{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:VGWG4DLN4WJE6LCZCMOV2RWQTA","short_pith_number":"pith:VGWG4DLN","canonical_record":{"source":{"id":"gr-qc/9710119","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1997-10-28T16:14:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bd86c5ea9f23e9a13daf403e95073db0f1129bc66f619724dd850037514a498b","abstract_canon_sha256":"2dd801b324efb57dbcecf8eeb03529ae2c3096f5c1f3e9209ce7f06d19658073"},"schema_version":"1.0"},"canonical_sha256":"a9ac6e0d6de5924f2c59131d5d46d09810e5dcc3a9087ad946ed2b5400ebbecb","source":{"kind":"arxiv","id":"gr-qc/9710119","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9710119","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9710119v2","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9710119","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"VGWG4DLN4WJE","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"VGWG4DLN4WJE6LCZ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"VGWG4DLN","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:VGWG4DLN4WJE6LCZCMOV2RWQTA","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/9710119","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1997-10-28T16:14:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bd86c5ea9f23e9a13daf403e95073db0f1129bc66f619724dd850037514a498b","abstract_canon_sha256":"2dd801b324efb57dbcecf8eeb03529ae2c3096f5c1f3e9209ce7f06d19658073"},"schema_version":"1.0"},"canonical_sha256":"a9ac6e0d6de5924f2c59131d5d46d09810e5dcc3a9087ad946ed2b5400ebbecb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:18.830771Z","signature_b64":"CWdkXNjNgsyO/P+l05C7Vk/LwM8+NCH77cjc89MTpn8GzgvmqmHinxRiKNsBFOfac93vW+1g9R7GtCWkhynBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9ac6e0d6de5924f2c59131d5d46d09810e5dcc3a9087ad946ed2b5400ebbecb","last_reissued_at":"2026-05-18T01:39:18.830103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:18.830103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/9710119","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":"2026-05-18T01:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/LgNxXO9/w3e2wE6HdblrDZnwpDwaL2QVuJXD8AgE9+5Xc/oq+Jmh2p6clTXRN2BxROmhn3U60CQzXQbdRHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:15:48.684381Z"},"content_sha256":"7ea742d2d55c2a3e63302eb71da60793a953a374be717322f1f91eb23a385593","schema_version":"1.0","event_id":"sha256:7ea742d2d55c2a3e63302eb71da60793a953a374be717322f1f91eb23a385593"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:VGWG4DLN4WJE6LCZCMOV2RWQTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geodesics and geodesic deviation for impulsive gravitational waves","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Roland Steinbauer","submitted_at":"1997-10-28T16:14:15Z","abstract_excerpt":"The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due to the nonlinearity of the equations and the presence of the Dirac $\\de$-distribution in the space time metric. Thus, strictly speaking, it cannot be treated within Schwartz's linear theory of distributions. To cope with this difficulty we proceed by first regularizing the $\\de$-singularity,then solving the regularized equation within classical smooth functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9710119","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":""},"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":"2026-05-18T01:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YUGLOi7D7byYEvoJTRScUO/wd6NQvvkrgzlOGnHOWhHMeqon+0VNBpw7GJGsTav5weHnxT1x9O7jgoXnChtpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:15:48.684734Z"},"content_sha256":"4f3b10af40f4f79dc12b50835d6bdf3ad6a641da7f51a2f0a8084c0358d136d1","schema_version":"1.0","event_id":"sha256:4f3b10af40f4f79dc12b50835d6bdf3ad6a641da7f51a2f0a8084c0358d136d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VGWG4DLN4WJE6LCZCMOV2RWQTA/bundle.json","state_url":"https://pith.science/pith/VGWG4DLN4WJE6LCZCMOV2RWQTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VGWG4DLN4WJE6LCZCMOV2RWQTA/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":"2026-05-28T12:15:48Z","links":{"resolver":"https://pith.science/pith/VGWG4DLN4WJE6LCZCMOV2RWQTA","bundle":"https://pith.science/pith/VGWG4DLN4WJE6LCZCMOV2RWQTA/bundle.json","state":"https://pith.science/pith/VGWG4DLN4WJE6LCZCMOV2RWQTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VGWG4DLN4WJE6LCZCMOV2RWQTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:VGWG4DLN4WJE6LCZCMOV2RWQTA","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":"2dd801b324efb57dbcecf8eeb03529ae2c3096f5c1f3e9209ce7f06d19658073","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"1997-10-28T16:14:15Z","title_canon_sha256":"bd86c5ea9f23e9a13daf403e95073db0f1129bc66f619724dd850037514a498b"},"schema_version":"1.0","source":{"id":"gr-qc/9710119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9710119","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9710119v2","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9710119","created_at":"2026-05-18T01:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"VGWG4DLN4WJE","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"VGWG4DLN4WJE6LCZ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"VGWG4DLN","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:4f3b10af40f4f79dc12b50835d6bdf3ad6a641da7f51a2f0a8084c0358d136d1","target":"graph","created_at":"2026-05-18T01:39:18Z","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":"The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due to the nonlinearity of the equations and the presence of the Dirac $\\de$-distribution in the space time metric. Thus, strictly speaking, it cannot be treated within Schwartz's linear theory of distributions. To cope with this difficulty we proceed by first regularizing the $\\de$-singularity,then solving the regularized equation within classical smooth functio","authors_text":"Roland Steinbauer","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"1997-10-28T16:14:15Z","title":"Geodesics and geodesic deviation for impulsive gravitational waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9710119","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":"sha256:7ea742d2d55c2a3e63302eb71da60793a953a374be717322f1f91eb23a385593","target":"record","created_at":"2026-05-18T01:39:18Z","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":"2dd801b324efb57dbcecf8eeb03529ae2c3096f5c1f3e9209ce7f06d19658073","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"1997-10-28T16:14:15Z","title_canon_sha256":"bd86c5ea9f23e9a13daf403e95073db0f1129bc66f619724dd850037514a498b"},"schema_version":"1.0","source":{"id":"gr-qc/9710119","kind":"arxiv","version":2}},"canonical_sha256":"a9ac6e0d6de5924f2c59131d5d46d09810e5dcc3a9087ad946ed2b5400ebbecb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9ac6e0d6de5924f2c59131d5d46d09810e5dcc3a9087ad946ed2b5400ebbecb","first_computed_at":"2026-05-18T01:39:18.830103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:18.830103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CWdkXNjNgsyO/P+l05C7Vk/LwM8+NCH77cjc89MTpn8GzgvmqmHinxRiKNsBFOfac93vW+1g9R7GtCWkhynBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:18.830771Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9710119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ea742d2d55c2a3e63302eb71da60793a953a374be717322f1f91eb23a385593","sha256:4f3b10af40f4f79dc12b50835d6bdf3ad6a641da7f51a2f0a8084c0358d136d1"],"state_sha256":"d4df70df99f6be77f6aa944e40ace682559b6d4a285bdb074869cd5021f9f6e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cg4PENc8fa2tFzm6AtVtnqSMwyyMxmjySyS0H5xZKGysqSXh3kOxLH/NWc3BbeC4mkV7tA59yCsbCUu19mqXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:15:48.686710Z","bundle_sha256":"76f3d895e65760b193e07d72de468b13bfd5d56c30d8595201693b184ce2ea39"}}