{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S2EKODSKVMGOZPV7DINVJOT2FP","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":"18c30f208f3a630f70bbf6148d5a883afa6753fe0e03dc13d8385068d9f3f36d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-03T09:50:14Z","title_canon_sha256":"92a76f109adedd6fb0ca8604edb7c3a9e06a29b580f21d7070d007e9f753ab1e"},"schema_version":"1.0","source":{"id":"1506.01183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01183","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01183v1","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01183","created_at":"2026-05-18T01:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"S2EKODSKVMGO","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S2EKODSKVMGOZPV7","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S2EKODSK","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:cebfdf72ed2ba4e804a8b57210b1e689fe6854a6897488b2b9bacfd0ae605822","target":"graph","created_at":"2026-05-18T01:58:24Z","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 investigate the Cauchy problem of a three-component Camassa-Holm system. By using the method of approximation of smooth solutions, a regularization technique and the special structure of the system, we prove the existence of global weak solutions to the system.","authors_text":"Wei Luo, Zhaoyang Yin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-03T09:50:14Z","title":"Global weak solutions for a three-component Camassa-Holm system with N-peakon solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01183","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:ffb174fbcee43a9e50c549cb831ad715d21689a6beab5a295e8e770fa9fd5fc1","target":"record","created_at":"2026-05-18T01:58:24Z","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":"18c30f208f3a630f70bbf6148d5a883afa6753fe0e03dc13d8385068d9f3f36d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-03T09:50:14Z","title_canon_sha256":"92a76f109adedd6fb0ca8604edb7c3a9e06a29b580f21d7070d007e9f753ab1e"},"schema_version":"1.0","source":{"id":"1506.01183","kind":"arxiv","version":1}},"canonical_sha256":"9688a70e4aab0cecbebf1a1b54ba7a2bf627064820b6427704596b63c321f412","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9688a70e4aab0cecbebf1a1b54ba7a2bf627064820b6427704596b63c321f412","first_computed_at":"2026-05-18T01:58:24.861822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:24.861822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m/4EbbVr8n5dst/KidFbCBfXXjISO2yE5hphOIdJI9mpTqT2I92tjCC/QIK3tWRAv4N/tmVtbCX/N7SGB3FyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:24.862426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffb174fbcee43a9e50c549cb831ad715d21689a6beab5a295e8e770fa9fd5fc1","sha256:cebfdf72ed2ba4e804a8b57210b1e689fe6854a6897488b2b9bacfd0ae605822"],"state_sha256":"318653547bb2b14aee47fbbb96ff47fa19116dc274bcf7e11084b925f6c6f8ed"}