL"},"agent_actions":{"view_html":"https://pith.science/pith/ESWHZVQLMI4FLEKRED7VAKCKR2","download_json":"https://pith.science/pith/ESWHZVQLMI4FLEKRED7VAKCKR2.json","view_paper":"https://pith.science/paper/ESWHZVQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5642&json=true","fetch_graph":"https://pith.science/api/pith-number/ESWHZVQLMI4FLEKRED7VAKCKR2/graph.json","fetch_events":"https://pith.science/api/pith-number/ESWHZVQLMI4FLEKRED7VAKCKR2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ESWHZVQLMI4FLEKRED7VAKCKR2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ESWHZVQLMI4FLEKRED7VAKCKR2/action/storage_attestation","attest_author":"https://pith.science/pith/ESWHZVQLMI4FLEKRED7VAKCKR2/action/author_attestation","sign_citation":"https://pith.science/pith/ESWHZVQLMI4FLEKRED7VAKCKR2/action/citation_signature","submit_replication":"https://pith.science/pith/ESWHZVQLMI4FLEKRED7VAKCKR2/action/replication_record"}},"created_at":"2026-05-18T01:49:47.004144+00:00","updated_at":"2026-05-18T01:49:47.004144+00:00"}