{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A3WD4QZPFD24NUJKGBZU4S5M6Y","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":"85d44b34fb919aa1d385ad7c30ab599ddfe1e665bd953da32d1a9f22dfac7a95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-08T16:47:12Z","title_canon_sha256":"9e88526e87ef2d2839f988a5f93a6b86d51fec520ae088c327212504d289d2b3"},"schema_version":"1.0","source":{"id":"1107.1675","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1675","created_at":"2026-05-18T02:01:21Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1675v2","created_at":"2026-05-18T02:01:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1675","created_at":"2026-05-18T02:01:21Z"},{"alias_kind":"pith_short_12","alias_value":"A3WD4QZPFD24","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A3WD4QZPFD24NUJK","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A3WD4QZP","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:f2aeba5451409f1da7762a09d854803e057749ebbf8a21d69d36731241ad510e","target":"graph","created_at":"2026-05-18T02:01:21Z","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 define pure radiation metrics with parallel rays to be n-dimensional pseudo-Riemannian metrics that admit a parallel null line bundle K and whose Ricci tensor vanishes on vectors that are orthogonal to K. We give necessary conditions in terms of the Weyl, Cotton and Bach tensors for a pseudo-Riemannian metric to be conformal to a pure radiation metric with parallel rays. Then we derive conditions in terms of tractor calculus that are equivalent to the existence of a pure radiation metric with parallel rays in a conformal class. We also give an analogous result for n-dimensional pseudo-Riema","authors_text":"Pawel Nurowski, Thomas Leistner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-08T16:47:12Z","title":"Conformal pure radiation with parallel rays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1675","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":"sha256:96e4ee4cf32cb5940e2d5a864ee6742985cd073e01c88ac90f9e0a2cd6610757","target":"record","created_at":"2026-05-18T02:01:21Z","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":"85d44b34fb919aa1d385ad7c30ab599ddfe1e665bd953da32d1a9f22dfac7a95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-08T16:47:12Z","title_canon_sha256":"9e88526e87ef2d2839f988a5f93a6b86d51fec520ae088c327212504d289d2b3"},"schema_version":"1.0","source":{"id":"1107.1675","kind":"arxiv","version":2}},"canonical_sha256":"06ec3e432f28f5c6d12a30734e4bacf6272f71e1ea1aa5dc0cffceec7df47d36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06ec3e432f28f5c6d12a30734e4bacf6272f71e1ea1aa5dc0cffceec7df47d36","first_computed_at":"2026-05-18T02:01:21.218408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:21.218408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lquV/oMe1VJMpr9j9NAcdoECoAO635T0YBhPkpUX+BWXfeC3oZMZhdvaEqmfMWF2FwOmWb/3yxxi85fqb3J0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:21.219190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1675","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96e4ee4cf32cb5940e2d5a864ee6742985cd073e01c88ac90f9e0a2cd6610757","sha256:f2aeba5451409f1da7762a09d854803e057749ebbf8a21d69d36731241ad510e"],"state_sha256":"534cdea6935216d1069df19e4073be7598c98ec9f8deb84ae710800ad76e0e0e"}