{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X4LJUBZI3D4EOIGJN47TCIICBU","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":"bff3fb08af4a8123c300505b12639c449f2228672d1696a2cb31cde8e4d8c619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-15T12:13:11Z","title_canon_sha256":"73c39c6956282a0b2ad18d537fdd5718cdcf9160cb8ff82e00bc873206b85ae0"},"schema_version":"1.0","source":{"id":"1601.03889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03889","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03889v1","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03889","created_at":"2026-05-18T01:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"X4LJUBZI3D4E","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X4LJUBZI3D4EOIGJ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X4LJUBZI","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:83b0aba6f8bef27674f90b164996c7cb1f0b42d015908bf79a9dea21a769cbb2","target":"graph","created_at":"2026-05-18T01:22:49Z","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 study the global well-posedness for the Camassa-Holm(C-H) equation with a forcing in $H^1(\\mathbb{R})$ by the characteristic method. Due to the forcing, many important properties to study the well posedness of weak solutions do not inherit from the C-H equation without a forcing, such as conservation laws, integrability. By exploiting the balance law and some new estimates, we prove the existence and uniqueness of global weak solutions for the C-H equation with a forcing in $H^1(\\mathbb{R})$.","authors_text":"Shihui Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-15T12:13:11Z","title":"Existence and Uniqueness of Global Weak solutions of the Camassa-Holm Equation with a Forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03889","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":"sha256:7199436815326406f629ae9f2d9ee7cfadd2bdd3890ea6a0d484bd7f0f892624","target":"record","created_at":"2026-05-18T01:22:49Z","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":"bff3fb08af4a8123c300505b12639c449f2228672d1696a2cb31cde8e4d8c619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-15T12:13:11Z","title_canon_sha256":"73c39c6956282a0b2ad18d537fdd5718cdcf9160cb8ff82e00bc873206b85ae0"},"schema_version":"1.0","source":{"id":"1601.03889","kind":"arxiv","version":1}},"canonical_sha256":"bf169a0728d8f84720c96f3f3121020d0dd05f81830dc748b01d807f24cfa74a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf169a0728d8f84720c96f3f3121020d0dd05f81830dc748b01d807f24cfa74a","first_computed_at":"2026-05-18T01:22:49.778024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:49.778024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"10TxDNp6Qy2j0kTu4Nyjik9MmNfqGgq9dGJDgj/w0RpaZq9aKOkdoGAoO4xzw5n2EBr8bhvlOxXQNfkh8ZtgAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:49.778478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7199436815326406f629ae9f2d9ee7cfadd2bdd3890ea6a0d484bd7f0f892624","sha256:83b0aba6f8bef27674f90b164996c7cb1f0b42d015908bf79a9dea21a769cbb2"],"state_sha256":"0d0ccbe6deb3230a47247c37d7707219a9acb13b94ace57242c5f08b6fe97413"}