{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WOBYUSYFQB5RMGRV7SWCMDWEZD","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":"3b78aa1909540cac1f1d0ef10ef80214ee78d93e3fb4040fb317d57be7331e4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-09T13:34:13Z","title_canon_sha256":"14e0d22ec1ed57ab35576b64f1b712a953212a4960602af8331613ace90f44ec"},"schema_version":"1.0","source":{"id":"1811.03893","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03893","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03893v1","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03893","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"WOBYUSYFQB5R","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WOBYUSYFQB5RMGRV","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WOBYUSYF","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:b440d051ce0863370585491e83ac2da8a44e412ebb53846e2ecca9fb8b8ed785","target":"graph","created_at":"2026-05-18T00:01:11Z","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":"The aim of this note is to discuss in more detail the Pohozaev-type identities that have been recently obtained by the author, Paul Laurain and Tristan Rivi\\`ere in the framework of half-harmonic maps defined either on $R$ or on the sphere $S^1$ with values into a closed manifold $N^n\\subset R^m$. Weak half-harmonic maps are critical points of the following nonlocal energy $$\\int_{R}|(-\\Delta)^{1/4}u|^2 dx~~\\mbox{or}~~\\int_{S^1}|(-\\Delta)^{1/4}u|^2\\ d\\theta.$$\n  If $u$ is a sufficiently smooth critical point of the above energy then it satisfies the following equation of stationarity $$\\frac{d","authors_text":"Francesca Da Lio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-09T13:34:13Z","title":"Some Remarks on Pohozaev-Type Identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03893","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:f7c65153ef9a0731da0de622ddc20442cd020b741a7dc7ed95878c40892815e6","target":"record","created_at":"2026-05-18T00:01:11Z","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":"3b78aa1909540cac1f1d0ef10ef80214ee78d93e3fb4040fb317d57be7331e4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-09T13:34:13Z","title_canon_sha256":"14e0d22ec1ed57ab35576b64f1b712a953212a4960602af8331613ace90f44ec"},"schema_version":"1.0","source":{"id":"1811.03893","kind":"arxiv","version":1}},"canonical_sha256":"b3838a4b05807b161a35fcac260ec4c8f0f877b2f36fd430bbe4959da1c200c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3838a4b05807b161a35fcac260ec4c8f0f877b2f36fd430bbe4959da1c200c2","first_computed_at":"2026-05-18T00:01:11.670302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:11.670302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IoBlx0jMEtgDjqyzYxv5SRP9MRZySE0sVlVvW+QjcHX8iRYUrJhaKcewNOMZ4yW+7bOKDPpv3jMUoabe8jgpBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:11.670869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03893","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7c65153ef9a0731da0de622ddc20442cd020b741a7dc7ed95878c40892815e6","sha256:b440d051ce0863370585491e83ac2da8a44e412ebb53846e2ecca9fb8b8ed785"],"state_sha256":"6260c35bd4a5f52f1484856aa4b9ef8af56189e4deddc083cb6d0fb0e4e66fb7"}