{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:27W5SQNIURSI5FNZLH5TWKFNOM","short_pith_number":"pith:27W5SQNI","canonical_record":{"source":{"id":"1003.0646","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-02T19:46:18Z","cross_cats_sorted":[],"title_canon_sha256":"7fcabbda8bc4757747cbab2048dba11f49ac6dff4c91ba9edc655706e63ba2d3","abstract_canon_sha256":"7078ce86199a14cd3b7b709fa6d372cac4c4fd63762a004458036f05cda25789"},"schema_version":"1.0"},"canonical_sha256":"d7edd941a8a4648e95b959fb3b28ad7322d8aeef5546de4d89eccf91f2a2dcea","source":{"kind":"arxiv","id":"1003.0646","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0646","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0646v2","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0646","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"pith_short_12","alias_value":"27W5SQNIURSI","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"27W5SQNIURSI5FNZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"27W5SQNI","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:27W5SQNIURSI5FNZLH5TWKFNOM","target":"record","payload":{"canonical_record":{"source":{"id":"1003.0646","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-02T19:46:18Z","cross_cats_sorted":[],"title_canon_sha256":"7fcabbda8bc4757747cbab2048dba11f49ac6dff4c91ba9edc655706e63ba2d3","abstract_canon_sha256":"7078ce86199a14cd3b7b709fa6d372cac4c4fd63762a004458036f05cda25789"},"schema_version":"1.0"},"canonical_sha256":"d7edd941a8a4648e95b959fb3b28ad7322d8aeef5546de4d89eccf91f2a2dcea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:54.624253Z","signature_b64":"K8i/15DaxgLNUMVjCrQAWjVd2UcJ2lQYOm08pBsbEVMmInYf6xp7Dn98RKO3eywEt07+VSLQk/Cwj0UoHt95BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7edd941a8a4648e95b959fb3b28ad7322d8aeef5546de4d89eccf91f2a2dcea","last_reissued_at":"2026-05-18T03:35:54.623440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:54.623440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.0646","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrRklOWiouoNMTEwccqhT4siB5rFEymWMmz1IF+oJ9jhc6yGHYd0SluBcuNmhB2fUetJIpZfjQeciROfs+96DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:25:56.012835Z"},"content_sha256":"af8c234e5e1762f15175e9b679c417b495d7c764903c067dc0c8e91187124a2d","schema_version":"1.0","event_id":"sha256:af8c234e5e1762f15175e9b679c417b495d7c764903c067dc0c8e91187124a2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:27W5SQNIURSI5FNZLH5TWKFNOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of n/2-harmonic maps into spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Schikorra","submitted_at":"2010-03-02T19:46:18Z","abstract_excerpt":"We prove Hoelder continuity for n/2-harmonic maps from subsets of Rn into a sphere. This extends a recent one-dimensional result by F. Da Lio and T. Riviere to arbitrary dimensions. The proof relies on compensation effects which we quantify adapting an approach for Wente's inequality by L. Tartar, instead of Besov-space arguments which were used in the one-dimensional case. Moreover, fractional analogues of Hodge decomposition and higher order Poincare inequalities as well as several localization effects for nonlocal operators similar to the fractional laplacian are developed and applied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0646","kind":"arxiv","version":2},"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":"2026-05-18T03:35:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZokqUZTKuWq+xmmuCdPePFwUUcun0cZ6VzymqIceXxeSUp4zeV5qrKOlWZvz6hquiyUWB5R6GljZWOfSfC3gDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:25:56.013169Z"},"content_sha256":"294517a55b303391484deb9cedd2916279196fbc256186ffb82f1a1586edd249","schema_version":"1.0","event_id":"sha256:294517a55b303391484deb9cedd2916279196fbc256186ffb82f1a1586edd249"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27W5SQNIURSI5FNZLH5TWKFNOM/bundle.json","state_url":"https://pith.science/pith/27W5SQNIURSI5FNZLH5TWKFNOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27W5SQNIURSI5FNZLH5TWKFNOM/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":"2026-06-11T09:25:56Z","links":{"resolver":"https://pith.science/pith/27W5SQNIURSI5FNZLH5TWKFNOM","bundle":"https://pith.science/pith/27W5SQNIURSI5FNZLH5TWKFNOM/bundle.json","state":"https://pith.science/pith/27W5SQNIURSI5FNZLH5TWKFNOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27W5SQNIURSI5FNZLH5TWKFNOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:27W5SQNIURSI5FNZLH5TWKFNOM","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":"7078ce86199a14cd3b7b709fa6d372cac4c4fd63762a004458036f05cda25789","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-02T19:46:18Z","title_canon_sha256":"7fcabbda8bc4757747cbab2048dba11f49ac6dff4c91ba9edc655706e63ba2d3"},"schema_version":"1.0","source":{"id":"1003.0646","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0646","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0646v2","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0646","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"pith_short_12","alias_value":"27W5SQNIURSI","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"27W5SQNIURSI5FNZ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"27W5SQNI","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:294517a55b303391484deb9cedd2916279196fbc256186ffb82f1a1586edd249","target":"graph","created_at":"2026-05-18T03:35:54Z","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 Hoelder continuity for n/2-harmonic maps from subsets of Rn into a sphere. This extends a recent one-dimensional result by F. Da Lio and T. Riviere to arbitrary dimensions. The proof relies on compensation effects which we quantify adapting an approach for Wente's inequality by L. Tartar, instead of Besov-space arguments which were used in the one-dimensional case. Moreover, fractional analogues of Hodge decomposition and higher order Poincare inequalities as well as several localization effects for nonlocal operators similar to the fractional laplacian are developed and applied.","authors_text":"Armin Schikorra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-02T19:46:18Z","title":"Regularity of n/2-harmonic maps into spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0646","kind":"arxiv","version":2},"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:af8c234e5e1762f15175e9b679c417b495d7c764903c067dc0c8e91187124a2d","target":"record","created_at":"2026-05-18T03:35:54Z","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":"7078ce86199a14cd3b7b709fa6d372cac4c4fd63762a004458036f05cda25789","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-03-02T19:46:18Z","title_canon_sha256":"7fcabbda8bc4757747cbab2048dba11f49ac6dff4c91ba9edc655706e63ba2d3"},"schema_version":"1.0","source":{"id":"1003.0646","kind":"arxiv","version":2}},"canonical_sha256":"d7edd941a8a4648e95b959fb3b28ad7322d8aeef5546de4d89eccf91f2a2dcea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7edd941a8a4648e95b959fb3b28ad7322d8aeef5546de4d89eccf91f2a2dcea","first_computed_at":"2026-05-18T03:35:54.623440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:54.623440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K8i/15DaxgLNUMVjCrQAWjVd2UcJ2lQYOm08pBsbEVMmInYf6xp7Dn98RKO3eywEt07+VSLQk/Cwj0UoHt95BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:54.624253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.0646","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af8c234e5e1762f15175e9b679c417b495d7c764903c067dc0c8e91187124a2d","sha256:294517a55b303391484deb9cedd2916279196fbc256186ffb82f1a1586edd249"],"state_sha256":"20fc80c6d381676fac7b1d6339c65fb2bd2bcf95e20d035221ce1d5bbc505c23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/DCq8v8PUbeczmnQ04ej19amU9XIVJUfS84v4ho0PZAL9SvKw9Q2LA9wPYAW3JEnghw1Ztal7VOxZ1wES4IAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:25:56.015072Z","bundle_sha256":"a2b4d632c0e894d0da7361d21a7e90aedbf2fc34fe028f8206048e80155fe3c8"}}