{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:C3NJWSKIVFUOJZ3G565G4YGJMG","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":"c9bad25fce280d99882086a4d4cf0253eb6eba6b8f7e9919a7f1b7d225065ed0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-29T13:49:49Z","title_canon_sha256":"ab05b8dff4a2903ec31b9e242547deba99929a17618f6f96af1e47abb2d94608"},"schema_version":"1.0","source":{"id":"1904.12709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12709","created_at":"2026-05-17T23:47:34Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12709v1","created_at":"2026-05-17T23:47:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12709","created_at":"2026-05-17T23:47:34Z"},{"alias_kind":"pith_short_12","alias_value":"C3NJWSKIVFUO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"C3NJWSKIVFUOJZ3G","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"C3NJWSKI","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:eb7c8d58c4d8b4edd00adc1442992eb5c51d7294a0594bb701d58d5e5906e59c","target":"graph","created_at":"2026-05-17T23:47:34Z","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 prove that the half-wave maps problem on $\\mathbb{R}^{4+1}$ with target $S^2$ is globally well-posed for smooth initial data which are small in the critical $l^1$ based Besov space. This is a formal analogue of the result for wave maps by Tataru.","authors_text":"Anna Kiesenhofer, Joachim Krieger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-29T13:49:49Z","title":"Small data global regularity for half-wave maps in $n = 4$ dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12709","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":"sha256:5dd50462dd804a4816cac4edc5d35adbb1812ad9f7356ac5d2c22e190737c8e6","target":"record","created_at":"2026-05-17T23:47:34Z","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":"c9bad25fce280d99882086a4d4cf0253eb6eba6b8f7e9919a7f1b7d225065ed0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-29T13:49:49Z","title_canon_sha256":"ab05b8dff4a2903ec31b9e242547deba99929a17618f6f96af1e47abb2d94608"},"schema_version":"1.0","source":{"id":"1904.12709","kind":"arxiv","version":1}},"canonical_sha256":"16da9b4948a968e4e766efba6e60c961b0d82f58c14ae8929e8e4e0cefe764ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16da9b4948a968e4e766efba6e60c961b0d82f58c14ae8929e8e4e0cefe764ad","first_computed_at":"2026-05-17T23:47:34.318925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:34.318925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3jLlG94hHCGHlSR+TUe6HUeQ+F/Wtkl7VXJOq5qno+YTOOUpTEsgonc1YtaXIbQv2C6e1JuP4Cd4cehzGOtsBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:34.319484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.12709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dd50462dd804a4816cac4edc5d35adbb1812ad9f7356ac5d2c22e190737c8e6","sha256:eb7c8d58c4d8b4edd00adc1442992eb5c51d7294a0594bb701d58d5e5906e59c"],"state_sha256":"e87e00e2e4294a53d416cf89d7221f24101215c012a759a9657024d60a252728"}