{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5LC56JDSOTIO6WLK725RQ7T5Z2","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":"2aed40d80f6d57e12c33082b8b86f5bc5ac87b189b8f1405546e38421085457c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-30T19:05:44Z","title_canon_sha256":"9ab3e08d757b732f89090a936ee621787547cc1a16cfb33290ea63998153c204"},"schema_version":"1.0","source":{"id":"1004.5592","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5592","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5592v2","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5592","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"5LC56JDSOTIO","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5LC56JDSOTIO6WLK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5LC56JDS","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:f2487e70a3da23c9b7e4ec0d1f4b67759b4a66cb47af302bd06c3d40d23e3591","target":"graph","created_at":"2026-05-18T02:24:09Z","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 study the initial value problem associated to the Benjamin-Ono equation. The aim is to establish persistence properties of the solution flow in the weighted Sobolev spaces $Z_{s,r}=H^s(\\R)\\cap L^2(|x|^{2r}dx)$, $s\\in\\R, \\,s\\geq 1$ and $s\\geq r$. We also prove some unique continuation properties of the solution flow in these spaces. In particular, these continuation principles demostrate that our persistence properties are sharp.","authors_text":"German Fonseca, Gustavo Ponce","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-30T19:05:44Z","title":"The IVP for the Benjamin-Ono equation in weighted Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5592","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":"sha256:9d71eaf596d604df783183544a3c09ba9b3abe16aaa26851a1ef796e883ad43c","target":"record","created_at":"2026-05-18T02:24:09Z","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":"2aed40d80f6d57e12c33082b8b86f5bc5ac87b189b8f1405546e38421085457c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-30T19:05:44Z","title_canon_sha256":"9ab3e08d757b732f89090a936ee621787547cc1a16cfb33290ea63998153c204"},"schema_version":"1.0","source":{"id":"1004.5592","kind":"arxiv","version":2}},"canonical_sha256":"eac5df247274d0ef596afebb187e7dce86de47e95de7e8ef5dfb00f5b1d735f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eac5df247274d0ef596afebb187e7dce86de47e95de7e8ef5dfb00f5b1d735f8","first_computed_at":"2026-05-18T02:24:09.740785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:09.740785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YrdCNK2GFG3P2Bt++gnCgfHIkxqs23nCv0wT7kd4/tH3zBg1x0MM+b63+I9YjUU7l6xQoH7PJ0/zB0w5yuEaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:09.741572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5592","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d71eaf596d604df783183544a3c09ba9b3abe16aaa26851a1ef796e883ad43c","sha256:f2487e70a3da23c9b7e4ec0d1f4b67759b4a66cb47af302bd06c3d40d23e3591"],"state_sha256":"70613a05468eec33c9cfd3039c76c25173fba8c287a1835cbbcad7e002369498"}