{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:QT4AAOE4VNNI4RIIKKGBQM7M2N","short_pith_number":"pith:QT4AAOE4","canonical_record":{"source":{"id":"0907.0798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-04T21:01:46Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b3ebe86d2b58b125ce54ab60c21a75c18231baca54d957fd98c2ed8838c6ca7b","abstract_canon_sha256":"834522b5de00fd7e507f37d6b8cb081514f0e83c79f4bc526c9abf72fdbb3db1"},"schema_version":"1.0"},"canonical_sha256":"84f800389cab5a8e4508528c1833ecd37381bfb248679040ea4e8842c6679254","source":{"kind":"arxiv","id":"0907.0798","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0798","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0798v1","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0798","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"QT4AAOE4VNNI","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QT4AAOE4VNNI4RII","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QT4AAOE4","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:QT4AAOE4VNNI4RIIKKGBQM7M2N","target":"record","payload":{"canonical_record":{"source":{"id":"0907.0798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-04T21:01:46Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b3ebe86d2b58b125ce54ab60c21a75c18231baca54d957fd98c2ed8838c6ca7b","abstract_canon_sha256":"834522b5de00fd7e507f37d6b8cb081514f0e83c79f4bc526c9abf72fdbb3db1"},"schema_version":"1.0"},"canonical_sha256":"84f800389cab5a8e4508528c1833ecd37381bfb248679040ea4e8842c6679254","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:43.734615Z","signature_b64":"E6R3kyFgpEzkaj4ixa7VrYxP94H5CeEflJg1qJIybvU/TDbNJzQl63NJ9V6yDb3L9E1DtheIvvs4Hvv6FxH4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84f800389cab5a8e4508528c1833ecd37381bfb248679040ea4e8842c6679254","last_reissued_at":"2026-05-18T04:32:43.734164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:43.734164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.0798","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":"2026-05-18T04:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OpU0fJdIW/IO5AmmRgE1sYMEra8DGQtrJDbLAnRXTEwE5UFpP7ZRV6Nxbxog/u2R6jiwLqqR45b3MevG0b68AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:48:31.847524Z"},"content_sha256":"059c24a830a45d4d95dc1ec7d3d60d61ca93d5a56d60f4b55ee5a1d90e721cc7","schema_version":"1.0","event_id":"sha256:059c24a830a45d4d95dc1ec7d3d60d61ca93d5a56d60f4b55ee5a1d90e721cc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:QT4AAOE4VNNI4RIIKKGBQM7M2N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An existence theorem of conformal scalar-flat metrics on manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Sergio Almaraz","submitted_at":"2009-07-04T21:01:46Z","abstract_excerpt":"Let (M,g) be a compact Riemannian manifold with boundary. This paper addresses the Yamabe-type problem of finding a conformal scalar-flat metric on M, which has the boundary as a constant mean curvature hypersurface. When the boundary is umbilic, we prove an existence theorem that finishes some remaining cases of this problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0798","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":"2026-05-18T04:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twTUKiAruWP0iXIFoPgY/Sd0JPhflwpVbsuywszcflDM5QtuQDhK2NukWnmb2Gxa5JoWx39VS2u1iNMN3VnfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:48:31.848129Z"},"content_sha256":"1c7d2441e3f87d9987d81ffe8c742fce3209aff2bfd6b13df0020a7036a3f5d4","schema_version":"1.0","event_id":"sha256:1c7d2441e3f87d9987d81ffe8c742fce3209aff2bfd6b13df0020a7036a3f5d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QT4AAOE4VNNI4RIIKKGBQM7M2N/bundle.json","state_url":"https://pith.science/pith/QT4AAOE4VNNI4RIIKKGBQM7M2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QT4AAOE4VNNI4RIIKKGBQM7M2N/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":"2026-06-06T21:48:31Z","links":{"resolver":"https://pith.science/pith/QT4AAOE4VNNI4RIIKKGBQM7M2N","bundle":"https://pith.science/pith/QT4AAOE4VNNI4RIIKKGBQM7M2N/bundle.json","state":"https://pith.science/pith/QT4AAOE4VNNI4RIIKKGBQM7M2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QT4AAOE4VNNI4RIIKKGBQM7M2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QT4AAOE4VNNI4RIIKKGBQM7M2N","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":"834522b5de00fd7e507f37d6b8cb081514f0e83c79f4bc526c9abf72fdbb3db1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-04T21:01:46Z","title_canon_sha256":"b3ebe86d2b58b125ce54ab60c21a75c18231baca54d957fd98c2ed8838c6ca7b"},"schema_version":"1.0","source":{"id":"0907.0798","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0798","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0798v1","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0798","created_at":"2026-05-18T04:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"QT4AAOE4VNNI","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QT4AAOE4VNNI4RII","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QT4AAOE4","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:1c7d2441e3f87d9987d81ffe8c742fce3209aff2bfd6b13df0020a7036a3f5d4","target":"graph","created_at":"2026-05-18T04:32:43Z","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 manifold with boundary. This paper addresses the Yamabe-type problem of finding a conformal scalar-flat metric on M, which has the boundary as a constant mean curvature hypersurface. When the boundary is umbilic, we prove an existence theorem that finishes some remaining cases of this problem.","authors_text":"Sergio Almaraz","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-04T21:01:46Z","title":"An existence theorem of conformal scalar-flat metrics on manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0798","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":"sha256:059c24a830a45d4d95dc1ec7d3d60d61ca93d5a56d60f4b55ee5a1d90e721cc7","target":"record","created_at":"2026-05-18T04:32:43Z","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":"834522b5de00fd7e507f37d6b8cb081514f0e83c79f4bc526c9abf72fdbb3db1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-04T21:01:46Z","title_canon_sha256":"b3ebe86d2b58b125ce54ab60c21a75c18231baca54d957fd98c2ed8838c6ca7b"},"schema_version":"1.0","source":{"id":"0907.0798","kind":"arxiv","version":1}},"canonical_sha256":"84f800389cab5a8e4508528c1833ecd37381bfb248679040ea4e8842c6679254","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84f800389cab5a8e4508528c1833ecd37381bfb248679040ea4e8842c6679254","first_computed_at":"2026-05-18T04:32:43.734164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:43.734164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E6R3kyFgpEzkaj4ixa7VrYxP94H5CeEflJg1qJIybvU/TDbNJzQl63NJ9V6yDb3L9E1DtheIvvs4Hvv6FxH4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:43.734615Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0798","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:059c24a830a45d4d95dc1ec7d3d60d61ca93d5a56d60f4b55ee5a1d90e721cc7","sha256:1c7d2441e3f87d9987d81ffe8c742fce3209aff2bfd6b13df0020a7036a3f5d4"],"state_sha256":"b072480778e7ea639af9fccc901f22b0568cda27004961bf517725153942b734"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7IZ5m2e1Q5l32kbJ7CpkdMu1GIb3tBPPI/zAYHYl5IO9Y2fZ9Y/Ci3TWcc1ToRK8F5XhCXMyXAINEUEm4u1CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:48:31.851576Z","bundle_sha256":"9f30bcd581af7e69e8bfe95ba13a616fa863ec68cf0e3a6c1004193a2d43db11"}}