{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3FKPCM4P6MNDRL3QW426COP3ML","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":"cad1d716a43ac1b8a6b2381c7b603beb03590eeda5558836cd2af02c20d5ad8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-22T00:22:56Z","title_canon_sha256":"7cbc707580a83f9a179e1435c5c737914d74abecf1f816cfcee9ae14ac7362fc"},"schema_version":"1.0","source":{"id":"1302.5456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5456","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5456v2","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5456","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"3FKPCM4P6MND","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3FKPCM4P6MNDRL3Q","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3FKPCM4P","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:bda5a9369376116f8dff7e09534ca1dd0474a10b273dda7cb0f8cec8235edc79","target":"graph","created_at":"2026-05-18T03:18:42Z","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":"We prove that the periodic modified Benjamin-Ono equation is locally well-posed in the energy space $H^{1/2}$. This ensures the global well-posedness in the defocusing case. The proof is based on an $X^{s,b}$ analysis of the system after gauge transform.","authors_text":"Luc Molinet, Yiquan Lin, Zihua Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-22T00:22:56Z","title":"Well-posedness in energy space for the periodic modified Benjamin-Ono equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5456","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":"sha256:1b97aae7f9c15c0793f325d9c9fda3a16aca0f2f66481a2d6879dcd33060a211","target":"record","created_at":"2026-05-18T03:18:42Z","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":"cad1d716a43ac1b8a6b2381c7b603beb03590eeda5558836cd2af02c20d5ad8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-22T00:22:56Z","title_canon_sha256":"7cbc707580a83f9a179e1435c5c737914d74abecf1f816cfcee9ae14ac7362fc"},"schema_version":"1.0","source":{"id":"1302.5456","kind":"arxiv","version":2}},"canonical_sha256":"d954f1338ff31a38af70b735e139fb62eee346f9c2cc1c1bfa710fc5c9812d75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d954f1338ff31a38af70b735e139fb62eee346f9c2cc1c1bfa710fc5c9812d75","first_computed_at":"2026-05-18T03:18:42.387542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:42.387542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+JLxQiHbIOsqRtYvwJAFQ98AmTBPxNTdqOlHk17xl+jtoaocBckGsOWi28OuowQl0iH2HVxm0MpktmrVLh0/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:42.388349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b97aae7f9c15c0793f325d9c9fda3a16aca0f2f66481a2d6879dcd33060a211","sha256:bda5a9369376116f8dff7e09534ca1dd0474a10b273dda7cb0f8cec8235edc79"],"state_sha256":"ccf2f37105b7fbb6a1546170a80d4d4728f5eaa63493cd32b497edb87af08962"}