{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7IW6ADSK46LOAILPG3DFJ7O6T3","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":"06c68477fc7884ac76664fe42172dec3baaf6f137ce5eff8d323d19fc56c78b5","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-07T23:45:18Z","title_canon_sha256":"0a5a1af06312841ebc0ccf9a87f28bbd9d3958e2bdc5ded0bd2dd2baa795facb"},"schema_version":"1.0","source":{"id":"1508.01838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01838","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01838v1","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01838","created_at":"2026-05-18T01:35:37Z"},{"alias_kind":"pith_short_12","alias_value":"7IW6ADSK46LO","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7IW6ADSK46LOAILP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7IW6ADSK","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:670aaa46f3ce4be4307d7a15c49bc93c8e031bead210574468b74ba93a7e2b36","target":"graph","created_at":"2026-05-18T01:35:37Z","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 develop the calculus for hypersurface variations based on variation of the hypersurface defining function. This is used to show that the functional gradient of a new Willmore-like, conformal hypersurface energy agrees exactly with the obstruction to smoothly solving the singular Yamabe problem for conformally compact four-manifolds. We give explicit hypersurface formulae for both the energy functional and the obstruction.","authors_text":"Andrew Waldron, A. Rod Gover, Matthew Halbasch, Michael Glaros","cross_cats":["gr-qc","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-07T23:45:18Z","title":"Singular Yamabe Problem Willmore Energies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01838","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:ec12eb3a77d328280cebcef515980efc6f30c11a8e2703f6983c4995d7cd3adb","target":"record","created_at":"2026-05-18T01:35:37Z","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":"06c68477fc7884ac76664fe42172dec3baaf6f137ce5eff8d323d19fc56c78b5","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-07T23:45:18Z","title_canon_sha256":"0a5a1af06312841ebc0ccf9a87f28bbd9d3958e2bdc5ded0bd2dd2baa795facb"},"schema_version":"1.0","source":{"id":"1508.01838","kind":"arxiv","version":1}},"canonical_sha256":"fa2de00e4ae796e0216f36c654fdde9eeaaf4e4fb85704ce606900fcbfa23448","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa2de00e4ae796e0216f36c654fdde9eeaaf4e4fb85704ce606900fcbfa23448","first_computed_at":"2026-05-18T01:35:37.793201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:37.793201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OSn77HZCsQvGxg/8kASez/mlwjuWrbneI5dBtqLyjC5U+dBn9/Nq3/HIPwdhE49+k0879Sg/1J6V7Jscj0AcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:37.793833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec12eb3a77d328280cebcef515980efc6f30c11a8e2703f6983c4995d7cd3adb","sha256:670aaa46f3ce4be4307d7a15c49bc93c8e031bead210574468b74ba93a7e2b36"],"state_sha256":"c6a260e61073d37e04db71d974d20b22e2bb88106263e048e5d79069b18f655e"}