{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:576E4US6CNZZLHBMJQNMJ23YAW","short_pith_number":"pith:576E4US6","canonical_record":{"source":{"id":"1806.06818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-18T16:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"6a1949477ee881a80999474b27ebc9a966e3803a3ff0ed63d94290e890891311","abstract_canon_sha256":"541e7a4c3a78e6b0c367ddf91f29b60fd82b8a933c0b08c2dbe56c860b1762bc"},"schema_version":"1.0"},"canonical_sha256":"effc4e525e1373959c2c4c1ac4eb7805a08df51001039d4fdb6fe112ba09f9f4","source":{"kind":"arxiv","id":"1806.06818","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06818","created_at":"2026-05-18T00:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06818v1","created_at":"2026-05-18T00:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06818","created_at":"2026-05-18T00:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"576E4US6CNZZ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"576E4US6CNZZLHBM","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"576E4US6","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:576E4US6CNZZLHBMJQNMJ23YAW","target":"record","payload":{"canonical_record":{"source":{"id":"1806.06818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-18T16:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"6a1949477ee881a80999474b27ebc9a966e3803a3ff0ed63d94290e890891311","abstract_canon_sha256":"541e7a4c3a78e6b0c367ddf91f29b60fd82b8a933c0b08c2dbe56c860b1762bc"},"schema_version":"1.0"},"canonical_sha256":"effc4e525e1373959c2c4c1ac4eb7805a08df51001039d4fdb6fe112ba09f9f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:59.036528Z","signature_b64":"QGyUu9VMlp4V80YAUx97LVezSfItlZy3QHJRCQBB4RCS8aYGPIguWhVz9s/MkZmLVSqZ24r05z18uq/30A+eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"effc4e525e1373959c2c4c1ac4eb7805a08df51001039d4fdb6fe112ba09f9f4","last_reissued_at":"2026-05-18T00:12:59.035985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:59.035985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.06818","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":"2026-05-18T00:12:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E983aw0hWC+DvEYXwx60GeaWmYY7AXuK9y/vegZ6SzhwKeW6GiRVaM1rI5TonqmYgreODpy/vdB4ng35/LlSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:05:46.714110Z"},"content_sha256":"2ac9349f2da3adac865d0eed7bcce4265de13c6095923b9784ee74edd338d6b8","schema_version":"1.0","event_id":"sha256:2ac9349f2da3adac865d0eed7bcce4265de13c6095923b9784ee74edd338d6b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:576E4US6CNZZLHBMJQNMJ23YAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global dissipative half-harmonic flows into spheres: small data in critical Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christof Melcher, Zisis N. Sakellaris","submitted_at":"2018-06-18T16:54:44Z","abstract_excerpt":"We establish global existence, uniqueness, regularity and long-time asymptotics of strong solutions to the half-harmonic heat flow and dissipative Landau-Lifshitz equation, valid for initial data that is small in the homogeneous Sobolev norm $\\dot{H}^{\\frac n 2}$ for space dimensions $n \\le 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06818","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":"2026-05-18T00:12:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iE9ZAMJhIDABFOh16MNcenGIak/Lum201pm3/tdVYkZoatWJYUbKLxbNIxuIZ4XMahCkny4qEQtzEtf/Dzs5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:05:46.714473Z"},"content_sha256":"74354d20923ea5ca7347931a1a6f12c9a321a1368d3321deac1c3634f49c1800","schema_version":"1.0","event_id":"sha256:74354d20923ea5ca7347931a1a6f12c9a321a1368d3321deac1c3634f49c1800"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/576E4US6CNZZLHBMJQNMJ23YAW/bundle.json","state_url":"https://pith.science/pith/576E4US6CNZZLHBMJQNMJ23YAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/576E4US6CNZZLHBMJQNMJ23YAW/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":"2026-06-22T01:05:46Z","links":{"resolver":"https://pith.science/pith/576E4US6CNZZLHBMJQNMJ23YAW","bundle":"https://pith.science/pith/576E4US6CNZZLHBMJQNMJ23YAW/bundle.json","state":"https://pith.science/pith/576E4US6CNZZLHBMJQNMJ23YAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/576E4US6CNZZLHBMJQNMJ23YAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:576E4US6CNZZLHBMJQNMJ23YAW","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":"541e7a4c3a78e6b0c367ddf91f29b60fd82b8a933c0b08c2dbe56c860b1762bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-18T16:54:44Z","title_canon_sha256":"6a1949477ee881a80999474b27ebc9a966e3803a3ff0ed63d94290e890891311"},"schema_version":"1.0","source":{"id":"1806.06818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06818","created_at":"2026-05-18T00:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06818v1","created_at":"2026-05-18T00:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06818","created_at":"2026-05-18T00:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"576E4US6CNZZ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"576E4US6CNZZLHBM","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"576E4US6","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:74354d20923ea5ca7347931a1a6f12c9a321a1368d3321deac1c3634f49c1800","target":"graph","created_at":"2026-05-18T00:12:59Z","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 global existence, uniqueness, regularity and long-time asymptotics of strong solutions to the half-harmonic heat flow and dissipative Landau-Lifshitz equation, valid for initial data that is small in the homogeneous Sobolev norm $\\dot{H}^{\\frac n 2}$ for space dimensions $n \\le 3$.","authors_text":"Christof Melcher, Zisis N. Sakellaris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-18T16:54:44Z","title":"Global dissipative half-harmonic flows into spheres: small data in critical Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06818","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":"sha256:2ac9349f2da3adac865d0eed7bcce4265de13c6095923b9784ee74edd338d6b8","target":"record","created_at":"2026-05-18T00:12:59Z","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":"541e7a4c3a78e6b0c367ddf91f29b60fd82b8a933c0b08c2dbe56c860b1762bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-18T16:54:44Z","title_canon_sha256":"6a1949477ee881a80999474b27ebc9a966e3803a3ff0ed63d94290e890891311"},"schema_version":"1.0","source":{"id":"1806.06818","kind":"arxiv","version":1}},"canonical_sha256":"effc4e525e1373959c2c4c1ac4eb7805a08df51001039d4fdb6fe112ba09f9f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"effc4e525e1373959c2c4c1ac4eb7805a08df51001039d4fdb6fe112ba09f9f4","first_computed_at":"2026-05-18T00:12:59.035985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:59.035985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QGyUu9VMlp4V80YAUx97LVezSfItlZy3QHJRCQBB4RCS8aYGPIguWhVz9s/MkZmLVSqZ24r05z18uq/30A+eBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:59.036528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ac9349f2da3adac865d0eed7bcce4265de13c6095923b9784ee74edd338d6b8","sha256:74354d20923ea5ca7347931a1a6f12c9a321a1368d3321deac1c3634f49c1800"],"state_sha256":"21707b0b288deae08433b5ccf5bf84addf46634e1c66b96d5610fcbb8e94154c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LFt3Xl3ajzk5truIbpxaokx8SSQDi9EZ3Qtu+0kQf7OW3xroQd++EvNpkylvqht7/0EcgO4uF6pTLTGlKu+OBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T01:05:46.716442Z","bundle_sha256":"dce6ad26a9825b39ac343da28d6408f84a88578ba459b118ecba4d25e02384e1"}}