{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DHWBISD5XZH5CMAANRJADQFYX7","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":"6e1a8c82b58a15db53f3aedc58ef42b6d467fa9077c2a5150dca28131ca2265e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-09T16:09:32Z","title_canon_sha256":"5023624bb91b9fe40e856d2e205bc29bad995057a7caef1644efd36e574ccfcc"},"schema_version":"1.0","source":{"id":"1210.2653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2653","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2653v1","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2653","created_at":"2026-05-18T03:43:41Z"},{"alias_kind":"pith_short_12","alias_value":"DHWBISD5XZH5","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DHWBISD5XZH5CMAA","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DHWBISD5","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:e2e76de38005d9360a735a7632df8508556cfb79b878d6c84cddd5aa2c31447a","target":"graph","created_at":"2026-05-18T03:43:41Z","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":"In this paper we study compactness and quantization properties of sequences of 1/2-harmonic maps $u_k\\colon\\R\\to {\\cal{S}}^{m-1}$ such that $|u_k|_{\\dot H^{1/2}(\\R,{\\cal{S}}^{m-1})}\\le C.$ More precisely we show that there exist a weak 1/2-harmonic map $u_\\infty\\colon\\R\\to {\\cal{S}}^{m-1}$, a possible empty set ${a_1,...,a_\\ell}$ in $\\R$ such that up to subsequences $$(|(-\\Delta)^{1/4}u_k|^2 \\rightharpoonup |(-\\Delta)^{1/4}u_{\\infty}|^2)dx+\\sum_{i=1}^{\\ell}\\lambda_i \\delta_{a_i}, in Radon measure,$$ as $k\\to +\\infty$, with $\\lambda_i\\ge 0.$\n  The convergence of $u_k$ to $u_\\infty$ is strong in","authors_text":"Francesca Da Lio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-09T16:09:32Z","title":"Compactness and Bubbles Analysis for 1/2-harmonic Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2653","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":"sha256:304e4fc405aae2eb09379fbb7db93c64dce6b1b83488118eef9d781570e0684e","target":"record","created_at":"2026-05-18T03:43:41Z","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":"6e1a8c82b58a15db53f3aedc58ef42b6d467fa9077c2a5150dca28131ca2265e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-09T16:09:32Z","title_canon_sha256":"5023624bb91b9fe40e856d2e205bc29bad995057a7caef1644efd36e574ccfcc"},"schema_version":"1.0","source":{"id":"1210.2653","kind":"arxiv","version":1}},"canonical_sha256":"19ec14487dbe4fd130006c5201c0b8bfcb18ea95b343cd61c025c6da21e8a558","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19ec14487dbe4fd130006c5201c0b8bfcb18ea95b343cd61c025c6da21e8a558","first_computed_at":"2026-05-18T03:43:41.029120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:41.029120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gZo/3xjyOaZXjvUA3CeWbrD/GC05xZZOjcXhOPLXzBP6kkfyMfs9Q2oC2V/yaU+WlLkFBbGuVh7WF6Yk3ojCDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:41.029694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:304e4fc405aae2eb09379fbb7db93c64dce6b1b83488118eef9d781570e0684e","sha256:e2e76de38005d9360a735a7632df8508556cfb79b878d6c84cddd5aa2c31447a"],"state_sha256":"8fa11240dc62b78f5eb0af32bc5eb157cf4ce8774706f30bdbefcf851cb2648c"}