{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:K4FL4MTEVWGTFDMUFS7MAQLLQS","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":"0ef090e7d0279758b3a7affe5c1ae8f79a878f357329808d28d163e9095bae2a","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-16T17:11:05Z","title_canon_sha256":"583ce58f3d1f5a4123c5aa1990f99bbdf44d4ddefa38add137308bcdfe3fdcc5"},"schema_version":"1.0","source":{"id":"0810.2903","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.2903","created_at":"2026-05-18T02:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"0810.2903v3","created_at":"2026-05-18T02:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.2903","created_at":"2026-05-18T02:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"K4FL4MTEVWGT","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"K4FL4MTEVWGTFDMU","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"K4FL4MTE","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:6db834a185f92cd540011a491ce4f8a2ba0e79602281589246a56d175301f565","target":"graph","created_at":"2026-05-18T02:15:24Z","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 provide an explicit formula for the Fefferman-Graham-ambient metric of an $n$-dimensional conformal $pp$-wave in those cases where it exists. In even dimensions we calculate the obstruction explicitly. Furthermore, we describe all 4-dimensional $pp$-waves that are Bach-flat, and give a large class of Bach-flat examples which are conformally Cotton-flat, but not conformally Einstein. Finally, as an application, we use the obtained ambient metric to show that even-dimensional $pp$-waves have vanishing critical $Q$-curvature.","authors_text":"Pawel Nurowski, Thomas Leistner","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-16T17:11:05Z","title":"Ambient metrics for $n$-dimensional $pp$-waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.2903","kind":"arxiv","version":3},"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":"sha256:0929584d8069dc5192f80ef514fdacfa77d7e7cb7c0c1f05af1386c4ba05267f","target":"record","created_at":"2026-05-18T02:15:24Z","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":"0ef090e7d0279758b3a7affe5c1ae8f79a878f357329808d28d163e9095bae2a","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-16T17:11:05Z","title_canon_sha256":"583ce58f3d1f5a4123c5aa1990f99bbdf44d4ddefa38add137308bcdfe3fdcc5"},"schema_version":"1.0","source":{"id":"0810.2903","kind":"arxiv","version":3}},"canonical_sha256":"570abe3264ad8d328d942cbec0416b8499f00e050bc96d086d6673e0fbac6872","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"570abe3264ad8d328d942cbec0416b8499f00e050bc96d086d6673e0fbac6872","first_computed_at":"2026-05-18T02:15:24.243590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:24.243590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q3DbKPLsKetlt0y+1NoPi/DK5WoDScIjzX03bMe+BUA1HzgZJ3WGnq6HTVQo+ds9kGorx+FQg/MUd8RwOG6ODw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:24.244340Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.2903","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0929584d8069dc5192f80ef514fdacfa77d7e7cb7c0c1f05af1386c4ba05267f","sha256:6db834a185f92cd540011a491ce4f8a2ba0e79602281589246a56d175301f565"],"state_sha256":"4808cce2d45be93e9bfb95cd8e448fa37c69a84350931999dcb641f27829d268"}