{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:QVKPUH4KWTG5TULIQZOMIXGUGO","short_pith_number":"pith:QVKPUH4K","canonical_record":{"source":{"id":"0810.4956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-10-28T17:32:50Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"ec545190d267d82c73e73c269386bc58902fa4493f6efe0bb738b28c03361275","abstract_canon_sha256":"10038f5d34a9aca5da9e3d0abca7bd854a643c182f004755533429b6d6a2f7e8"},"schema_version":"1.0"},"canonical_sha256":"8554fa1f8ab4cdd9d168865cc45cd433857a723a49308a1ed9b22b08cdd40f42","source":{"kind":"arxiv","id":"0810.4956","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.4956","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"0810.4956v2","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4956","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"QVKPUH4KWTG5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"QVKPUH4KWTG5TULI","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"QVKPUH4K","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:QVKPUH4KWTG5TULIQZOMIXGUGO","target":"record","payload":{"canonical_record":{"source":{"id":"0810.4956","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-10-28T17:32:50Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"ec545190d267d82c73e73c269386bc58902fa4493f6efe0bb738b28c03361275","abstract_canon_sha256":"10038f5d34a9aca5da9e3d0abca7bd854a643c182f004755533429b6d6a2f7e8"},"schema_version":"1.0"},"canonical_sha256":"8554fa1f8ab4cdd9d168865cc45cd433857a723a49308a1ed9b22b08cdd40f42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:02.109532Z","signature_b64":"QPYz1uAT/34O/k56AcGBF6f6K9Pm7IUyQe+Gjd3UFpwvRpXJ2IjQ/2RSlyUrhaCvrrZw+i2M6WTKVFcoISuAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8554fa1f8ab4cdd9d168865cc45cd433857a723a49308a1ed9b22b08cdd40f42","last_reissued_at":"2026-05-18T04:25:02.108979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:02.108979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.4956","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":"2026-05-18T04:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7hyvO33jub92dQjVNeADL9UGcDDXTQI65z2uRdWH8gn/KAlwNQjOnl5YVGFTHbOE1E8msUM3BLksWqBFXHXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:18:51.284742Z"},"content_sha256":"9b1fb8626a573236fd54dbfd2e4707843453d1c74dd6fcbf8bb2f477c39f90fc","schema_version":"1.0","event_id":"sha256:9b1fb8626a573236fd54dbfd2e4707843453d1c74dd6fcbf8bb2f477c39f90fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:QVKPUH4KWTG5TULIQZOMIXGUGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More on Lensing by a Cosmological Constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph","authors_text":"Jason Dossett (The University of Texas at Dallas), Mustapha Ishak, Wolfgang Rindler","submitted_at":"2008-10-28T17:32:50Z","abstract_excerpt":"The question of whether or not the cosmological constant affects the bending of light around a concentrated mass has been the subject of some recent papers. We present here a simple, specific and transparent example where $\\Lambda$ bending clearly takes place, and where it is clearly neither a coordinate effect nor an aberration effect. We then show that in some recent works using perturbation theory the $\\Lambda$ contribution was missed because of initial too-stringent smallness assumptions. Namely: Our method has been to insert a Kottler (Schwarzschild with $\\Lambda$) vacuole into a Friedman"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4956","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":"2026-05-18T04:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1rylkBjDhDAYotp/M9wk3fUgd9fceBERkmQ8GxcDrNDSX5wZ9P//EPEdjsxMFB5e+JwjvFgtxcaaWZgbrbO8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:18:51.285087Z"},"content_sha256":"16f3cf11387caa332d7c2666cea950229a70d29b16770e3a75934c4cf9830b5c","schema_version":"1.0","event_id":"sha256:16f3cf11387caa332d7c2666cea950229a70d29b16770e3a75934c4cf9830b5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVKPUH4KWTG5TULIQZOMIXGUGO/bundle.json","state_url":"https://