{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AWJG5LUCFY5H7PIRJYGEAQHT5T","short_pith_number":"pith:AWJG5LUC","canonical_record":{"source":{"id":"1505.00086","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-01T04:47:30Z","cross_cats_sorted":[],"title_canon_sha256":"4e01baa24a458ac6b018acaa52abd2f1fc6a804869fdfeea78ea4d174bcd8ed4","abstract_canon_sha256":"d68664df6366344745a780b713ace9a049c88cda9dda4d6347318698ef6adaee"},"schema_version":"1.0"},"canonical_sha256":"05926eae822e3a7fbd114e0c4040f3ecd48f4d1ae335e61ed5fcd3e9d4a1f979","source":{"kind":"arxiv","id":"1505.00086","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00086","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00086v2","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00086","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"pith_short_12","alias_value":"AWJG5LUCFY5H","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AWJG5LUCFY5H7PIR","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AWJG5LUC","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AWJG5LUCFY5H7PIRJYGEAQHT5T","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00086","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-01T04:47:30Z","cross_cats_sorted":[],"title_canon_sha256":"4e01baa24a458ac6b018acaa52abd2f1fc6a804869fdfeea78ea4d174bcd8ed4","abstract_canon_sha256":"d68664df6366344745a780b713ace9a049c88cda9dda4d6347318698ef6adaee"},"schema_version":"1.0"},"canonical_sha256":"05926eae822e3a7fbd114e0c4040f3ecd48f4d1ae335e61ed5fcd3e9d4a1f979","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:41.593429Z","signature_b64":"5173e3P3/1oNmv9O742E0fQMAQmy9L0QAPsoMV31Dze02TuCrSLwoPp2rSDsLl/DiyjV16JkeZro8Q9cT37NBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05926eae822e3a7fbd114e0c4040f3ecd48f4d1ae335e61ed5fcd3e9d4a1f979","last_reissued_at":"2026-05-18T01:36:41.592783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:41.592783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00086","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhc0eoYd/0MzFMQad8UAhlQThJ9QUQZUn9QJFicllLCVaqHFmuCkG313BTwOiLPhK3nvHG+m7gIBBoIW7jGIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:32:53.445940Z"},"content_sha256":"d7aed78ddf4abdadd7b228a50f056e9321ed740fe156a2979b6d0583920347f7","schema_version":"1.0","event_id":"sha256:d7aed78ddf4abdadd7b228a50f056e9321ed740fe156a2979b6d0583920347f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AWJG5LUCFY5H7PIRJYGEAQHT5T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xi Tu, Zhaoyang Yin","submitted_at":"2015-05-01T04:47:30Z","abstract_excerpt":"In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the equation in Besov spaces. Then we give a simply blow-up criterion for the Cauchy problem of the equation. we present a blow-up result and the exact blow-up rate of strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion.Finally, we verify that the system possesses peakon solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00086","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ofiOcWy9+bD/BUDD9BNKCuQzjcygtC0Xs6/JiFEbLVfME4xF818bQI/2Hnh0AzqeT0ITQfgC6qxfDKiNMwLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:32:53.446628Z"},"content_sha256":"34032b6990554241ebefb2dafbc3aea22cb5c747cb385e6991a9a85fc8398531","schema_version":"1.0","event_id":"sha256:34032b6990554241ebefb2dafbc3aea22cb5c747cb385e6991a9a85fc8398531"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWJG5LUCFY5H7PIRJYGEAQHT5T/bundle.json","state_url":"https://pith.science/pith/AWJG5LUCFY5H7PIRJYGEAQHT5T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWJG5LUCFY5H7PIRJYGEAQHT5T/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T08:32:53Z","links":{"resolver":"https://pith.science/pith/AWJG5LUCFY5H7PIRJYGEAQHT5T","bundle":"https://pith.science/pith/AWJG5LUCFY5H7PIRJYGEAQHT5T/bundle.json","state":"https://pith.science/pith/AWJG5LUCFY5H7PIRJYGEAQHT5T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWJG5LUCFY5H7PIRJYGEAQHT5T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AWJG5LUCFY5H7PIRJYGEAQHT5T","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":"d68664df6366344745a780b713ace9a049c88cda9dda4d6347318698ef6adaee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-01T04:47:30Z","title_canon_sha256":"4e01baa24a458ac6b018acaa52abd2f1fc6a804869fdfeea78ea4d174bcd8ed4"},"schema_version":"1.0","source":{"id":"1505.00086","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00086","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00086v2","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00086","created_at":"2026-05-18T01:36:41Z"},{"alias_kind":"pith_short_12","alias_value":"AWJG5LUCFY5H","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AWJG5LUCFY5H7PIR","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AWJG5LUC","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:34032b6990554241ebefb2dafbc3aea22cb5c747cb385e6991a9a85fc8398531","target":"graph","created_at":"2026-05-18T01:36:41Z","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 mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the equation in Besov spaces. Then we give a simply blow-up criterion for the Cauchy problem of the equation. we present a blow-up result and the exact blow-up rate of strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion.Finally, we verify that the system possesses peakon solutions.","authors_text":"Xi Tu, Zhaoyang Yin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-01T04:47:30Z","title":"Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00086","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:d7aed78ddf4abdadd7b228a50f056e9321ed740fe156a2979b6d0583920347f7","target":"record","created_at":"2026-05-18T01:36:41Z","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":"d68664df6366344745a780b713ace9a049c88cda9dda4d6347318698ef6adaee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-01T04:47:30Z","title_canon_sha256":"4e01baa24a458ac6b018acaa52abd2f1fc6a804869fdfeea78ea4d174bcd8ed4"},"schema_version":"1.0","source":{"id":"1505.00086","kind":"arxiv","version":2}},"canonical_sha256":"05926eae822e3a7fbd114e0c4040f3ecd48f4d1ae335e61ed5fcd3e9d4a1f979","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05926eae822e3a7fbd114e0c4040f3ecd48f4d1ae335e61ed5fcd3e9d4a1f979","first_computed_at":"2026-05-18T01:36:41.592783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:41.592783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5173e3P3/1oNmv9O742E0fQMAQmy9L0QAPsoMV31Dze02TuCrSLwoPp2rSDsLl/DiyjV16JkeZro8Q9cT37NBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:41.593429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00086","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7aed78ddf4abdadd7b228a50f056e9321ed740fe156a2979b6d0583920347f7","sha256:34032b6990554241ebefb2dafbc3aea22cb5c747cb385e6991a9a85fc8398531"],"state_sha256":"bafd7c7dbe5f6c01f0685ed0cb42432318891170d33d5d786061be65194a02a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HRp9n4iZSg29YLDUGJD0f8Sp8XtTjah/HKFEE8fh7o8EXldLeQHEnM3EpMmoEQF90VFfUew3vDRK/XhXDWyxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:32:53.450026Z","bundle_sha256":"fa2299c0776f7ebc94ded872aa5a7f55d69b2791f5d5903e758f098980b74a0f"}}