{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:H4MHYSQNKAZVRGATXEWBMMW2B2","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":"2def670babfa2215b3da234a4fbcb91c03284c1250931cf713372d50a6b9eb85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-12T11:41:50Z","title_canon_sha256":"830d014277c26c4072e916d93166b555ff1d1c0c58af7b5da51a2177afe6ed84"},"schema_version":"1.0","source":{"id":"1409.3706","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3706","created_at":"2026-05-18T02:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3706v2","created_at":"2026-05-18T02:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3706","created_at":"2026-05-18T02:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"H4MHYSQNKAZV","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"H4MHYSQNKAZVRGAT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"H4MHYSQN","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:7399602011df369587c259b6135b4b23811ede567ebf48d341862b8a22c5c6aa","target":"graph","created_at":"2026-05-18T02:29:52Z","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 obtain global well-posedness in low order Sobolev spaces of higher order KdV type equations with dissipation. The result is optimal in the sense that the flow-map is not twice continuously differentiable in rougher spaces. The solution is shown to be smooth for positive times.","authors_text":"Mikael Signahl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-12T11:41:50Z","title":"Almost Sharp Global Well-Posedness for a class of Dissipative and Dispersive Equations on R in Low Regularity Sobolev Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3706","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":"sha256:7c09a8871e34fdddab96341fa120f2f1e43abd0cfd448cb902284e84da052aba","target":"record","created_at":"2026-05-18T02:29:52Z","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":"2def670babfa2215b3da234a4fbcb91c03284c1250931cf713372d50a6b9eb85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-12T11:41:50Z","title_canon_sha256":"830d014277c26c4072e916d93166b555ff1d1c0c58af7b5da51a2177afe6ed84"},"schema_version":"1.0","source":{"id":"1409.3706","kind":"arxiv","version":2}},"canonical_sha256":"3f187c4a0d5033589813b92c1632da0e8b6f958b6ece18d6315242f91f8d6585","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f187c4a0d5033589813b92c1632da0e8b6f958b6ece18d6315242f91f8d6585","first_computed_at":"2026-05-18T02:29:52.865347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:52.865347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qqpAvyLfyVIxIBMeHtXS2ZFS57qYM/UuXDLEGy+grouks0Iqul79vZZkqDJXxOwh6OYcMo9B660JY4sgb/DDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:52.866601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3706","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c09a8871e34fdddab96341fa120f2f1e43abd0cfd448cb902284e84da052aba","sha256:7399602011df369587c259b6135b4b23811ede567ebf48d341862b8a22c5c6aa"],"state_sha256":"8fedd6017cdd9a2c08469bace6f4801b80b2a1b0e41bfeadd7c63321a1743d95"}