{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VJLBKG7F4IQQ4PWHJTT327SQED","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":"c43693e8772ad289adfde67cb5c80125437a6ab142a15375dc5622ab600c1ca6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-09-19T10:27:08Z","title_canon_sha256":"ae308b63ccf6e3533eecc84cfb07b22cfc77a17f42c91a46d38b711bf88f5ace"},"schema_version":"1.0","source":{"id":"1109.3990","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3990","created_at":"2026-05-18T02:00:29Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3990v1","created_at":"2026-05-18T02:00:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3990","created_at":"2026-05-18T02:00:29Z"},{"alias_kind":"pith_short_12","alias_value":"VJLBKG7F4IQQ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VJLBKG7F4IQQ4PWH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VJLBKG7F","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:d7cd079d632c60bd0f044d02db7bd93944e541eecdf558533d47a6b2abc8f68d","target":"graph","created_at":"2026-05-18T02:00:29Z","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":"This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not exist","authors_text":"M. Sharif, Saira Waheed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-09-19T10:27:08Z","title":"Energy Content of Colliding Plane Waves using Approximate Noether Symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3990","kind":"arxiv","version":1},"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:c20d7018b59d3d45c7553568b2098392365ca81284e95273b278fbee9c85c09a","target":"record","created_at":"2026-05-18T02:00:29Z","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":"c43693e8772ad289adfde67cb5c80125437a6ab142a15375dc5622ab600c1ca6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-09-19T10:27:08Z","title_canon_sha256":"ae308b63ccf6e3533eecc84cfb07b22cfc77a17f42c91a46d38b711bf88f5ace"},"schema_version":"1.0","source":{"id":"1109.3990","kind":"arxiv","version":1}},"canonical_sha256":"aa56151be5e2210e3ec74ce7bd7e5020def49dc465a1cc9b617cdaaec565a9ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa56151be5e2210e3ec74ce7bd7e5020def49dc465a1cc9b617cdaaec565a9ff","first_computed_at":"2026-05-18T02:00:29.447063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:29.447063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Stj8M/pksdFSbAWCfwbLIhC84T8fkx8N93bwD++HgX8GIR0wsoOdmnNATp+KeEgQb8fXEuOS0RMSjKHeU6lBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:29.447708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3990","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c20d7018b59d3d45c7553568b2098392365ca81284e95273b278fbee9c85c09a","sha256:d7cd079d632c60bd0f044d02db7bd93944e541eecdf558533d47a6b2abc8f68d"],"state_sha256":"f7e61f6a68b80073356a9b1028d5b833ab981bea8e6992ac7b0b7d57d8804588"}