{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:55SQ2NVDJLPBJZWFZ5VJ4RVGO6","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":"e945cef992cf9707794c0b755465d018d0763dba20fc2f1b2fa45ea81cbb88b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-18T20:30:14Z","title_canon_sha256":"4986adf873cb581bd796c6f5a3820c56d32aa0cb42582c8a91e87ae74c01bfad"},"schema_version":"1.0","source":{"id":"1407.5110","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5110","created_at":"2026-05-18T02:43:34Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5110v2","created_at":"2026-05-18T02:43:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5110","created_at":"2026-05-18T02:43:34Z"},{"alias_kind":"pith_short_12","alias_value":"55SQ2NVDJLPB","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"55SQ2NVDJLPBJZWF","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"55SQ2NVD","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:fd21d49454e4ad4dbcbb79a2d358d1d9a051c7e40829c2d5935747dc8510756b","target":"graph","created_at":"2026-05-18T02:43:34Z","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 special regularity and decay properties of solutions to the IVP associated to the $k$-generalized KdV equations. In particular, for datum $u_0\\in H^{3/4^+}(\\mathbb R)$ whose restriction belongs to $H^l((b,\\infty))$ for some $l\\in\\mathbb Z^+$ and $b\\in \\mathbb R$ we prove that the restriction of the corresponding solution $u(\\cdot,t)$ belongs to $H^l((\\beta,\\infty))$ for any $\\beta \\in \\mathbb R$ and any $t\\in (0,T)$. Thus, this type of regularity propagates with infinite speed to its left as time evolves.","authors_text":"Felipe Linares, Gustavo Ponce, Pedro Isaza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-18T20:30:14Z","title":"Propagation of regularity and decay of solutions to the $k$-generalized Korteweg-de Vries equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5110","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":"sha256:995806b96d61d6c12ae16754b73689ae00898f2ced4abe84831e62bae2ca12bd","target":"record","created_at":"2026-05-18T02:43:34Z","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":"e945cef992cf9707794c0b755465d018d0763dba20fc2f1b2fa45ea81cbb88b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-18T20:30:14Z","title_canon_sha256":"4986adf873cb581bd796c6f5a3820c56d32aa0cb42582c8a91e87ae74c01bfad"},"schema_version":"1.0","source":{"id":"1407.5110","kind":"arxiv","version":2}},"canonical_sha256":"ef650d36a34ade14e6c5cf6a9e46a677ae32e4af9a76c20d4c59048d31ac35ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef650d36a34ade14e6c5cf6a9e46a677ae32e4af9a76c20d4c59048d31ac35ba","first_computed_at":"2026-05-18T02:43:34.261824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:34.261824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z1mLJadptdyrw2uEqDXpprMzUwX+z5aRhvGrXrqrIDFjyRUGJu6mHvhOZGRfQla7ZX+WjR//g7wlVK0fS2ZRDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:34.262444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5110","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:995806b96d61d6c12ae16754b73689ae00898f2ced4abe84831e62bae2ca12bd","sha256:fd21d49454e4ad4dbcbb79a2d358d1d9a051c7e40829c2d5935747dc8510756b"],"state_sha256":"1ab574d5b816db56cacdbad65cb36d0ab1557c159efd9a208b187a288d33da25"}