{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LIRBVNHPAAUUZ4IKSTS6BPBKVH","short_pith_number":"pith:LIRBVNHP","canonical_record":{"source":{"id":"1801.04474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T18:39:47Z","cross_cats_sorted":[],"title_canon_sha256":"e0ca9f3e63a96b328e2b056b4d80995adb9d998d48eb7be7220d298715aee203","abstract_canon_sha256":"280f516da79d97291a8a6f6d7e35106a7bf6ceb65e9d533f9fd596c897fb3787"},"schema_version":"1.0"},"canonical_sha256":"5a221ab4ef00294cf10a94e5e0bc2aa9facc992e2ffc9a287000611af5fe919f","source":{"kind":"arxiv","id":"1801.04474","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04474","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04474v1","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04474","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"pith_short_12","alias_value":"LIRBVNHPAAUU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LIRBVNHPAAUUZ4IK","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LIRBVNHP","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LIRBVNHPAAUUZ4IKSTS6BPBKVH","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T18:39:47Z","cross_cats_sorted":[],"title_canon_sha256":"e0ca9f3e63a96b328e2b056b4d80995adb9d998d48eb7be7220d298715aee203","abstract_canon_sha256":"280f516da79d97291a8a6f6d7e35106a7bf6ceb65e9d533f9fd596c897fb3787"},"schema_version":"1.0"},"canonical_sha256":"5a221ab4ef00294cf10a94e5e0bc2aa9facc992e2ffc9a287000611af5fe919f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:06.371523Z","signature_b64":"2uOE2p+QArzZ3LRyhpawp4OKXBUt0tkIRs70t0Y9uRruEqJnFyXonjaCHmUBhOREa8AhlAWYBj/lF7E3QLZyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a221ab4ef00294cf10a94e5e0bc2aa9facc992e2ffc9a287000611af5fe919f","last_reissued_at":"2026-05-18T00:26:06.370910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:06.370910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04474","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":"2026-05-18T00:26:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nec4I/BAyx60Mv2rfMot85WoccuWPh/RAqcL1XO5iCLx3oCcyo0gTCE1/tSOcJfT8tKSk7XSoUbpvs2Q9q91Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:16:31.702047Z"},"content_sha256":"a4a5b7a719126eb926c7a822c51cf7f7302d187b9bdefeb378e5397fb150e75e","schema_version":"1.0","event_id":"sha256:a4a5b7a719126eb926c7a822c51cf7f7302d187b9bdefeb378e5397fb150e75e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LIRBVNHPAAUUZ4IKSTS6BPBKVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An invariant related to the existence of conformally compact Einstein fillings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Matthew J. Gursky, Qing Han, Stephan Stolz","submitted_at":"2018-01-13T18:39:47Z","abstract_excerpt":"We define an invariant for compact spin manifolds $X$ of dimension $4k$ equipped with a metric $h$ of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of $h$ to be the conformal infinity of a conformally compact Einstein metric on $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04474","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":"2026-05-18T00:26:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sYfn5cr0GQrF0OkKcesBuk1xUWoFm1/ca9AZr3M30/6XfiXHl9uNJ0OAZoafeL7Q6POP+wuKWHXkm7QgN6S9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:16:31.702472Z"},"content_sha256":"04384589a61b4d1813648a24fe5b7b1cce7a4237670161251e88c4ee22e265da","schema_version":"1.0","event_id":"sha256:04384589a61b4d1813648a24fe5b7b1cce7a4237670161251e88c4ee22e265da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LIRBVNHPAAUUZ4IKSTS6BPBKVH/bundle.json","state_url":"https://pith.science/pith/LIRBVNHPAAUUZ4IKSTS6BPBKVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LIRBVNHPAAUUZ4IKSTS6BPBKVH/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":"2026-06-02T07:16:31Z","links":{"resolver":"https://pith.science/pith/LIRBVNHPAAUUZ4IKSTS6BPBKVH","bundle":"https://pith.science/pith/LIRBVNHPAAUUZ4IKSTS6BPBKVH/bundle.json","state":"https://pith.science/pith/LIRBVNHPAAUUZ4IKSTS6BPBKVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LIRBVNHPAAUUZ4IKSTS6BPBKVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LIRBVNHPAAUUZ4IKSTS6BPBKVH","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":"280f516da79d97291a8a6f6d7e35106a7bf6ceb65e9d533f9fd596c897fb3787","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T18:39:47Z","title_canon_sha256":"e0ca9f3e63a96b328e2b056b4d80995adb9d998d48eb7be7220d298715aee203"},"schema_version":"1.0","source":{"id":"1801.04474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04474","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04474v1","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04474","created_at":"2026-05-18T00:26:06Z"},{"alias_kind":"pith_short_12","alias_value":"LIRBVNHPAAUU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LIRBVNHPAAUUZ4IK","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LIRBVNHP","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:04384589a61b4d1813648a24fe5b7b1cce7a4237670161251e88c4ee22e265da","target":"graph","created_at":"2026-05-18T00:26:06Z","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 define an invariant for compact spin manifolds $X$ of dimension $4k$ equipped with a metric $h$ of positive Yamabe invariant on its boundary. The vanishing of this invariant is a necessary condition for the conformal class of $h$ to be the conformal infinity of a conformally compact Einstein metric on $X$.","authors_text":"Matthew J. Gursky, Qing Han, Stephan Stolz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T18:39:47Z","title":"An invariant related to the existence of conformally compact Einstein fillings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04474","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:a4a5b7a719126eb926c7a822c51cf7f7302d187b9bdefeb378e5397fb150e75e","target":"record","created_at":"2026-05-18T00:26:06Z","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":"280f516da79d97291a8a6f6d7e35106a7bf6ceb65e9d533f9fd596c897fb3787","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T18:39:47Z","title_canon_sha256":"e0ca9f3e63a96b328e2b056b4d80995adb9d998d48eb7be7220d298715aee203"},"schema_version":"1.0","source":{"id":"1801.04474","kind":"arxiv","version":1}},"canonical_sha256":"5a221ab4ef00294cf10a94e5e0bc2aa9facc992e2ffc9a287000611af5fe919f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a221ab4ef00294cf10a94e5e0bc2aa9facc992e2ffc9a287000611af5fe919f","first_computed_at":"2026-05-18T00:26:06.370910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:06.370910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2uOE2p+QArzZ3LRyhpawp4OKXBUt0tkIRs70t0Y9uRruEqJnFyXonjaCHmUBhOREa8AhlAWYBj/lF7E3QLZyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:06.371523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4a5b7a719126eb926c7a822c51cf7f7302d187b9bdefeb378e5397fb150e75e","sha256:04384589a61b4d1813648a24fe5b7b1cce7a4237670161251e88c4ee22e265da"],"state_sha256":"e82dcd27fdf6a0d43708f19e6fea3f9ab0c7fe7729ad5dba0562db9bf9bd1abe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OHNi8cCzmki1lEl4lhsYUXLwSH58e6Z+8OaQv0F2NqbqsC2nmbJqG+pcNFjoDWEhbzp8lvCMR8iE5Qk1i/+8BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:16:31.704509Z","bundle_sha256":"9b4672a533e8114bc71bd9751847ce1b7d73c2ea0dcb6e8ba77279e814c03470"}}