{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:72C4VQA6TIAN6KWQM63TDZPJIX","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":"036fa298f10c8dee5d9b25be70e3c5a4cfea2df22bd60043ca19dec48f414dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-29T01:02:01Z","title_canon_sha256":"cb0349332926f05ec3721b64d84007b66dccd392d5e14f7afc93ea4c50113135"},"schema_version":"1.0","source":{"id":"1009.5726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5726","created_at":"2026-05-18T03:57:12Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5726v2","created_at":"2026-05-18T03:57:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5726","created_at":"2026-05-18T03:57:12Z"},{"alias_kind":"pith_short_12","alias_value":"72C4VQA6TIAN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"72C4VQA6TIAN6KWQ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"72C4VQA6","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:4d1c5621929a06c2ff7b740b9360951b5942cf00585c3cfb63e21552d9112069","target":"graph","created_at":"2026-05-18T03:57:12Z","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 show that the Cauchy problem for the defocusing generalized Boussinesq equation $u_{tt}-u_{xx}+u_{xxxx}-(|u|^{2k}u)_{xx}=0$, $k\\geq1$, on the real line is globally well-posed in $H^{s}(\\R)$ for $s>1-({1}/{3k})$. We use the \"$I$-method\" to define a modification of the energy functional that is \"almost conserved\" in time. Our result extends the previous one obtained by Farah and Linares (2010 \\textit{J. London Math. Soc.} \\textbf{81} 241-254) when $k=1$.","authors_text":"Hongwei Wang, Luiz Gustavo Farah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-29T01:02:01Z","title":"Global solutions for the generalized Boussinesq equation in low-order Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5726","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":"sha256:2615dab4c1de09267d8aadd1218cce594e2759f8ac5ba28e8d6d43f03392ec05","target":"record","created_at":"2026-05-18T03:57:12Z","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":"036fa298f10c8dee5d9b25be70e3c5a4cfea2df22bd60043ca19dec48f414dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-29T01:02:01Z","title_canon_sha256":"cb0349332926f05ec3721b64d84007b66dccd392d5e14f7afc93ea4c50113135"},"schema_version":"1.0","source":{"id":"1009.5726","kind":"arxiv","version":2}},"canonical_sha256":"fe85cac01e9a00df2ad067b731e5e945c774541641569e07d5585a3a007158ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe85cac01e9a00df2ad067b731e5e945c774541641569e07d5585a3a007158ba","first_computed_at":"2026-05-18T03:57:12.975326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:12.975326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"woW8snqItIMsEa0jA9bqu27BLI7nDu6WnMCItZhpVNavl9EnJD7nUzQaJ8eOz3mdevagf9d69POda+93/fMrDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:12.976020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2615dab4c1de09267d8aadd1218cce594e2759f8ac5ba28e8d6d43f03392ec05","sha256:4d1c5621929a06c2ff7b740b9360951b5942cf00585c3cfb63e21552d9112069"],"state_sha256":"0516c0564951eff7e2801eeacfb97256dd1a82db5056255eb5743048661ed851"}