{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:G3DUGWOVYBLGUHTZJA6S2C2VDD","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":"e1923309956fb3b8dd619259ee7f58be44e404611da3c905f54681bd771a46da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-27T09:20:02Z","title_canon_sha256":"4957e86cd352b0de9c01eaeb226e8c6a080cafacb2e951888f35a8e9f0c48dc9"},"schema_version":"1.0","source":{"id":"2411.18163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18163","created_at":"2026-07-05T09:41:12Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18163v1","created_at":"2026-07-05T09:41:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18163","created_at":"2026-07-05T09:41:12Z"},{"alias_kind":"pith_short_12","alias_value":"G3DUGWOVYBLG","created_at":"2026-07-05T09:41:12Z"},{"alias_kind":"pith_short_16","alias_value":"G3DUGWOVYBLGUHTZ","created_at":"2026-07-05T09:41:12Z"},{"alias_kind":"pith_short_8","alias_value":"G3DUGWOV","created_at":"2026-07-05T09:41:12Z"}],"graph_snapshots":[{"event_id":"sha256:a7a78c05836ea903933add7ca5a1527383936e48714f972ca3881de888f12c38","target":"graph","created_at":"2026-07-05T09:41:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.18163/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove the global well-posedness of the energy-critical nonlinear Schr\\\"odinger equations on the torus $\\mathbb{T}^{d}$ for general dimensions. This result is new for dimensions $d\\ge5$, extending previous results for $d=3,4$ [10,22]. Compared to the cases $d=3,4$, the regularity theory for higher $d$, developed in the underlying local well-posedness result [17], is less understood. In particular, stability theory and inverse inequalities, which are ingredients in [10,22] and more generally in the widely used concentration compactness framework since [13], are too weak to be a","authors_text":"Beomjong Kwak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-27T09:20:02Z","title":"Global well-posedness of the energy-critical nonlinear Schr\\\"odinger equations on $\\mathbb{T}^{d}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18163","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":"sha256:32c463f786d358f133cc616eb99077d53ca80422ea27f6498f1345211127c590","target":"record","created_at":"2026-07-05T09:41:12Z","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":"e1923309956fb3b8dd619259ee7f58be44e404611da3c905f54681bd771a46da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-27T09:20:02Z","title_canon_sha256":"4957e86cd352b0de9c01eaeb226e8c6a080cafacb2e951888f35a8e9f0c48dc9"},"schema_version":"1.0","source":{"id":"2411.18163","kind":"arxiv","version":1}},"canonical_sha256":"36c74359d5c0566a1e79483d2d0b5518cf3f2e632660c8e775830e8951bf5dbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36c74359d5c0566a1e79483d2d0b5518cf3f2e632660c8e775830e8951bf5dbb","first_computed_at":"2026-07-05T09:41:12.750440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:12.750440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j+4Dyk22ahjZrcw68LAUu0RmDivUchuKpmD2kss7dwItmYogfWf7QhSeTiRBFEA107rKysbqEx1tPjgKBrf+Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:12.750887Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32c463f786d358f133cc616eb99077d53ca80422ea27f6498f1345211127c590","sha256:a7a78c05836ea903933add7ca5a1527383936e48714f972ca3881de888f12c38"],"state_sha256":"e2865da3e4dc08c5a1fdeb631cc68e21901db3fe48787bc0ac2ade0034fa35f4"}