{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4A2Y5NZ5VFPRBQUUCC52EREKZM","short_pith_number":"pith:4A2Y5NZ5","canonical_record":{"source":{"id":"1612.04015","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T03:38:14Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"43d0fd27bb909c2a23e1308f48326a5c44a0a4c4cf32678948b034452d717eef","abstract_canon_sha256":"8d2df655f7ee7a2318e5f6f623b1a73812b9af90c348985ece0deb6d63afff1f"},"schema_version":"1.0"},"canonical_sha256":"e0358eb73da95f10c29410bba2448acb05268a23ccba7d04ca2c8bcd814d347f","source":{"kind":"arxiv","id":"1612.04015","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04015","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04015v1","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04015","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"4A2Y5NZ5VFPR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4A2Y5NZ5VFPRBQUU","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4A2Y5NZ5","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4A2Y5NZ5VFPRBQUUCC52EREKZM","target":"record","payload":{"canonical_record":{"source":{"id":"1612.04015","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T03:38:14Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"43d0fd27bb909c2a23e1308f48326a5c44a0a4c4cf32678948b034452d717eef","abstract_canon_sha256":"8d2df655f7ee7a2318e5f6f623b1a73812b9af90c348985ece0deb6d63afff1f"},"schema_version":"1.0"},"canonical_sha256":"e0358eb73da95f10c29410bba2448acb05268a23ccba7d04ca2c8bcd814d347f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:05.829583Z","signature_b64":"cNu/+wZGvRyibQBmbZH+0B+rs99U5+7Zdc5QXi3DLo1hudwVxawBYG6kHwsAOz5TCVin2aUXpJTTc2t+PZNEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0358eb73da95f10c29410bba2448acb05268a23ccba7d04ca2c8bcd814d347f","last_reissued_at":"2026-05-18T00:55:05.828887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:05.828887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.04015","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":"2026-05-18T00:55:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"74F2MqpjDaZclcBeO5QnqQW9PADyUPGpADpiBFdZ6qadrZNSuwsmGspWB5yFiM6OPDfFek+5lFq6mfD3HuqVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:20:31.957123Z"},"content_sha256":"ca85204d5a34ac6cb85459aa35c745e27b9cb26ecf8b5df66001e8b192a21f62","schema_version":"1.0","event_id":"sha256:ca85204d5a34ac6cb85459aa35c745e27b9cb26ecf8b5df66001e8b192a21f62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4A2Y5NZ5VFPRBQUUCC52EREKZM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence results for the fractional Q-curvature problem on three dimensional CR sphere","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Chungen Liu, Yafang Wang","submitted_at":"2016-12-13T03:38:14Z","abstract_excerpt":"In this paper the fractional Q-curvature problem on three dimensional CR sphere is considered. By using the critical points theory at infinity, an existence result is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04015","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":"2026-05-18T00:55:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0CaoBtAvZ0mHa00hfS7aMr1CXpsozbuLmjvSXfv4hs4T4aYD6zIgSPTIvjlCOwnDjEbbNgagNVpT5NNyggL5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:20:31.957488Z"},"content_sha256":"52ccaee26983a95ea141ab4658fd8916a6611fe4cf9abe0c5307986197210c74","schema_version":"1.0","event_id":"sha256:52ccaee26983a95ea141ab4658fd8916a6611fe4cf9abe0c5307986197210c74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4A2Y5NZ5VFPRBQUUCC52EREKZM/bundle.json","state_url":"https://pith.science/pith/4A2Y5NZ5VFPRBQUUCC52EREKZM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4A2Y5NZ5VFPRBQUUCC52EREKZM/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":"2026-05-28T02:20:31Z","links":{"resolver":"https://pith.science/pith/4A2Y5NZ5VFPRBQUUCC52EREKZM","bundle":"https://pith.science/pith/4A2Y5NZ5VFPRBQUUCC52EREKZM/bundle.json","state":"https://pith.science/pith/4A2Y5NZ5VFPRBQUUCC52EREKZM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4A2Y5NZ5VFPRBQUUCC52EREKZM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4A2Y5NZ5VFPRBQUUCC52EREKZM","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":"8d2df655f7ee7a2318e5f6f623b1a73812b9af90c348985ece0deb6d63afff1f","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T03:38:14Z","title_canon_sha256":"43d0fd27bb909c2a23e1308f48326a5c44a0a4c4cf32678948b034452d717eef"},"schema_version":"1.0","source":{"id":"1612.04015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04015","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04015v1","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04015","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"4A2Y5NZ5VFPR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4A2Y5NZ5VFPRBQUU","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4A2Y5NZ5","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:52ccaee26983a95ea141ab4658fd8916a6611fe4cf9abe0c5307986197210c74","target":"graph","created_at":"2026-05-18T00:55:05Z","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":"In this paper the fractional Q-curvature problem on three dimensional CR sphere is considered. By using the critical points theory at infinity, an existence result is obtained.","authors_text":"Chungen Liu, Yafang Wang","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T03:38:14Z","title":"Existence results for the fractional Q-curvature problem on three dimensional CR sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04015","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:ca85204d5a34ac6cb85459aa35c745e27b9cb26ecf8b5df66001e8b192a21f62","target":"record","created_at":"2026-05-18T00:55:05Z","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":"8d2df655f7ee7a2318e5f6f623b1a73812b9af90c348985ece0deb6d63afff1f","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-13T03:38:14Z","title_canon_sha256":"43d0fd27bb909c2a23e1308f48326a5c44a0a4c4cf32678948b034452d717eef"},"schema_version":"1.0","source":{"id":"1612.04015","kind":"arxiv","version":1}},"canonical_sha256":"e0358eb73da95f10c29410bba2448acb05268a23ccba7d04ca2c8bcd814d347f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0358eb73da95f10c29410bba2448acb05268a23ccba7d04ca2c8bcd814d347f","first_computed_at":"2026-05-18T00:55:05.828887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:05.828887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cNu/+wZGvRyibQBmbZH+0B+rs99U5+7Zdc5QXi3DLo1hudwVxawBYG6kHwsAOz5TCVin2aUXpJTTc2t+PZNEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:05.829583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca85204d5a34ac6cb85459aa35c745e27b9cb26ecf8b5df66001e8b192a21f62","sha256:52ccaee26983a95ea141ab4658fd8916a6611fe4cf9abe0c5307986197210c74"],"state_sha256":"4b1e44acd98e966c319328e538394f110ab00befa47090e43611a41363769c1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rn/8UTra6ziwVkutDA0pG2D04Tsd4NCNbluPPn1wpzpXBqS4g5CK2/Zv31l2SJKAbR8mNr/RY6HJTEVYPobXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:20:31.959465Z","bundle_sha256":"6a1dedc8baeeab29e18f34968dce646d844b2ecd76624e19ad31c1310d23d2dc"}}