{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MIZTA4UF55IQ6VFHOCZUCB6C27","short_pith_number":"pith:MIZTA4UF","canonical_record":{"source":{"id":"1508.02647","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-11T16:18:57Z","cross_cats_sorted":["astro-ph.GA"],"title_canon_sha256":"3631d77c5077f3de41c7795392c0b76063f2e8d75f7d538c7515ee6eb9c5fcb8","abstract_canon_sha256":"c9e831d6c7a6341b258314b5b0a0cb8973b3d8f83ceef6512c8aff177b8016ad"},"schema_version":"1.0"},"canonical_sha256":"6233307285ef510f54a770b34107c2d7f74012a6321cec4052673d95695097e6","source":{"kind":"arxiv","id":"1508.02647","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02647","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02647v2","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02647","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"pith_short_12","alias_value":"MIZTA4UF55IQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MIZTA4UF55IQ6VFH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MIZTA4UF","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MIZTA4UF55IQ6VFHOCZUCB6C27","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02647","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-11T16:18:57Z","cross_cats_sorted":["astro-ph.GA"],"title_canon_sha256":"3631d77c5077f3de41c7795392c0b76063f2e8d75f7d538c7515ee6eb9c5fcb8","abstract_canon_sha256":"c9e831d6c7a6341b258314b5b0a0cb8973b3d8f83ceef6512c8aff177b8016ad"},"schema_version":"1.0"},"canonical_sha256":"6233307285ef510f54a770b34107c2d7f74012a6321cec4052673d95695097e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:33.812056Z","signature_b64":"er+YiRdnb+XmgKPAnybSmgoLRtXjDf8NwgfeNLJ1MJkehujdepBv40Gyf6Pul+l4PVQbf/4kFkAMHn4ET4ApDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6233307285ef510f54a770b34107c2d7f74012a6321cec4052673d95695097e6","last_reissued_at":"2026-05-18T00:29:33.811562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:33.811562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02647","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":"2026-05-18T00:29:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LfXgB0L3H7tCs4Ic030PjT8dn96sZR/jxrZR1rO/5+6aXdkaEWhaScf2U7RZl19yBo8OhHUIJtw8G8xN7QsmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:01:54.415412Z"},"content_sha256":"5152f49f5d0c2776c30cefd2e00a48ed89ad634b483e64fd18c20c8d0333c9b1","schema_version":"1.0","event_id":"sha256:5152f49f5d0c2776c30cefd2e00a48ed89ad634b483e64fd18c20c8d0333c9b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MIZTA4UF55IQ6VFHOCZUCB6C27","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distinguishing f(R) theories from general relativity by gravitational lensing effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA"],"primary_cat":"gr-qc","authors_text":"Haida Li, Hongguang Liu, Xin Wang, Yongge Ma","submitted_at":"2015-08-11T16:18:57Z","abstract_excerpt":"The post-Newtonian formulation of a general class of f(R) theories is set up to 3rd order approximation. It turns out that the information of a specific form of f(R) gravity is encoded in the Yukawa potential, which is contained in the perturbative expansion of the metric components. Although the Yukawa potential is canceled in the 2nd order expression of the effective refraction index of light, detailed analysis shows that the difference of the lensing effect between the f(R) gravity and general relativity does appear at the 3rd order when $\\sqrt{f''(0)/f'(0)}$ is larger than the distance $d_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02647","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":"2026-05-18T00:29:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icD9AKUUPLAgoL4ddMYptJOI95pAGnpSTBsTc6AFfb5YHEWewzstw+uETaMgaXI5IrUIF6Kg21cTQgwRyPULAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:01:54.415785Z"},"content_sha256":"25aba5b84f7ab5c836a2805ab79b9a72a51539ac526120268cc178355c1a43a4","schema_version":"1.0","event_id":"sha256:25aba5b84f7ab5c836a2805ab79b9a72a51539ac526120268cc178355c1a43a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIZTA4UF55IQ6VFHOCZUCB6C27/bundle.json","state_url":"https://pith.science/pith/MIZTA4UF55IQ6VFHOCZUCB6C27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIZTA4UF55IQ6VFHOCZUCB6C27/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":"2026-06-11T14:01:54Z","links":{"resolver":"https://pith.science/pith/MIZTA4UF55IQ6VFHOCZUCB6C27","bundle":"https://pith.science/pith/MIZTA4UF55IQ6VFHOCZUCB6C27/bundle.json","state":"https://pith.science/pith/MIZTA4UF55IQ6VFHOCZUCB6C27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIZTA4UF55IQ6VFHOCZUCB6C27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MIZTA4UF55IQ6VFHOCZUCB6C27","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":"c9e831d6c7a6341b258314b5b0a0cb8973b3d8f83ceef6512c8aff177b8016ad","cross_cats_sorted":["astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-11T16:18:57Z","title_canon_sha256":"3631d77c5077f3de41c7795392c0b76063f2e8d75f7d538c7515ee6eb9c5fcb8"},"schema_version":"1.0","source":{"id":"1508.02647","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02647","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02647v2","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02647","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"pith_short_12","alias_value":"MIZTA4UF55IQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MIZTA4UF55IQ6VFH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MIZTA4UF","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:25aba5b84f7ab5c836a2805ab79b9a72a51539ac526120268cc178355c1a43a4","target":"graph","created_at":"2026-05-18T00:29:33Z","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 post-Newtonian formulation of a general class of f(R) theories is set up to 3rd order approximation. It turns out that the information of a specific form of f(R) gravity is encoded in the Yukawa potential, which is contained in the perturbative expansion of the metric components. Although the Yukawa potential is canceled in the 2nd order expression of the effective refraction index of light, detailed analysis shows that the difference of the lensing effect between the f(R) gravity and general relativity does appear at the 3rd order when $\\sqrt{f''(0)/f'(0)}$ is larger than the distance $d_","authors_text":"Haida Li, Hongguang Liu, Xin Wang, Yongge Ma","cross_cats":["astro-ph.GA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-11T16:18:57Z","title":"Distinguishing f(R) theories from general relativity by gravitational lensing effect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02647","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":"sha256:5152f49f5d0c2776c30cefd2e00a48ed89ad634b483e64fd18c20c8d0333c9b1","target":"record","created_at":"2026-05-18T00:29:33Z","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":"c9e831d6c7a6341b258314b5b0a0cb8973b3d8f83ceef6512c8aff177b8016ad","cross_cats_sorted":["astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-11T16:18:57Z","title_canon_sha256":"3631d77c5077f3de41c7795392c0b76063f2e8d75f7d538c7515ee6eb9c5fcb8"},"schema_version":"1.0","source":{"id":"1508.02647","kind":"arxiv","version":2}},"canonical_sha256":"6233307285ef510f54a770b34107c2d7f74012a6321cec4052673d95695097e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6233307285ef510f54a770b34107c2d7f74012a6321cec4052673d95695097e6","first_computed_at":"2026-05-18T00:29:33.811562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:33.811562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"er+YiRdnb+XmgKPAnybSmgoLRtXjDf8NwgfeNLJ1MJkehujdepBv40Gyf6Pul+l4PVQbf/4kFkAMHn4ET4ApDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:33.812056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02647","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5152f49f5d0c2776c30cefd2e00a48ed89ad634b483e64fd18c20c8d0333c9b1","sha256:25aba5b84f7ab5c836a2805ab79b9a72a51539ac526120268cc178355c1a43a4"],"state_sha256":"7bb423f8b485649e8086ff82df52ec1f7755fedfcd65ee892ee99e8113c2b672"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5BxFJFvTlP8p7rsUDUNEO2AewBUlafN27N3w1b0PreNyqZXh2xT3+GcT57Cg0seOshb8sACit1eAf39HD/h4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:01:54.417720Z","bundle_sha256":"e055ceaac0298040bf4d2aaa0d3115a25ef2400f24777ce2be6192cce2706431"}}