{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KJ532KCMRFKO25N3ILD56VACXR","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":"3dc5fcae2448e8f65a0a1e32550ce081d3ac7cfd8052edb31704afbf3fa2d8c4","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-14T03:59:18Z","title_canon_sha256":"acf77064ad6b35e91e00598cc6277d2139c901d06ceb9e8560495045ba3597cf"},"schema_version":"1.0","source":{"id":"1707.04377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04377","created_at":"2026-05-18T00:40:18Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04377v1","created_at":"2026-05-18T00:40:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04377","created_at":"2026-05-18T00:40:18Z"},{"alias_kind":"pith_short_12","alias_value":"KJ532KCMRFKO","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KJ532KCMRFKO25N3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KJ532KCM","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:03158581c48aa668dd807e159c9c80bb529b8bca02639d7194bd5002a147136f","target":"graph","created_at":"2026-05-18T00:40:18Z","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 study conformal deformation problems on manifolds with boundary which include prescribing $\\sigma_k\\equiv0$ in the interior. In particular, we prove a Dirichlet principle when the induced metric on the boundary is fixed and an Obata-type theorem on the upper hemisphere. We introduce some conformally covariant multilinear operators as a key technical tool.","authors_text":"Jeffrey S. Case, Yi Wang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-14T03:59:18Z","title":"Boundary operators associated to the $\\sigma_k$-curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04377","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:e2d732be5818d684310faebee62b174451f57a813a89c2fe75d00c1c48ecbe88","target":"record","created_at":"2026-05-18T00:40:18Z","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":"3dc5fcae2448e8f65a0a1e32550ce081d3ac7cfd8052edb31704afbf3fa2d8c4","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-07-14T03:59:18Z","title_canon_sha256":"acf77064ad6b35e91e00598cc6277d2139c901d06ceb9e8560495045ba3597cf"},"schema_version":"1.0","source":{"id":"1707.04377","kind":"arxiv","version":1}},"canonical_sha256":"527bbd284c8954ed75bb42c7df5402bc5cdacf950f085478496f90c32c96d532","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"527bbd284c8954ed75bb42c7df5402bc5cdacf950f085478496f90c32c96d532","first_computed_at":"2026-05-18T00:40:18.412329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:18.412329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SdsvKYsHYTC3kU3cSb1osFOXexGtq1InQqTsvKP46+sDPc0ROxfIUi8c502LnXEo8rDYqJIYfLEOiReNPYQHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:18.413032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2d732be5818d684310faebee62b174451f57a813a89c2fe75d00c1c48ecbe88","sha256:03158581c48aa668dd807e159c9c80bb529b8bca02639d7194bd5002a147136f"],"state_sha256":"d3131056691b5a122ebc0c2e8a115b33733379582623832dd98681f3a186d113"}