{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:VXVG6ER7RYZOYJQLU75OP6DNVM","short_pith_number":"pith:VXVG6ER7","canonical_record":{"source":{"id":"2207.03591","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-07-07T21:39:48Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"527b1af55609c53acb51648d83208d698c3c6f8c4e19104cf7f7dfd7067725d2","abstract_canon_sha256":"aa68768df11f1711670430221b11921e0761b71ac18c40eb9ad87b273958e772"},"schema_version":"1.0"},"canonical_sha256":"adea6f123f8e32ec260ba7fae7f86dab38e130cf0caa80d6eab4afb1e226e500","source":{"kind":"arxiv","id":"2207.03591","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.03591","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"2207.03591v2","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.03591","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"VXVG6ER7RYZO","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"pith_short_16","alias_value":"VXVG6ER7RYZOYJQL","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"pith_short_8","alias_value":"VXVG6ER7","created_at":"2026-07-05T05:50:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:VXVG6ER7RYZOYJQLU75OP6DNVM","target":"record","payload":{"canonical_record":{"source":{"id":"2207.03591","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-07-07T21:39:48Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"527b1af55609c53acb51648d83208d698c3c6f8c4e19104cf7f7dfd7067725d2","abstract_canon_sha256":"aa68768df11f1711670430221b11921e0761b71ac18c40eb9ad87b273958e772"},"schema_version":"1.0"},"canonical_sha256":"adea6f123f8e32ec260ba7fae7f86dab38e130cf0caa80d6eab4afb1e226e500","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:50:43.606123Z","signature_b64":"6nLdN+ib02qqF/0AIS/Ji6cGFpxA8jueOv88ViO+aMLVt3mGAQDFf3OGRkNea7vkbg+qbw3fY0Yy2hOPW99GAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adea6f123f8e32ec260ba7fae7f86dab38e130cf0caa80d6eab4afb1e226e500","last_reissued_at":"2026-07-05T05:50:43.605640Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:50:43.605640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.03591","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8QmRNv/Vm6l/R8LiVEpbzcMuHgs6ntwdQ87kVTMKpF/EOC7u6UbMv6YtjU62hWgQXa6MY4ZaN5YbvRidmC7lBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:08:08.101097Z"},"content_sha256":"8d40116e4c4b5f7d62658910e11d01f43c906bdbe88189357814f28bd1121855","schema_version":"1.0","event_id":"sha256:8d40116e4c4b5f7d62658910e11d01f43c906bdbe88189357814f28bd1121855"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:VXVG6ER7RYZOYJQLU75OP6DNVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Parallel Waves in General Relativity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Amir Babak Aazami, Carla Cederbaum, Cian Roche","submitted_at":"2022-07-07T21:39:48Z","abstract_excerpt":"We conduct a review of the basic definitions and the principal results in the study of wavelike spacetimes, that is spacetimes whose metric models massless radiation moving at the speed of light, focusing in particular on those geometries with parallel rays. In particular, we motivate and connect their various definitions, outline their coordinate descriptions and present some classical results in their study in a language more accessible to modern readers, including the existence of \"null coordinates\" and the construction of Penrose limits. We also present a thorough summary of recent work on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.03591","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.03591/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"McbmJH2rBFwFi7rYCTLcmH6sNUwE1HU2leYrY7+OnFDRkTDpk9VMLcW99h+ukAU3TN/mpGFe3Oab+f++NqLfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:08:08.101615Z"},"content_sha256":"9880764d6fd23dc69854e9482a3744da130b2d5346b539306a61a0304978c96f","schema_version":"1.0","event_id":"sha256:9880764d6fd23dc69854e9482a3744da130b2d5346b539306a61a0304978c96f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXVG6ER7RYZOYJQLU75OP6DNVM/bundle.json","state_url":"https://pith.science/pith/VXVG6ER7RYZOYJQLU75OP6DNVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXVG6ER7RYZOYJQLU75OP6DNVM/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":"2026-08-08T12:08:08Z","links":{"resolver":"https://pith.science/pith/VXVG6ER7RYZOYJQLU75OP6DNVM","bundle":"https://pith.science/pith/VXVG6ER7RYZOYJQLU75OP6DNVM/bundle.json","state":"https://pith.science/pith/VXVG6ER7RYZOYJQLU75OP6DNVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXVG6ER7RYZOYJQLU75OP6DNVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VXVG6ER7RYZOYJQLU75OP6DNVM","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":"aa68768df11f1711670430221b11921e0761b71ac18c40eb9ad87b273958e772","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-07-07T21:39:48Z","title_canon_sha256":"527b1af55609c53acb51648d83208d698c3c6f8c4e19104cf7f7dfd7067725d2"},"schema_version":"1.0","source":{"id":"2207.03591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.03591","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"2207.03591v2","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.03591","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"VXVG6ER7RYZO","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"pith_short_16","alias_value":"VXVG6ER7RYZOYJQL","created_at":"2026-07-05T05:50:43Z"},{"alias_kind":"pith_short_8","alias_value":"VXVG6ER7","created_at":"2026-07-05T05:50:43Z"}],"graph_snapshots":[{"event_id":"sha256:9880764d6fd23dc69854e9482a3744da130b2d5346b539306a61a0304978c96f","target":"graph","created_at":"2026-07-05T05:50:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.03591/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We conduct a review of the basic definitions and the principal results in the study of wavelike spacetimes, that is spacetimes whose metric models massless radiation moving at the speed of light, focusing in particular on those geometries with parallel rays. In particular, we motivate and connect their various definitions, outline their coordinate descriptions and present some classical results in their study in a language more accessible to modern readers, including the existence of \"null coordinates\" and the construction of Penrose limits. We also present a thorough summary of recent work on","authors_text":"Amir Babak Aazami, Carla Cederbaum, Cian Roche","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-07-07T21:39:48Z","title":"Exact Parallel Waves in General Relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.03591","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":"sha256:8d40116e4c4b5f7d62658910e11d01f43c906bdbe88189357814f28bd1121855","target":"record","created_at":"2026-07-05T05:50:43Z","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":"aa68768df11f1711670430221b11921e0761b71ac18c40eb9ad87b273958e772","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2022-07-07T21:39:48Z","title_canon_sha256":"527b1af55609c53acb51648d83208d698c3c6f8c4e19104cf7f7dfd7067725d2"},"schema_version":"1.0","source":{"id":"2207.03591","kind":"arxiv","version":2}},"canonical_sha256":"adea6f123f8e32ec260ba7fae7f86dab38e130cf0caa80d6eab4afb1e226e500","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adea6f123f8e32ec260ba7fae7f86dab38e130cf0caa80d6eab4afb1e226e500","first_computed_at":"2026-07-05T05:50:43.605640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:50:43.605640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6nLdN+ib02qqF/0AIS/Ji6cGFpxA8jueOv88ViO+aMLVt3mGAQDFf3OGRkNea7vkbg+qbw3fY0Yy2hOPW99GAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:50:43.606123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.03591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d40116e4c4b5f7d62658910e11d01f43c906bdbe88189357814f28bd1121855","sha256:9880764d6fd23dc69854e9482a3744da130b2d5346b539306a61a0304978c96f"],"state_sha256":"2061627672936cfebe248fd5f5ac826873ed94bc89513ffd2447996beafe76cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyDnSerEAkNU7zAKSTxuWvMFQMpeJrhWH3xSJ4XDERRSseFKGpvfHx5LSYmS3q/toN34giqrEfFKyPKrAbO5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T12:08:08.108113Z","bundle_sha256":"e32b01797a2543c6794fac4d0b796f26183fd21cf79b337bd7630e57aefa9613"}}