{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5D35WQJSK3TIM5PRM27R4KU3O3","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":"49a71798abe13f6b186602fd0a407ca509d0b59028923d74b5432523ba51593d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-03T07:15:27Z","title_canon_sha256":"70e362ee6a2bbea3ce5b7c2bf2be46d36993a8e0560abeac0cc769ff242020f1"},"schema_version":"1.0","source":{"id":"1602.01212","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01212","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01212v2","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01212","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"5D35WQJSK3TI","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5D35WQJSK3TIM5PR","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5D35WQJS","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:420c610d73c184857b1cff3a3dafd9f22543460270636cffb5e0b7c539f3641d","target":"graph","created_at":"2026-05-18T00:20:59Z","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":"In this article, we define a symmetric 2-tensor canonically associated to Q-curvature called J-tensor on any Riemannian manifold with dimension at least three. The relation between J-tensor and Q-curvature is precisely like Ricci tensor and scalar curvature. Thus it can be interpreted as a higher-order analogue of Ricci tensor. This tensor can also be used to understand Chang-Gursky-Yang's theorem on 4-dimensional Q-singular metrics. Moreover, we show an Almost-Schur Lemma holds for Q-curvature, which gives an estimate of Q-curvature on closed manifolds.","authors_text":"Wei Yuan, Yueh-Ju Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-03T07:15:27Z","title":"A symmetric 2-tensor canonically associated to Q-curvature and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01212","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":"sha256:5ef7d7f0a6cfd1b62f34324c99534a6630a9f606dbc8dae558d4edb7ba12ea18","target":"record","created_at":"2026-05-18T00:20:59Z","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":"49a71798abe13f6b186602fd0a407ca509d0b59028923d74b5432523ba51593d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-03T07:15:27Z","title_canon_sha256":"70e362ee6a2bbea3ce5b7c2bf2be46d36993a8e0560abeac0cc769ff242020f1"},"schema_version":"1.0","source":{"id":"1602.01212","kind":"arxiv","version":2}},"canonical_sha256":"e8f7db413256e68675f166bf1e2a9b76c8f971f599c15f80aee08fe92ab3025c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8f7db413256e68675f166bf1e2a9b76c8f971f599c15f80aee08fe92ab3025c","first_computed_at":"2026-05-18T00:20:59.873707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:59.873707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2neKfeTIQgrzEYmxQ9t56raDVA8iLFzfIbPAhfIEEAdgIRiYYb2tMgsKA0SZhkdms1YaKiwlqa72nod1A9uyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:59.874416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01212","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ef7d7f0a6cfd1b62f34324c99534a6630a9f606dbc8dae558d4edb7ba12ea18","sha256:420c610d73c184857b1cff3a3dafd9f22543460270636cffb5e0b7c539f3641d"],"state_sha256":"a6662841adb1ab6b94c2fdfeacb068930f0f3c21b06e1cd11f2e91c986adfbd7"}