{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DHD5GHQT26ZJEXCN3ZBNFK2CVI","short_pith_number":"pith:DHD5GHQT","canonical_record":{"source":{"id":"1309.7426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T04:58:09Z","cross_cats_sorted":[],"title_canon_sha256":"b9b10bcc4c227e5b99ddd8b58c047f908371dd05dfad7764b60d787f0d452358","abstract_canon_sha256":"62258414a5bdab21113fbd1a01ed268f71c65945e20ed8db1f6f535edef2e958"},"schema_version":"1.0"},"canonical_sha256":"19c7d31e13d7b2925c4dde42d2ab42aa0f036b988440d5c6b1f6d1fb1407d02d","source":{"kind":"arxiv","id":"1309.7426","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7426","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7426v1","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7426","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"DHD5GHQT26ZJ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DHD5GHQT26ZJEXCN","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DHD5GHQT","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DHD5GHQT26ZJEXCN3ZBNFK2CVI","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T04:58:09Z","cross_cats_sorted":[],"title_canon_sha256":"b9b10bcc4c227e5b99ddd8b58c047f908371dd05dfad7764b60d787f0d452358","abstract_canon_sha256":"62258414a5bdab21113fbd1a01ed268f71c65945e20ed8db1f6f535edef2e958"},"schema_version":"1.0"},"canonical_sha256":"19c7d31e13d7b2925c4dde42d2ab42aa0f036b988440d5c6b1f6d1fb1407d02d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:58.738920Z","signature_b64":"+EKVxw6g4vUHS/hHTj0oLKv5Z8VXmvqHqbWuBNPpHKPz4i4z33rhImcjFIZF6df/tR/5Ip0pyEm77hqAsmJqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19c7d31e13d7b2925c4dde42d2ab42aa0f036b988440d5c6b1f6d1fb1407d02d","last_reissued_at":"2026-05-18T03:11:58.738141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:58.738141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7426","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":"2026-05-18T03:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWEoKtkVfJL/mrIp7SCNZde8ROmQ5R7k6VmsD4mrBF50DCOZUsfQyefxEH2hXhGo3p44KAesAjCdw50iPGlbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:54:05.945203Z"},"content_sha256":"2c98046d7d99ecfd13f590b655bbbce9d365c6a867b8d40f0a357187e4069f68","schema_version":"1.0","event_id":"sha256:2c98046d7d99ecfd13f590b655bbbce9d365c6a867b8d40f0a357187e4069f68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DHD5GHQT26ZJEXCN3ZBNFK2CVI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Well-Posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baishun Lai, Changyou Wang, Junyu Lin","submitted_at":"2013-09-28T04:58:09Z","abstract_excerpt":"We establish the global well-posedness of the Landau-Lifshitz-Gilbert equation in $\\mathbb R^n$ for any initial data ${\\bf m}_0\\in H^1_*(\\mathbb R^n,\\mathbb S^2)$ whose gradient belongs to the Morrey space $M^{2,2}(\\mathbb R^n)$ with small norm $\\displaystyle\\|\\nabla {\\bf m}_0\\|_{M^{2,2}(\\mathbb R^n)}$. The method is based on priori estimates of a dissipative Schr\\\"odinger equation of Ginzburg-Landau types obtained from the Landau-Lifshitz-Gilbert equation by the moving frame technique."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7426","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":"2026-05-18T03:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jkPRyeNX7TnJC3fB9ZGxOPI8PPqyoM8ovihBjVKkgKOUYzpQMAXCVVJp7iobykGw7lpCPU8CsFd0+XENK3vICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:54:05.945570Z"},"content_sha256":"f41ff9075f91d571ec42af9de000144c3fcd2ed373bc9a88e27ea3775b570ae1","schema_version":"1.0","event_id":"sha256:f41ff9075f91d571ec42af9de000144c3fcd2ed373bc9a88e27ea3775b570ae1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHD5GHQT26ZJEXCN3ZBNFK2CVI/bundle.json","state_url":"https://pith.science/pith/DHD5GHQT26ZJEXCN3ZBNFK2CVI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHD5GHQT26ZJEXCN3ZBNFK2CVI/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":"2026-06-01T07:54:05Z","links":{"resolver":"https://pith.science/pith/DHD5GHQT26ZJEXCN3ZBNFK2CVI","bundle":"https://pith.science/pith/DHD5GHQT26ZJEXCN3ZBNFK2CVI/bundle.json","state":"https://pith.science/pith/DHD5GHQT26ZJEXCN3ZBNFK2CVI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHD5GHQT26ZJEXCN3ZBNFK2CVI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DHD5GHQT26ZJEXCN3ZBNFK2CVI","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":"62258414a5bdab21113fbd1a01ed268f71c65945e20ed8db1f6f535edef2e958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T04:58:09Z","title_canon_sha256":"b9b10bcc4c227e5b99ddd8b58c047f908371dd05dfad7764b60d787f0d452358"},"schema_version":"1.0","source":{"id":"1309.7426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7426","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7426v1","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7426","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"DHD5GHQT26ZJ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DHD5GHQT26ZJEXCN","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DHD5GHQT","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:f41ff9075f91d571ec42af9de000144c3fcd2ed373bc9a88e27ea3775b570ae1","target":"graph","created_at":"2026-05-18T03:11:58Z","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 establish the global well-posedness of the Landau-Lifshitz-Gilbert equation in $\\mathbb R^n$ for any initial data ${\\bf m}_0\\in H^1_*(\\mathbb R^n,\\mathbb S^2)$ whose gradient belongs to the Morrey space $M^{2,2}(\\mathbb R^n)$ with small norm $\\displaystyle\\|\\nabla {\\bf m}_0\\|_{M^{2,2}(\\mathbb R^n)}$. The method is based on priori estimates of a dissipative Schr\\\"odinger equation of Ginzburg-Landau types obtained from the Landau-Lifshitz-Gilbert equation by the moving frame technique.","authors_text":"Baishun Lai, Changyou Wang, Junyu Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T04:58:09Z","title":"Global Well-Posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7426","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":"sha256:2c98046d7d99ecfd13f590b655bbbce9d365c6a867b8d40f0a357187e4069f68","target":"record","created_at":"2026-05-18T03:11:58Z","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":"62258414a5bdab21113fbd1a01ed268f71c65945e20ed8db1f6f535edef2e958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T04:58:09Z","title_canon_sha256":"b9b10bcc4c227e5b99ddd8b58c047f908371dd05dfad7764b60d787f0d452358"},"schema_version":"1.0","source":{"id":"1309.7426","kind":"arxiv","version":1}},"canonical_sha256":"19c7d31e13d7b2925c4dde42d2ab42aa0f036b988440d5c6b1f6d1fb1407d02d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19c7d31e13d7b2925c4dde42d2ab42aa0f036b988440d5c6b1f6d1fb1407d02d","first_computed_at":"2026-05-18T03:11:58.738141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:58.738141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+EKVxw6g4vUHS/hHTj0oLKv5Z8VXmvqHqbWuBNPpHKPz4i4z33rhImcjFIZF6df/tR/5Ip0pyEm77hqAsmJqAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:58.738920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c98046d7d99ecfd13f590b655bbbce9d365c6a867b8d40f0a357187e4069f68","sha256:f41ff9075f91d571ec42af9de000144c3fcd2ed373bc9a88e27ea3775b570ae1"],"state_sha256":"f2e009188a9ee939ebde3cb76b479a119d0ceb50232ea37547a9d394609baa30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elTsaNAUCu5ZGdJ1Yj65F9pLcjirzpcKTZ4hHptd+q1DtaUJjAqk+cMjjMN4hkBJx9P26CUy3OJeca22tjRUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:54:05.947518Z","bundle_sha256":"66c31f4b3605f539d533f9fb0266657b80c98882d896112a593166c572c9ca22"}}