{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E2RJN242LJ5JYOFUEMC74X4XPZ","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":"f9a081d74b1cb543d5f7e0b9d95c033dfd5f3cc471ddea40293e3a36615aa8da","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-10T04:10:01Z","title_canon_sha256":"e8fe98a879994d414de50ac9a32e9001a1547f747f84e930318375a336e3192e"},"schema_version":"1.0","source":{"id":"1509.03003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03003","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03003v2","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03003","created_at":"2026-05-18T01:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"E2RJN242LJ5J","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E2RJN242LJ5JYOFU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E2RJN242","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:ac75aafae2be095fc2aebff11b48e975492915224c4d0ddb86fcc5638061b073","target":"graph","created_at":"2026-05-18T01:32:51Z","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 discuss some open problems and recent progress related to the 4th order Paneitz operator and Q curvature in dimensions other than 4.","authors_text":"Fengbo Hang, Paul C. Yang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-10T04:10:01Z","title":"Lectures on the fourth order Q curvature equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03003","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":"sha256:343de4fa062d4120aa9bbafac4995d45e72e5c1a8a825e0e8747947aef237beb","target":"record","created_at":"2026-05-18T01:32:51Z","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":"f9a081d74b1cb543d5f7e0b9d95c033dfd5f3cc471ddea40293e3a36615aa8da","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-10T04:10:01Z","title_canon_sha256":"e8fe98a879994d414de50ac9a32e9001a1547f747f84e930318375a336e3192e"},"schema_version":"1.0","source":{"id":"1509.03003","kind":"arxiv","version":2}},"canonical_sha256":"26a296eb9a5a7a9c38b42305fe5f977e60e2f0614a00a326f89b45c28206f5aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26a296eb9a5a7a9c38b42305fe5f977e60e2f0614a00a326f89b45c28206f5aa","first_computed_at":"2026-05-18T01:32:51.957864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:51.957864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mYjFszFDDZQPGzllsbx5gA5VnbGauFmQNHbuisUPM1dr325hxQ8YkYqwudL4YaCAmhR35odNMV/uIt2JJwYiBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:51.958467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:343de4fa062d4120aa9bbafac4995d45e72e5c1a8a825e0e8747947aef237beb","sha256:ac75aafae2be095fc2aebff11b48e975492915224c4d0ddb86fcc5638061b073"],"state_sha256":"b5b18c62343d24b625ad6c5e2d6286094f1a8980c80565a70cd52aca959b07fe"}