{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DWMQXNTI4LATEGOP57UJZ4WRSL","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":"8decc56f2887e516a40ad54aad9a6fa9e21dc30000079fae5744585fd602eeb5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-02-05T13:22:37Z","title_canon_sha256":"051163092082c1285d6698f35150ccb8e1bde8c8855c922981852f36eb54388f"},"schema_version":"1.0","source":{"id":"2502.03151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.03151","created_at":"2026-07-05T10:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"2502.03151v1","created_at":"2026-07-05T10:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.03151","created_at":"2026-07-05T10:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"DWMQXNTI4LAT","created_at":"2026-07-05T10:10:00Z"},{"alias_kind":"pith_short_16","alias_value":"DWMQXNTI4LATEGOP","created_at":"2026-07-05T10:10:00Z"},{"alias_kind":"pith_short_8","alias_value":"DWMQXNTI","created_at":"2026-07-05T10:10:00Z"}],"graph_snapshots":[{"event_id":"sha256:515040ba803d7ec533d6b76b939cb0c180db96e2514d3c9ea9d7236a24e64f06","target":"graph","created_at":"2026-07-05T10:10:00Z","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/2502.03151/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the $L^{p}$-estimates for the solution to the $2\\mathrm{D}$-wave equation with a scaling-critical magnetic potential. Inspired by the work of \\cite{FZZ}, we show that the operators $(I+\\mathcal{L}_{\\mathbf{A}})^{-\\gamma}e^{it\\sqrt{\\mathcal{L}_{\\mathbf{A}}}}$ is bounded in $L^{p}(\\mathbb{R}^{2})$ for $1<p<+\\infty$ when $\\gamma>|1/p-1/2|$ and $t>0$, where $\\mathcal{L}_{\\mathbf{A}}$ is a magnetic Schr\\\"odinger operator. In particular, we derive the $L^{p}$-bounds for the sine wave propagator $\\sin(t\\sqrt{\\mathcal{L}_{\\mathbf{A}}})\\mathcal{L}^{-\\frac12}_{\\mathbf{A}}$. The k","authors_text":"Fang Zhang, Jialu Wang, Jiqiang Zheng, Junyong Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-02-05T13:22:37Z","title":"$L^p$-estimates for the 2D wave equation in the scaling-critical magnetic field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03151","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":"sha256:724dda4c1489da526bcd72b56ebc77851983104e21ac8e2b8475d74707b53f49","target":"record","created_at":"2026-07-05T10:10:00Z","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":"8decc56f2887e516a40ad54aad9a6fa9e21dc30000079fae5744585fd602eeb5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-02-05T13:22:37Z","title_canon_sha256":"051163092082c1285d6698f35150ccb8e1bde8c8855c922981852f36eb54388f"},"schema_version":"1.0","source":{"id":"2502.03151","kind":"arxiv","version":1}},"canonical_sha256":"1d990bb668e2c13219cfefe89cf2d192f6b86e1fbef9d3859bd05f33ccfd8513","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d990bb668e2c13219cfefe89cf2d192f6b86e1fbef9d3859bd05f33ccfd8513","first_computed_at":"2026-07-05T10:10:00.539098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:10:00.539098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9FZ0DG7qbrLmVqA4ki9sMR+aoCoDkUOWUtwNeD3XWjR7grkmigqtQ1lyYjA/PLa/2haNOJrwi/plvkS8Mkv6Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:10:00.539464Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.03151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:724dda4c1489da526bcd72b56ebc77851983104e21ac8e2b8475d74707b53f49","sha256:515040ba803d7ec533d6b76b939cb0c180db96e2514d3c9ea9d7236a24e64f06"],"state_sha256":"4b555c6e385d7e16a770a7b38f27fdc2caec13adf75e1354fd2bddcb0f5bcc17"}