{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LHN6L43XB4C3BVGHOJ7X65B5GH","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":"8e991c9517642465baaeafe9197a2a5d02f40ff062b48ac3491cf22278e8fd36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-22T02:22:43Z","title_canon_sha256":"ffeee2967ccc5a572f53d6501418dae9703a249524f0bdd46c8bd69699ef0859"},"schema_version":"1.0","source":{"id":"1103.4190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4190","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4190v2","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4190","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"LHN6L43XB4C3","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LHN6L43XB4C3BVGH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LHN6L43X","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:987bbd952d730ff782fb23234d494f9387b5fb001e477c7696eb82b99192d599","target":"graph","created_at":"2026-05-18T04:25:37Z","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":"The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for $H^s$ initial data, $s>-1/2$, and for any $s_1<\\min(3s+1,s+1)$, the difference of the nonlinear and linear evolutions is in $H^{s_1}$ for all times, with at most polynomially growing $H^{s_1}$ norm. The result also extends to KdV with a smooth, mean zero, time-dependent potential in the case $s\\geq 0$. Our result and a theorem of Oskolkov for the Airy evolution imply that if one starts with continuous and bounded variation initial data then the solution of KdV (given by the $L^2$ theory o","authors_text":"Burak Erdogan, Nikolaos Tzirakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-22T02:22:43Z","title":"Global Smoothing for the Periodic KdV Evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4190","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:f51fe22c51c3da351710ed54e31d0e188d7e284d129cd226db35b23c78d00958","target":"record","created_at":"2026-05-18T04:25:37Z","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":"8e991c9517642465baaeafe9197a2a5d02f40ff062b48ac3491cf22278e8fd36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-22T02:22:43Z","title_canon_sha256":"ffeee2967ccc5a572f53d6501418dae9703a249524f0bdd46c8bd69699ef0859"},"schema_version":"1.0","source":{"id":"1103.4190","kind":"arxiv","version":2}},"canonical_sha256":"59dbe5f3770f05b0d4c7727f7f743d31c5720f7eebd18015268096b857a31379","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59dbe5f3770f05b0d4c7727f7f743d31c5720f7eebd18015268096b857a31379","first_computed_at":"2026-05-18T04:25:37.531922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:37.531922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iQYGl9zKcB0sjjLah7vWdhMSlk4WIm3Y9EYGlIoL+2KqNTPgXP2GKW5AmHHta7X0IjkO7lVsDH23Q/oUxVPpDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:37.532452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f51fe22c51c3da351710ed54e31d0e188d7e284d129cd226db35b23c78d00958","sha256:987bbd952d730ff782fb23234d494f9387b5fb001e477c7696eb82b99192d599"],"state_sha256":"651fac91a99be162791901d50d06eb36f4bdb28d2f470a429eebb15db0016575"}