{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:32CJA6SNP5TR5DHV2KZCCAZQRW","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":"835aacee676d3a01c69a8c96ede73b3efd600af2112b4ab5c0f12a995f8e8cdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-26T06:30:12Z","title_canon_sha256":"2402228f0d998416f10f42f79d31e93620edc08ffa486fe2d8d3e1eceda1b79d"},"schema_version":"1.0","source":{"id":"2411.17147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.17147","created_at":"2026-07-05T09:40:28Z"},{"alias_kind":"arxiv_version","alias_value":"2411.17147v1","created_at":"2026-07-05T09:40:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17147","created_at":"2026-07-05T09:40:28Z"},{"alias_kind":"pith_short_12","alias_value":"32CJA6SNP5TR","created_at":"2026-07-05T09:40:28Z"},{"alias_kind":"pith_short_16","alias_value":"32CJA6SNP5TR5DHV","created_at":"2026-07-05T09:40:28Z"},{"alias_kind":"pith_short_8","alias_value":"32CJA6SN","created_at":"2026-07-05T09:40:28Z"}],"graph_snapshots":[{"event_id":"sha256:4d9ba587cb4623051cc6a6a873a7912705282dd595d0190e9d15bfd6afbbb1e3","target":"graph","created_at":"2026-07-05T09:40:28Z","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/2411.17147/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the local well-posedness of nonlinear Schr\\\"odinger equations on tori $\\mathbb{T}^{d}$ at the critical regularity. We focus on cases where the nonlinearity $|u|^{a}u$ is non-algebraic with small $a>0$. We prove the local well-posedness for a wide range covering the mass-supercritical regime. Moreover, we supplementarily investigate the regularity of the solution map. In pursuit of lowering $a$, we prove a bilinear estimate for the Schr\\\"odinger operator on tori $\\mathbb{T}^{d}$, which enhances previously known multilinear estimates. We design a function space adapted to","authors_text":"Beomjong Kwak, Soonsik Kwon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-26T06:30:12Z","title":"Critical local well-posedness of the nonlinear Schr\\\"odinger equation on the torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17147","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":"sha256:9745991664fc06e730858ef40623a7c3147e122b5dd103b599ab88ada76dee57","target":"record","created_at":"2026-07-05T09:40:28Z","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":"835aacee676d3a01c69a8c96ede73b3efd600af2112b4ab5c0f12a995f8e8cdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-26T06:30:12Z","title_canon_sha256":"2402228f0d998416f10f42f79d31e93620edc08ffa486fe2d8d3e1eceda1b79d"},"schema_version":"1.0","source":{"id":"2411.17147","kind":"arxiv","version":1}},"canonical_sha256":"de84907a4d7f671e8cf5d2b22103308d8605580c4c556fcfe8608f627d41a98b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de84907a4d7f671e8cf5d2b22103308d8605580c4c556fcfe8608f627d41a98b","first_computed_at":"2026-07-05T09:40:28.332847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:28.332847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/4G2+1OqFCQgbAK8qB43L0+Pbh1p2lVvH0xbEjg2509IjAsaoO9tX7IYTRhsY4x53L+J1cTKPcUacnbcRbWDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:28.333337Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.17147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9745991664fc06e730858ef40623a7c3147e122b5dd103b599ab88ada76dee57","sha256:4d9ba587cb4623051cc6a6a873a7912705282dd595d0190e9d15bfd6afbbb1e3"],"state_sha256":"71c40decff14fa0b641c5eabdab84482242909dd14af86af1b8a4e37f3449c6b"}