{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IVP2I7X6CWJXMF2DMY6EXALTRL","short_pith_number":"pith:IVP2I7X6","canonical_record":{"source":{"id":"1405.6080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-23T14:42:34Z","cross_cats_sorted":[],"title_canon_sha256":"d504e9addec91d1e18d8a755f64c9047aff8244e428112caa63516e943ad2431","abstract_canon_sha256":"21a93669c977a2a19ce466c6de9816b4cd6e1089ca4f2c329a705d226dd170ea"},"schema_version":"1.0"},"canonical_sha256":"455fa47efe1593761743663c4b81738aeadc04ddefe6b5055b5f664473b64623","source":{"kind":"arxiv","id":"1405.6080","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6080","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6080v1","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6080","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"IVP2I7X6CWJX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IVP2I7X6CWJXMF2D","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IVP2I7X6","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IVP2I7X6CWJXMF2DMY6EXALTRL","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-23T14:42:34Z","cross_cats_sorted":[],"title_canon_sha256":"d504e9addec91d1e18d8a755f64c9047aff8244e428112caa63516e943ad2431","abstract_canon_sha256":"21a93669c977a2a19ce466c6de9816b4cd6e1089ca4f2c329a705d226dd170ea"},"schema_version":"1.0"},"canonical_sha256":"455fa47efe1593761743663c4b81738aeadc04ddefe6b5055b5f664473b64623","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:14.116452Z","signature_b64":"ffOomM3oNwo+TRbZ9DB2Sma24qlJETgILHnWU2xhW0oZYTu5aZSJDrXcqeJ4zwMGIvUIJ2Hr+St+Q/Ir4G8ADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"455fa47efe1593761743663c4b81738aeadc04ddefe6b5055b5f664473b64623","last_reissued_at":"2026-05-18T02:51:14.115928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:14.115928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6080","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jkHp/RkQoVcj6QTYl/DibyiK5388GlUs0+SkNRuw3ECnLdRX8cZN7sVbcrLBjkDKTSB30nZWy5pIxpVa6hF3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:39:22.594776Z"},"content_sha256":"58ac5ab24daa01c289e687bfe67a791708977a387b714498b80b981e8e8be867","schema_version":"1.0","event_id":"sha256:58ac5ab24daa01c289e687bfe67a791708977a387b714498b80b981e8e8be867"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IVP2I7X6CWJXMF2DMY6EXALTRL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical Metrics for Riemannian Curvature Functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeff A. Viaclovsky","submitted_at":"2014-05-23T14:42:34Z","abstract_excerpt":"This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6080","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZDEUPVX9sUDNBI3CuRjRmSy6I+1FbokOi7fHkLnJP86jsLm8efvdNcJPrbxn3GIoTGuE//oaKoExc/P5AQUmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:39:22.595115Z"},"content_sha256":"a1ef057f16b2fc470d2aa5e0080da2b68f6683f2e807d26b1b5b101e02164f73","schema_version":"1.0","event_id":"sha256:a1ef057f16b2fc470d2aa5e0080da2b68f6683f2e807d26b1b5b101e02164f73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVP2I7X6CWJXMF2DMY6EXALTRL/bundle.json","state_url":"https://pith.science/pith/IVP2I7X6CWJXMF2DMY6EXALTRL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVP2I7X6CWJXMF2DMY6EXALTRL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T13:39:22Z","links":{"resolver":"https://pith.science/pith/IVP2I7X6CWJXMF2DMY6EXALTRL","bundle":"https://pith.science/pith/IVP2I7X6CWJXMF2DMY6EXALTRL/bundle.json","state":"https://pith.science/pith/IVP2I7X6CWJXMF2DMY6EXALTRL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVP2I7X6CWJXMF2DMY6EXALTRL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IVP2I7X6CWJXMF2DMY6EXALTRL","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":"21a93669c977a2a19ce466c6de9816b4cd6e1089ca4f2c329a705d226dd170ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-23T14:42:34Z","title_canon_sha256":"d504e9addec91d1e18d8a755f64c9047aff8244e428112caa63516e943ad2431"},"schema_version":"1.0","source":{"id":"1405.6080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6080","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6080v1","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6080","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"IVP2I7X6CWJX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IVP2I7X6CWJXMF2D","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IVP2I7X6","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:a1ef057f16b2fc470d2aa5e0080da2b68f6683f2e807d26b1b5b101e02164f73","target":"graph","created_at":"2026-05-18T02:51:14Z","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":"This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.","authors_text":"Jeff A. Viaclovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-23T14:42:34Z","title":"Critical Metrics for Riemannian Curvature Functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6080","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":"sha256:58ac5ab24daa01c289e687bfe67a791708977a387b714498b80b981e8e8be867","target":"record","created_at":"2026-05-18T02:51:14Z","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":"21a93669c977a2a19ce466c6de9816b4cd6e1089ca4f2c329a705d226dd170ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-23T14:42:34Z","title_canon_sha256":"d504e9addec91d1e18d8a755f64c9047aff8244e428112caa63516e943ad2431"},"schema_version":"1.0","source":{"id":"1405.6080","kind":"arxiv","version":1}},"canonical_sha256":"455fa47efe1593761743663c4b81738aeadc04ddefe6b5055b5f664473b64623","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"455fa47efe1593761743663c4b81738aeadc04ddefe6b5055b5f664473b64623","first_computed_at":"2026-05-18T02:51:14.115928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:14.115928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ffOomM3oNwo+TRbZ9DB2Sma24qlJETgILHnWU2xhW0oZYTu5aZSJDrXcqeJ4zwMGIvUIJ2Hr+St+Q/Ir4G8ADA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:14.116452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58ac5ab24daa01c289e687bfe67a791708977a387b714498b80b981e8e8be867","sha256:a1ef057f16b2fc470d2aa5e0080da2b68f6683f2e807d26b1b5b101e02164f73"],"state_sha256":"60b3abd9e0cb1d4eb4e395342045c8c75a2f3cf04e457f0d56f7b280532a9f9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DRWwALo/N8RpzIko4bVKrOarWYr6FVGkCk0GYSrdb9t+Eex5Ra8nPGwP5lmf/qDz+WhPW+vfSI6kc3dNOI1kBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:39:22.597143Z","bundle_sha256":"e3500a9966f645970a3f248d1b5a579400d61e6f1d4e94f27382801d60e20d43"}}