pith.science/pith/QVKPUH4KWTG5TULIQZOMIXGUGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVKPUH4KWTG5TULIQZOMIXGUGO/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":"2026-06-04T10:18:51Z","links":{"resolver":"https://pith.science/pith/QVKPUH4KWTG5TULIQZOMIXGUGO","bundle":"https://pith.science/pith/QVKPUH4KWTG5TULIQZOMIXGUGO/bundle.json","state":"https://pith.science/pith/QVKPUH4KWTG5TULIQZOMIXGUGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVKPUH4KWTG5TULIQZOMIXGUGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QVKPUH4KWTG5TULIQZOMIXGUGO","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":"10038f5d34a9aca5da9e3d0abca7bd854a643c182f004755533429b6d6a2f7e8","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-10-28T17:32:50Z","title_canon_sha256":"ec545190d267d82c73e73c269386bc58902fa4493f6efe0bb738b28c03361275"},"schema_version":"1.0","source":{"id":"0810.4956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.4956","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"0810.4956v2","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4956","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"QVKPUH4KWTG5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"QVKPUH4KWTG5TULI","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"QVKPUH4K","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:16f3cf11387caa332d7c2666cea950229a70d29b16770e3a75934c4cf9830b5c","target":"graph","created_at":"2026-05-18T04:25:02Z","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 question of whether or not the cosmological constant affects the bending of light around a concentrated mass has been the subject of some recent papers. We present here a simple, specific and transparent example where $\\Lambda$ bending clearly takes place, and where it is clearly neither a coordinate effect nor an aberration effect. We then show that in some recent works using perturbation theory the $\\Lambda$ contribution was missed because of initial too-stringent smallness assumptions. Namely: Our method has been to insert a Kottler (Schwarzschild with $\\Lambda$) vacuole into a Friedman","authors_text":"Jason Dossett (The University of Texas at Dallas), Mustapha Ishak, Wolfgang Rindler","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-10-28T17:32:50Z","title":"More on Lensing by a Cosmological Constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4956","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":"sha256:9b1fb8626a573236fd54dbfd2e4707843453d1c74dd6fcbf8bb2f477c39f90fc","target":"record","created_at":"2026-05-18T04:25:02Z","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":"10038f5d34a9aca5da9e3d0abca7bd854a643c182f004755533429b6d6a2f7e8","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-10-28T17:32:50Z","title_canon_sha256":"ec545190d267d82c73e73c269386bc58902fa4493f6efe0bb738b28c03361275"},"schema_version":"1.0","source":{"id":"0810.4956","kind":"arxiv","version":2}},"canonical_sha256":"8554fa1f8ab4cdd9d168865cc45cd433857a723a49308a1ed9b22b08cdd40f42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8554fa1f8ab4cdd9d168865cc45cd433857a723a49308a1ed9b22b08cdd40f42","first_computed_at":"2026-05-18T04:25:02.108979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:02.108979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QPYz1uAT/34O/k56AcGBF6f6K9Pm7IUyQe+Gjd3UFpwvRpXJ2IjQ/2RSlyUrhaCvrrZw+i2M6WTKVFcoISuAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:02.109532Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.4956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b1fb8626a573236fd54dbfd2e4707843453d1c74dd6fcbf8bb2f477c39f90fc","sha256:16f3cf11387caa332d7c2666cea950229a70d29b16770e3a75934c4cf9830b5c"],"state_sha256":"eab5e211020e448fcb32eb3e07f9fa6e54c081e73b39bc22fe3fc1b9cfced621"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7SPGjIjAbvQrwEdX9DJn1sQg7k2ftzAkkLR9EXgF7bQu6GA4Xb0BvqQFwBZmbVfnoyrFQOzLotgDNFLsuvICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:18:51.287030Z","bundle_sha256":"e4f8aa2b588716359c85ca86bcdecd664856bdc7e7e35e01da56c1eae707976e"}}