{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SSWOBKTTTFTBRCFYREXWKKCR3R","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":"03b1a6788efa969d5b2b0132c419e4284e6faae8006a4f6a5dd5d6df964a702e","cross_cats_sorted":["astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-07-17T19:43:25Z","title_canon_sha256":"1d067cb393532aa1f9ed2ca86f03e383aaf57695bba782ce2369a7994f8580f2"},"schema_version":"1.0","source":{"id":"1807.07424","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07424","created_at":"2026-05-18T00:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07424v3","created_at":"2026-05-18T00:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07424","created_at":"2026-05-18T00:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"SSWOBKTTTFTB","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SSWOBKTTTFTBRCFY","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SSWOBKTT","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:9383ea1152cb70e0a5fca0db76627804108cea881d03e9552925ff0f59c067b1","target":"graph","created_at":"2026-05-18T00:00:51Z","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 investigate the solution of Maxwell's equations in curved spacetime within the framework of Modified Gravity (MOG). We show that besides the null-geodesic treatment of photons in MOG, using Maxwell's equations and covariant coupling with the extra vector sector of gravitation in MOG, we can extract the equation for the propagation of light. We obtain Fermat's potential and calculate the deflection angle of light during lensing from a point-like star. Our results show that the deflection angle obtained from the solution of the wave equation in MOG for the large-scale structures with larger i","authors_text":"J. W. Moffat, S. Rahvar","cross_cats":["astro-ph.GA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-07-17T19:43:25Z","title":"Propagation of Electromagnetic Waves in MOG: Gravitational Lensing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07424","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":"sha256:3c3896fc086fe8c651a4be54e76853f3a2367be2ac1a7f83942b6746e87afce5","target":"record","created_at":"2026-05-18T00:00:51Z","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":"03b1a6788efa969d5b2b0132c419e4284e6faae8006a4f6a5dd5d6df964a702e","cross_cats_sorted":["astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-07-17T19:43:25Z","title_canon_sha256":"1d067cb393532aa1f9ed2ca86f03e383aaf57695bba782ce2369a7994f8580f2"},"schema_version":"1.0","source":{"id":"1807.07424","kind":"arxiv","version":3}},"canonical_sha256":"94ace0aa7399661888b8892f652851dc7df4fea2873ec2b98eeaf0eb2b4b0bdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ace0aa7399661888b8892f652851dc7df4fea2873ec2b98eeaf0eb2b4b0bdb","first_computed_at":"2026-05-18T00:00:51.946885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:51.946885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u56Zc4lNMyQ5gnc/mruA4SmiBP38hi58iQVem9597IuAiwHpp6RgVZpXsH0lIm6M106u2wV/075Y4Xfixz1bAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:51.947573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07424","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c3896fc086fe8c651a4be54e76853f3a2367be2ac1a7f83942b6746e87afce5","sha256:9383ea1152cb70e0a5fca0db76627804108cea881d03e9552925ff0f59c067b1"],"state_sha256":"701e0739096fc396b9af46db686ffcbb6ffdb94d23bc6106f8888a05531993cd"}