{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PVOTSI63XZVCE5BCYPDEHQPRGA","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":"def5d5fe5e1dc4433d0fd0b9d1e78d611a65a2ca271b4b590010e93fd82524f6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-23T14:41:00Z","title_canon_sha256":"df9200d035bf537c76a867c79ed7ff12caf00bc69e41a1c0d59e16ef65cec598"},"schema_version":"1.0","source":{"id":"1205.5188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5188","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5188v1","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5188","created_at":"2026-05-18T02:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"PVOTSI63XZVC","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PVOTSI63XZVCE5BC","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PVOTSI63","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:a09a5f8a979bf5fe3bf9a684db284d56ef9c82461c698815d49ede1340a4aead","target":"graph","created_at":"2026-05-18T02:21:09Z","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 consider the cubic defocusing nonlinear Schr\\\"odinger equation in the two dimensional torus. Fix $s>1$. Colliander, Keel, Staffilani, Tao and Takaoka proved in \\cite{CollianderKSTT10} the existence of solutions with $s$-Sobolev norm growing in time.\n  We establish the existence of solutions with polynomial time estimates. More exactly, there is $c>0$ such that for any $\\mathcal{K}\\gg 1$ we find a solution $u$ and a time $T$ such that $\\| u(T)\\|_{H^s}\\geq\\mathcal{K} \\| u(0)\\|_{H^s}$. Moreover, time $T$ satisfies polynomial bound $0<T<\\mathcal{K}^c$.","authors_text":"Marcel Guardia, Vadim Kaloshin","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-23T14:41:00Z","title":"Growth of Sobolev norms in the cubic defocusing nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5188","kind":"arxiv","version":1},"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":"sha256:1dada00de4bd8bf6529f5c05cf14fca4c43869e64d31e967becac116a9c6abc6","target":"record","created_at":"2026-05-18T02:21:09Z","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":"def5d5fe5e1dc4433d0fd0b9d1e78d611a65a2ca271b4b590010e93fd82524f6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-23T14:41:00Z","title_canon_sha256":"df9200d035bf537c76a867c79ed7ff12caf00bc69e41a1c0d59e16ef65cec598"},"schema_version":"1.0","source":{"id":"1205.5188","kind":"arxiv","version":1}},"canonical_sha256":"7d5d3923dbbe6a227422c3c643c1f13034d5e10cf112219fd17d1bf82b2f3b8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d5d3923dbbe6a227422c3c643c1f13034d5e10cf112219fd17d1bf82b2f3b8c","first_computed_at":"2026-05-18T02:21:09.981168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:09.981168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5wjihVRBSUOwylytJUGyCt85/tNDGIdSswTYFvl2f5qrVM4KGtxFbx4udNunngnXL8n1s4XW1rQKKu/g+uMvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:09.981740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dada00de4bd8bf6529f5c05cf14fca4c43869e64d31e967becac116a9c6abc6","sha256:a09a5f8a979bf5fe3bf9a684db284d56ef9c82461c698815d49ede1340a4aead"],"state_sha256":"b22ceb3b909fa9ba5d8bb6a16c8af8d08f0c8ef3f7dc642987eefee70fcf7b74"}