{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G6HARXOBSSB33ZIAK3ZFLK22EH","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":"a4bb1dde98206a52e763af305f92cf38f695e0f73baa8e692e1745004a7bf5fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-02T05:06:51Z","title_canon_sha256":"4464215d73927a2103eb008523260098e20c12ede30b9aec38dd2b30522b7fc0"},"schema_version":"1.0","source":{"id":"1602.00789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00789","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00789v2","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00789","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"G6HARXOBSSB3","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G6HARXOBSSB33ZIA","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G6HARXOB","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:98b0b6572fe450184f1f3dbed668596008bb2b748520da3b0b5906954b065d49","target":"graph","created_at":"2026-05-18T00:38:13Z","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 the Strichartz estimates for the magnetic Schr\\\"odinger equation in dimension $n\\geq3$. More specifically, for all Schr\\\"odinger admissible pairs $(r,q)$, we establish the estimate\n  $$\n  \\|e^{itH}f\\|_{L^{q}_{t}(\\mathbb{R}; L^{r}_{x}(\\mathbb{R}^n))} \\leq C_{n,r,q,H} \\|f\\|_{L^2(\\mathbb{R}^n)}\n  $$ when the operator $H= -\\Delta_A +V$ satisfies suitable conditions. In the purely electric case $A\\equiv0$, we extend the class of potentials $V$ to the Fefferman-Phong class. In doing so, we apply a weighted estimate for the Schr\\\"odinger equation developed by Ruiz and Vega. Moreover, for the","authors_text":"Seonghak Kim, Youngwoo Koh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-02T05:06:51Z","title":"Strichartz estimates for the magnetic Schr\\\"odinger equation with potentials $V$ of critical decay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00789","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":"sha256:171934f37496c7f166e988acd6e5da3a0ac08efb17410bf117f6bc460e720b81","target":"record","created_at":"2026-05-18T00:38:13Z","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":"a4bb1dde98206a52e763af305f92cf38f695e0f73baa8e692e1745004a7bf5fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-02T05:06:51Z","title_canon_sha256":"4464215d73927a2103eb008523260098e20c12ede30b9aec38dd2b30522b7fc0"},"schema_version":"1.0","source":{"id":"1602.00789","kind":"arxiv","version":2}},"canonical_sha256":"378e08ddc19483bde50056f255ab5a21c297abc31155b7fdbb2a35a1fa39bcd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"378e08ddc19483bde50056f255ab5a21c297abc31155b7fdbb2a35a1fa39bcd6","first_computed_at":"2026-05-18T00:38:13.968222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:13.968222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2w59SSgV3DvpahtQiia7jVuBD6C2EIykcuxEBM5UFt4Le8g8YwVf15tBTUjfJ+fomh2NHzZjYehDCwhDvrt/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:13.968804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:171934f37496c7f166e988acd6e5da3a0ac08efb17410bf117f6bc460e720b81","sha256:98b0b6572fe450184f1f3dbed668596008bb2b748520da3b0b5906954b065d49"],"state_sha256":"c242c7cfb744b18bb69492d46bfef8eb292ba9f426a5d2177f6035e0f22a02f2"}