{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:B5R7HA3KOIOFJ42DLYEMLWFRNT","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":"44faf048975c697c4e364abd6dbd0b7fe12d3e56424539dc5f96fec38dd37c3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-27T03:06:39Z","title_canon_sha256":"1692afa0234160deba094da35137068d61d809a95c1351e07f7c726e5bbb7ffe"},"schema_version":"1.0","source":{"id":"1110.5967","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5967","created_at":"2026-05-18T03:41:11Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5967v2","created_at":"2026-05-18T03:41:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5967","created_at":"2026-05-18T03:41:11Z"},{"alias_kind":"pith_short_12","alias_value":"B5R7HA3KOIOF","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"B5R7HA3KOIOFJ42D","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"B5R7HA3K","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:2aa917d61f99a389c24547eb545926980e2907fe8c06cdd5e1e7f5f6b60db1fb","target":"graph","created_at":"2026-05-18T03:41:11Z","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 dispersion generalized Benjamin-Ono equation. Our aim is to establish well posedness results in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model.","authors_text":"Felipe Linares, German Fonseca, Gustavo Ponce","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-27T03:06:39Z","title":"The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5967","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":"sha256:35c5d506c38e9155f7f62967b1536866e9f31b0d994d5e481c3844c424a2212a","target":"record","created_at":"2026-05-18T03:41:11Z","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":"44faf048975c697c4e364abd6dbd0b7fe12d3e56424539dc5f96fec38dd37c3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-27T03:06:39Z","title_canon_sha256":"1692afa0234160deba094da35137068d61d809a95c1351e07f7c726e5bbb7ffe"},"schema_version":"1.0","source":{"id":"1110.5967","kind":"arxiv","version":2}},"canonical_sha256":"0f63f3836a721c54f3435e08c5d8b16cfaa064a8218384908327b5bf00e3c834","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f63f3836a721c54f3435e08c5d8b16cfaa064a8218384908327b5bf00e3c834","first_computed_at":"2026-05-18T03:41:11.029131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:11.029131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+EG22ErD1/u7m7yHH2BEg6sd72aH0mF8HEDicz3fmX3k+lo66eArNYUI5LRVkjps+czIviX7cAv2b6RGMza7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:11.029701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5967","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35c5d506c38e9155f7f62967b1536866e9f31b0d994d5e481c3844c424a2212a","sha256:2aa917d61f99a389c24547eb545926980e2907fe8c06cdd5e1e7f5f6b60db1fb"],"state_sha256":"ba5dcee05b82c33d8d2a7ae22d2a3fcf909474ad19fa2975f885c38b9acdfe64"}