{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P3LTWGF6SZPTU3YLKKLGOUR72W","short_pith_number":"pith:P3LTWGF6","canonical_record":{"source":{"id":"1303.6005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-25T00:30:58Z","cross_cats_sorted":[],"title_canon_sha256":"344550c213bc55fea64daddc890e85fe20fa9a8bb0ef608be11a7b1a9903af5e","abstract_canon_sha256":"44631467d5d01da0e0d9a8c933c5d5bf4338252d4830e579349aacbc17493a55"},"schema_version":"1.0"},"canonical_sha256":"7ed73b18be965f3a6f0b529667523fd5930f60c4157b02ca913c2b9ac1b4d209","source":{"kind":"arxiv","id":"1303.6005","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6005","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6005v1","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6005","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"P3LTWGF6SZPT","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P3LTWGF6SZPTU3YL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P3LTWGF6","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P3LTWGF6SZPTU3YLKKLGOUR72W","target":"record","payload":{"canonical_record":{"source":{"id":"1303.6005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-25T00:30:58Z","cross_cats_sorted":[],"title_canon_sha256":"344550c213bc55fea64daddc890e85fe20fa9a8bb0ef608be11a7b1a9903af5e","abstract_canon_sha256":"44631467d5d01da0e0d9a8c933c5d5bf4338252d4830e579349aacbc17493a55"},"schema_version":"1.0"},"canonical_sha256":"7ed73b18be965f3a6f0b529667523fd5930f60c4157b02ca913c2b9ac1b4d209","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:52.273880Z","signature_b64":"WqAtSb9TvLVqNEhbwtamfyzP5p/jqVEIcPsmNdOztS78Mf8IjsVVFw1vDASAoI7+vhOZyBzflDZRZdf5W2JYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ed73b18be965f3a6f0b529667523fd5930f60c4157b02ca913c2b9ac1b4d209","last_reissued_at":"2026-05-18T03:29:52.273170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:52.273170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.6005","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kByBWLyIEEmBvrAZelbaRLEkvVzVhBnAMft6hNE2fclf40Pe45MHkDbdF2dFOnbSV2pwWVo7g4qwErfbtimKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:22:45.614055Z"},"content_sha256":"0bddceffbfaa6874b98b386e2a4ef190a2c052231ade27cb9be8c16a92e79db4","schema_version":"1.0","event_id":"sha256:0bddceffbfaa6874b98b386e2a4ef190a2c052231ade27cb9be8c16a92e79db4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P3LTWGF6SZPTU3YLKKLGOUR72W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commutator estimates in Besov-Morrey spaces with applications to the well-posedness of the Euler equations and ideal MHD system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiang Xu, Yong Zhou","submitted_at":"2013-03-25T00:30:58Z","abstract_excerpt":"We develop commutator estimates in the framework of Besov-Morrey spaces, which are modeled on Besov spaces and the underlying norm is of Morrey space rather than the usual $L^{p}$ space. As direct applications of commutator estimates, we establish the local well-posedness and blow-up criterion of solutions in Besov-Morrey spaces for the incompressible Euler equations and ideal MHD system. Main analysis tools are the Littlewood-Paley decomposition and Bony's para-product formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6005","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IaSNgsuaM+dM7A7gwOoZrjVFiT8DrjR9oVsjVhsYFTFMhJTHxeYpxrL+A+yz1GdaGyvFDwpSdR5fviR1SYz5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:22:45.614419Z"},"content_sha256":"2695cbb7e0d742d61225b19e20ed0fcce9794f2926eed78728eb9b42e571c6d9","schema_version":"1.0","event_id":"sha256:2695cbb7e0d742d61225b19e20ed0fcce9794f2926eed78728eb9b42e571c6d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3LTWGF6SZPTU3YLKKLGOUR72W/bundle.json","state_url":"https://pith.science/pith/P3LTWGF6SZPTU3YLKKLGOUR72W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3LTWGF6SZPTU3YLKKLGOUR72W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T11:22:45Z","links":{"resolver":"https://pith.science/pith/P3LTWGF6SZPTU3YLKKLGOUR72W","bundle":"https://pith.science/pith/P3LTWGF6SZPTU3YLKKLGOUR72W/bundle.json","state":"https://pith.science/pith/P3LTWGF6SZPTU3YLKKLGOUR72W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3LTWGF6SZPTU3YLKKLGOUR72W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P3LTWGF6SZPTU3YLKKLGOUR72W","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":"44631467d5d01da0e0d9a8c933c5d5bf4338252d4830e579349aacbc17493a55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-25T00:30:58Z","title_canon_sha256":"344550c213bc55fea64daddc890e85fe20fa9a8bb0ef608be11a7b1a9903af5e"},"schema_version":"1.0","source":{"id":"1303.6005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6005","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6005v1","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6005","created_at":"2026-05-18T03:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"P3LTWGF6SZPT","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P3LTWGF6SZPTU3YL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P3LTWGF6","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:2695cbb7e0d742d61225b19e20ed0fcce9794f2926eed78728eb9b42e571c6d9","target":"graph","created_at":"2026-05-18T03:29:52Z","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 develop commutator estimates in the framework of Besov-Morrey spaces, which are modeled on Besov spaces and the underlying norm is of Morrey space rather than the usual $L^{p}$ space. As direct applications of commutator estimates, we establish the local well-posedness and blow-up criterion of solutions in Besov-Morrey spaces for the incompressible Euler equations and ideal MHD system. Main analysis tools are the Littlewood-Paley decomposition and Bony's para-product formula.","authors_text":"Jiang Xu, Yong Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-25T00:30:58Z","title":"Commutator estimates in Besov-Morrey spaces with applications to the well-posedness of the Euler equations and ideal MHD system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6005","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":"sha256:0bddceffbfaa6874b98b386e2a4ef190a2c052231ade27cb9be8c16a92e79db4","target":"record","created_at":"2026-05-18T03:29:52Z","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":"44631467d5d01da0e0d9a8c933c5d5bf4338252d4830e579349aacbc17493a55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-25T00:30:58Z","title_canon_sha256":"344550c213bc55fea64daddc890e85fe20fa9a8bb0ef608be11a7b1a9903af5e"},"schema_version":"1.0","source":{"id":"1303.6005","kind":"arxiv","version":1}},"canonical_sha256":"7ed73b18be965f3a6f0b529667523fd5930f60c4157b02ca913c2b9ac1b4d209","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ed73b18be965f3a6f0b529667523fd5930f60c4157b02ca913c2b9ac1b4d209","first_computed_at":"2026-05-18T03:29:52.273170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:52.273170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WqAtSb9TvLVqNEhbwtamfyzP5p/jqVEIcPsmNdOztS78Mf8IjsVVFw1vDASAoI7+vhOZyBzflDZRZdf5W2JYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:52.273880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bddceffbfaa6874b98b386e2a4ef190a2c052231ade27cb9be8c16a92e79db4","sha256:2695cbb7e0d742d61225b19e20ed0fcce9794f2926eed78728eb9b42e571c6d9"],"state_sha256":"cdb0ac608043f841c6f5a4f7ff1980d815bfbeaac9e3a97fd985e7cd92b71652"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDsVNGMRWHsIJYtcV7NucHdLM5AdxvjTaQXsQn9fyD6ykHkPKNyrsGr1DasYe9sdQp6y0VSnQPncd+dMKo+EBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:22:45.616373Z","bundle_sha256":"c320b0c55d76b1f16f0c8274868291e68ab61eaa439655ea35a9f8c3c9749f8e"}}