{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZE67KVWILEWEH5JAWMKPPWA4DJ","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":"98cab303a7b04cc5bf3e293f66695d9426f86e0e78b01b6bb86a050232243a8f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-03T06:30:47Z","title_canon_sha256":"1b2874b17630e19831c76e1a9d81fea1d167e4dfb0880690396634fabcb5c976"},"schema_version":"1.0","source":{"id":"1603.00990","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00990","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00990v1","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00990","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZE67KVWILEWE","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZE67KVWILEWEH5JA","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZE67KVWI","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:709dea6c836b12ccb2ebd43a9ffcd35474b87140c287fef4490c627389ea5272","target":"graph","created_at":"2026-05-18T01:19:39Z","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":"Let $u_n$ be a sequence of mappings from a closed Riemannian surface $M$ to a general Riemannian manifold $N$. If $u_n$ satisfies \\beno \\sup_{n}\\big(\\|\\nabla u_n\\|_{L^2(M)}+\\|\\tau(u_n)\\|_{L^{p}(M)}\\big)\\leq \\Lambda\\quad \\text{for some}\\,\\,p>1, \\eeno where $\\tau(u_n)$ is the tension field of $u_n$, then there hold the so called energy identity and neckless property during blowing up. This result is sharp by Parker's example, where the tension fields of the mappings from Riemannian surface are bounded in $L^1(M)$ but the energy identity fails.","authors_text":"Dongyi Wei, Wendong Wang, Zhifei Zhang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-03T06:30:47Z","title":"Energy identity for approximate harmonic maps from surface to general targets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00990","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:ceeee6c1f9172147b480cb0f836095dd0236e3f63770912b20ea007fa9dddfb3","target":"record","created_at":"2026-05-18T01:19:39Z","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":"98cab303a7b04cc5bf3e293f66695d9426f86e0e78b01b6bb86a050232243a8f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-03T06:30:47Z","title_canon_sha256":"1b2874b17630e19831c76e1a9d81fea1d167e4dfb0880690396634fabcb5c976"},"schema_version":"1.0","source":{"id":"1603.00990","kind":"arxiv","version":1}},"canonical_sha256":"c93df556c8592c43f520b314f7d81c1a6887137ea24af217edfb0713da3757bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c93df556c8592c43f520b314f7d81c1a6887137ea24af217edfb0713da3757bf","first_computed_at":"2026-05-18T01:19:39.911761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:39.911761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggqf2FU4dxsnCJsq6EwBKlTjyJkpUW74F//Ofuj5F1xSHivPR0zSfIBaxOoev5eJ+4tuIlN1oowuysXStAUyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:39.912441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00990","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ceeee6c1f9172147b480cb0f836095dd0236e3f63770912b20ea007fa9dddfb3","sha256:709dea6c836b12ccb2ebd43a9ffcd35474b87140c287fef4490c627389ea5272"],"state_sha256":"ae4ffd718f699c0f64846020233b4b0de3b7b9457fbb7911c0ea160d9ee0daf4"}