{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LPLSF6WA6AYPI7TURCAPW6VPQG","short_pith_number":"pith:LPLSF6WA","canonical_record":{"source":{"id":"1808.06203","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-08-19T12:42:44Z","cross_cats_sorted":["astro-ph.HE"],"title_canon_sha256":"6e98ec8dab9dc7e1d7c760e82884180b995b5a42e1522a661465e95bd1330206","abstract_canon_sha256":"92a320cd4c8bb6be624b5295291547309fec7c9642e1ac904b22b7129669cad5"},"schema_version":"1.0"},"canonical_sha256":"5bd722fac0f030f47e748880fb7aaf818a4e96b89c6a9aebfad779d02a7267cb","source":{"kind":"arxiv","id":"1808.06203","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.06203","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"arxiv_version","alias_value":"1808.06203v2","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06203","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"pith_short_12","alias_value":"LPLSF6WA6AYP","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LPLSF6WA6AYPI7TU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LPLSF6WA","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LPLSF6WA6AYPI7TURCAPW6VPQG","target":"record","payload":{"canonical_record":{"source":{"id":"1808.06203","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-08-19T12:42:44Z","cross_cats_sorted":["astro-ph.HE"],"title_canon_sha256":"6e98ec8dab9dc7e1d7c760e82884180b995b5a42e1522a661465e95bd1330206","abstract_canon_sha256":"92a320cd4c8bb6be624b5295291547309fec7c9642e1ac904b22b7129669cad5"},"schema_version":"1.0"},"canonical_sha256":"5bd722fac0f030f47e748880fb7aaf818a4e96b89c6a9aebfad779d02a7267cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:53.025822Z","signature_b64":"0L1tYtcUBKgxLhjnG+Sisel3Wfr00smnMI44IbMuh2Uwb5iEc3RnhQzI9P9PsS9VAHq0TqSadRvLMoWUBz3UAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bd722fac0f030f47e748880fb7aaf818a4e96b89c6a9aebfad779d02a7267cb","last_reissued_at":"2026-05-17T23:56:53.025459Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:53.025459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.06203","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":"2026-05-17T23:56:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jg0z5TpzeGWSMSG7SBmadm2MD5sB0S88Kf5LFccZVqeLGo2wVm7IT0e+411miNOiprWuPCMvKC8icw0resxpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:24:06.416619Z"},"content_sha256":"cca7cf60a4ff21f0b19982c41e8f16d40e4b2ed5fe78c85356f502479d6cbad2","schema_version":"1.0","event_id":"sha256:cca7cf60a4ff21f0b19982c41e8f16d40e4b2ed5fe78c85356f502479d6cbad2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LPLSF6WA6AYPI7TURCAPW6VPQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational lensing beyond geometric optics: I. Formalism and observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.HE"],"primary_cat":"gr-qc","authors_text":"Abraham I. Harte","submitted_at":"2018-08-19T12:42:44Z","abstract_excerpt":"The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of high-frequency fields are shown to scale with different powers of their frequencies. Additionally, finite-frequency corrections are identified for a number of conservation laws and observables. Among these observables are a field's energy and momentum densities, as well as several candidates for its corrected \"propagation directions.\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06203","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":"2026-05-17T23:56:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q208HZkljhz0ne365ffd7RyjQoBpIRD8ANR8FWJmzRtk6d9+tVJdpAGVUnvVqP8W/NfQ+tzSpIZTMDnHzCK5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:24:06.417082Z"},"content_sha256":"351bdf930b136fa112e6b5ea784820fc14611727e8397db34d48429984bb8d77","schema_version":"1.0","event_id":"sha256:351bdf930b136fa112e6b5ea784820fc14611727e8397db34d48429984bb8d77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LPLSF6WA6AYPI7TURCAPW6VPQG/bundle.json","state_url":"https://pith.science/pith/LPLSF6WA6AYPI7TURCAPW6VPQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LPLSF6WA6AYPI7TURCAPW6VPQG/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":"2026-08-05T00:24:06Z","links":{"resolver":"https://pith.science/pith/LPLSF6WA6AYPI7TURCAPW6VPQG","bundle":"https://pith.science/pith/LPLSF6WA6AYPI7TURCAPW6VPQG/bundle.json","state":"https://pith.science/pith/LPLSF6WA6AYPI7TURCAPW6VPQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LPLSF6WA6AYPI7TURCAPW6VPQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LPLSF6WA6AYPI7TURCAPW6VPQG","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":"92a320cd4c8bb6be624b5295291547309fec7c9642e1ac904b22b7129669cad5","cross_cats_sorted":["astro-ph.HE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-08-19T12:42:44Z","title_canon_sha256":"6e98ec8dab9dc7e1d7c760e82884180b995b5a42e1522a661465e95bd1330206"},"schema_version":"1.0","source":{"id":"1808.06203","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.06203","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"arxiv_version","alias_value":"1808.06203v2","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06203","created_at":"2026-05-17T23:56:53Z"},{"alias_kind":"pith_short_12","alias_value":"LPLSF6WA6AYP","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LPLSF6WA6AYPI7TU","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LPLSF6WA","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:351bdf930b136fa112e6b5ea784820fc14611727e8397db34d48429984bb8d77","target":"graph","created_at":"2026-05-17T23:56:53Z","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 laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of high-frequency fields are shown to scale with different powers of their frequencies. Additionally, finite-frequency corrections are identified for a number of conservation laws and observables. Among these observables are a field's energy and momentum densities, as well as several candidates for its corrected \"propagation directions.\"","authors_text":"Abraham I. Harte","cross_cats":["astro-ph.HE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-08-19T12:42:44Z","title":"Gravitational lensing beyond geometric optics: I. Formalism and observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06203","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:cca7cf60a4ff21f0b19982c41e8f16d40e4b2ed5fe78c85356f502479d6cbad2","target":"record","created_at":"2026-05-17T23:56:53Z","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":"92a320cd4c8bb6be624b5295291547309fec7c9642e1ac904b22b7129669cad5","cross_cats_sorted":["astro-ph.HE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-08-19T12:42:44Z","title_canon_sha256":"6e98ec8dab9dc7e1d7c760e82884180b995b5a42e1522a661465e95bd1330206"},"schema_version":"1.0","source":{"id":"1808.06203","kind":"arxiv","version":2}},"canonical_sha256":"5bd722fac0f030f47e748880fb7aaf818a4e96b89c6a9aebfad779d02a7267cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bd722fac0f030f47e748880fb7aaf818a4e96b89c6a9aebfad779d02a7267cb","first_computed_at":"2026-05-17T23:56:53.025459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:53.025459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0L1tYtcUBKgxLhjnG+Sisel3Wfr00smnMI44IbMuh2Uwb5iEc3RnhQzI9P9PsS9VAHq0TqSadRvLMoWUBz3UAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:53.025822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.06203","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cca7cf60a4ff21f0b19982c41e8f16d40e4b2ed5fe78c85356f502479d6cbad2","sha256:351bdf930b136fa112e6b5ea784820fc14611727e8397db34d48429984bb8d77"],"state_sha256":"0ad110240043197d8779b033f2a3e29268d9345c2fdbe5248495c25feb87bd60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYXofa6AXDal7FkZABfsTjL427dFZ/JyD9AueOzs7Wwypi9YEjurrGCOwIsYwybPnuwZx+nm5f20qTLbM3T/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T00:24:06.420756Z","bundle_sha256":"e1341e379f1212f0f834f05e60558b00625b66a9d4406b8aed0d812dc6d99cb2"}}