{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UXUHF5KD536PIIVD3PUW2P3UEE","short_pith_number":"pith:UXUHF5KD","canonical_record":{"source":{"id":"1807.08406","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-23T02:32:33Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ec6c33a61401572ed27728b5b4e94632fe8fc8c5f343e525cf746af2447dce2d","abstract_canon_sha256":"952c0754e148f36f7b88e06040824fd33cffcbc32a2d99beffe0a425a94600df"},"schema_version":"1.0"},"canonical_sha256":"a5e872f543eefcf422a3dbe96d3f74210bd3296f1b8532d295930745bcbb38ce","source":{"kind":"arxiv","id":"1807.08406","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08406","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08406v2","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08406","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"UXUHF5KD536P","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UXUHF5KD536PIIVD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UXUHF5KD","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UXUHF5KD536PIIVD3PUW2P3UEE","target":"record","payload":{"canonical_record":{"source":{"id":"1807.08406","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-23T02:32:33Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ec6c33a61401572ed27728b5b4e94632fe8fc8c5f343e525cf746af2447dce2d","abstract_canon_sha256":"952c0754e148f36f7b88e06040824fd33cffcbc32a2d99beffe0a425a94600df"},"schema_version":"1.0"},"canonical_sha256":"a5e872f543eefcf422a3dbe96d3f74210bd3296f1b8532d295930745bcbb38ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:59.748909Z","signature_b64":"QO4+vp0z6nTydQRqqoxLOnPAov0JP+4QxoBonUkfma8lGekF/gwHJlrCwZLL5QCAcpzFLKO2fwKsthPmZ8hUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5e872f543eefcf422a3dbe96d3f74210bd3296f1b8532d295930745bcbb38ce","last_reissued_at":"2026-05-17T23:47:59.748332Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:59.748332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.08406","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y7L8mteA4DFb07nr0Lue8odMvvE0vFyC+MDfpQIdktP4AwNMZgf9K3DT8jtuQeBXzvY5xOB1eie/Mx/CsSrOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:50:20.363992Z"},"content_sha256":"04a93eb640d17cdbc9d7339fb98b3c883f1b1bb8301f4c0f1bc6e8651416aa17","schema_version":"1.0","event_id":"sha256:04a93eb640d17cdbc9d7339fb98b3c883f1b1bb8301f4c0f1bc6e8651416aa17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UXUHF5KD536PIIVD3PUW2P3UEE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A compactness theorem for scalar-flat metrics on 3-manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Olivaine S. de Queiroz, Sergio Almaraz, Shaodong Wang","submitted_at":"2018-07-23T02:32:33Z","abstract_excerpt":"Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. This involves a blow-up analysis of a Yamabe-type equation with critical Sobolev exponent on the boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08406","kind":"arxiv","version":2},"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":"2026-05-17T23:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JF4wf95cem4OB1/lq36jSwtevXw1bw0Wzn6qNMnAaKn1EvVmn00gyi0EGtaElXTRsG8htgYpTmu74HwW7DCPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:50:20.364673Z"},"content_sha256":"1a76210c5c866772e8b0414ef6b61179c2d136db47228c2519635e7434f5024a","schema_version":"1.0","event_id":"sha256:1a76210c5c866772e8b0414ef6b61179c2d136db47228c2519635e7434f5024a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXUHF5KD536PIIVD3PUW2P3UEE/bundle.json","state_url":"https://pith.science/pith/UXUHF5KD536PIIVD3PUW2P3UEE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXUHF5KD536PIIVD3PUW2P3UEE/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":"2026-05-27T00:50:20Z","links":{"resolver":"https://pith.science/pith/UXUHF5KD536PIIVD3PUW2P3UEE","bundle":"https://pith.science/pith/UXUHF5KD536PIIVD3PUW2P3UEE/bundle.json","state":"https://pith.science/pith/UXUHF5KD536PIIVD3PUW2P3UEE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXUHF5KD536PIIVD3PUW2P3UEE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UXUHF5KD536PIIVD3PUW2P3UEE","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":"952c0754e148f36f7b88e06040824fd33cffcbc32a2d99beffe0a425a94600df","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-23T02:32:33Z","title_canon_sha256":"ec6c33a61401572ed27728b5b4e94632fe8fc8c5f343e525cf746af2447dce2d"},"schema_version":"1.0","source":{"id":"1807.08406","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08406","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08406v2","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08406","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"UXUHF5KD536P","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UXUHF5KD536PIIVD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UXUHF5KD","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:1a76210c5c866772e8b0414ef6b61179c2d136db47228c2519635e7434f5024a","target":"graph","created_at":"2026-05-17T23:47:59Z","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":"Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. This involves a blow-up analysis of a Yamabe-type equation with critical Sobolev exponent on the boundary.","authors_text":"Olivaine S. de Queiroz, Sergio Almaraz, Shaodong Wang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-23T02:32:33Z","title":"A compactness theorem for scalar-flat metrics on 3-manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08406","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":"sha256:04a93eb640d17cdbc9d7339fb98b3c883f1b1bb8301f4c0f1bc6e8651416aa17","target":"record","created_at":"2026-05-17T23:47:59Z","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":"952c0754e148f36f7b88e06040824fd33cffcbc32a2d99beffe0a425a94600df","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-23T02:32:33Z","title_canon_sha256":"ec6c33a61401572ed27728b5b4e94632fe8fc8c5f343e525cf746af2447dce2d"},"schema_version":"1.0","source":{"id":"1807.08406","kind":"arxiv","version":2}},"canonical_sha256":"a5e872f543eefcf422a3dbe96d3f74210bd3296f1b8532d295930745bcbb38ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5e872f543eefcf422a3dbe96d3f74210bd3296f1b8532d295930745bcbb38ce","first_computed_at":"2026-05-17T23:47:59.748332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:59.748332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QO4+vp0z6nTydQRqqoxLOnPAov0JP+4QxoBonUkfma8lGekF/gwHJlrCwZLL5QCAcpzFLKO2fwKsthPmZ8hUBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:59.748909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08406","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04a93eb640d17cdbc9d7339fb98b3c883f1b1bb8301f4c0f1bc6e8651416aa17","sha256:1a76210c5c866772e8b0414ef6b61179c2d136db47228c2519635e7434f5024a"],"state_sha256":"d55eb6db35e50d28a4001c21e2d95612341b7f14f460709ed5dacd599b49dc87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yBNVvy7dVNzUHiRWhkkx+2QjN8L3z2C3GjmelJZx2dSsGlXgc39UToi+NlNhB5I2LIDx1r32ceDlBucoS18cCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:50:20.368145Z","bundle_sha256":"afa80d14d0f72b7828b0d3c4cb5aed458c87bdc58d8b585d20f5ca5fce83a99f"}}