{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:Z6OK42G3QINNMWNFVS6STQVGUB","short_pith_number":"pith:Z6OK42G3","schema_version":"1.0","canonical_sha256":"cf9cae68db821ad659a5acbd29c2a6a05bfbfc986e0aa07724c92325197242f3","source":{"kind":"arxiv","id":"1108.5368","version":3},"attestation_state":"computed","paper":{"title":"On the Cauchy problem for the integrable Camassa-Holm type equation with cubic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Changzheng Qu, Guilong Gui, Ying Fu, Yue Liu","submitted_at":"2011-08-26T18:40:43Z","abstract_excerpt":"Considered in this paper is the modified Camassa-Holm equation with cubic nonlinearity, which is integrable and admits the single peaked solitons and multi-peakon solutions. The short-wave limit of this equation is known as the short-pulse equation. The main investigation is the Cauchy problem of the modified Camassa-Holm equation with qualitative properties of its solutions. It is firstly shown that the equation is locally well-posed in a range of the Besov spaces. The blow-up scenario and the lower bound of the maximal time of existence are then determined. A blow-up mechanism for solutions "},"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":"1108.5368","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-26T18:40:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ad40ef0d8ebcc2cb208924f669dbeea1aa8ba50780ecea0366c1d5f11e25d813","abstract_canon_sha256":"b85edab73da4f5617f0cec8693f47f48287f2c10d31e9138391c04cd402c647f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:01.391889Z","signature_b64":"nCcjEb/jSout+QogG9DZ6I98E36DekKfInaavoY1T1PH38diGjhf/fV8yIuAEZLNvPSmu12O2xtTWQggjQO+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf9cae68db821ad659a5acbd29c2a6a05bfbfc986e0aa07724c92325197242f3","last_reissued_at":"2026-05-18T03:47:01.391236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:01.391236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Cauchy problem for the integrable Camassa-Holm type equation with cubic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Changzheng Qu, Guilong Gui, Ying Fu, Yue Liu","submitted_at":"2011-08-26T18:40:43Z","abstract_excerpt":"Considered in this paper is the modified Camassa-Holm equation with cubic nonlinearity, which is integrable and admits the single peaked solitons and multi-peakon solutions. The short-wave limit of this equation is known as the short-pulse equation. The main investigation is the Cauchy problem of the modified Camassa-Holm equation with qualitative properties of its solutions. It is firstly shown that the equation is locally well-posed in a range of the Besov spaces. The blow-up scenario and the lower bound of the maximal time of existence are then determined. A blow-up mechanism for solutions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5368","kind":"arxiv","version":3},"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":"1108.5368","created_at":"2026-05-18T03:47:01.391331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5368v3","created_at":"2026-05-18T03:47:01.391331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5368","created_at":"2026-05-18T03:47:01.391331+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z6OK42G3QINN","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z6OK42G3QINNMWNF","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z6OK42G3","created_at":"2026-05-18T12:26:47.523578+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/Z6OK42G3QINNMWNFVS6STQVGUB","json":"https://pith.science/pith/Z6OK42G3QINNMWNFVS6STQVGUB.json","graph_json":"https://pith.science/api/pith-number/Z6OK42G3QINNMWNFVS6STQVGUB/graph.json","events_json":"https://pith.science/api/pith-number/Z6OK42G3QINNMWNFVS6STQVGUB/events.json","paper":"https://pith.science/paper/Z6OK42G3"},"agent_actions":{"view_html":"https://pith.science/pith/Z6OK42G3QINNMWNFVS6STQVGUB","download_json":"https://pith.science/pith/Z6OK42G3QINNMWNFVS6STQVGUB.json","view_paper":"https://pith.science/paper/Z6OK42G3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5368&json=true","fetch_graph":"https://pith.science/api/pith-number/Z6OK42G3QINNMWNFVS6STQVGUB/graph.json","fetch_events":"https://pith.science/api/pith-number/Z6OK42G3QINNMWNFVS6STQVGUB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z6OK42G3QINNMWNFVS6STQVGUB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z6OK42G3QINNMWNFVS6STQVGUB/action/storage_attestation","attest_author":"https://pith.science/pith/Z6OK42G3QINNMWNFVS6STQVGUB/action/author_attestation","sign_citation":"https://pith.science/pith/Z6OK42G3QINNMWNFVS6STQVGUB/action/citation_signature","submit_replication":"https://pith.science/pith/Z6OK42G3QINNMWNFVS6STQVGUB/action/replication_record"}},"created_at":"2026-05-18T03:47:01.391331+00:00","updated_at":"2026-05-18T03:47:01.391331+00:00"}