{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:QVWUJOZVHLIPN44UCOQGXSJWHE","short_pith_number":"pith:QVWUJOZV","canonical_record":{"source":{"id":"2112.04149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-12-08T07:34:28Z","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"title_canon_sha256":"d49e4b060318728a1226f73788c688c169585ff60fe433219cc0f42c7373031b","abstract_canon_sha256":"0b13f8e249747193e2fdb9819171bc560fa168ec7a9827eccecdbabcdc29f311"},"schema_version":"1.0"},"canonical_sha256":"856d44bb353ad0f6f39413a06bc936393159d0f2205edd7833561c9a646c240f","source":{"kind":"arxiv","id":"2112.04149","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.04149","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"2112.04149v1","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04149","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"QVWUJOZVHLIP","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"pith_short_16","alias_value":"QVWUJOZVHLIPN44U","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"pith_short_8","alias_value":"QVWUJOZV","created_at":"2026-07-05T03:39:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:QVWUJOZVHLIPN44UCOQGXSJWHE","target":"record","payload":{"canonical_record":{"source":{"id":"2112.04149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-12-08T07:34:28Z","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"title_canon_sha256":"d49e4b060318728a1226f73788c688c169585ff60fe433219cc0f42c7373031b","abstract_canon_sha256":"0b13f8e249747193e2fdb9819171bc560fa168ec7a9827eccecdbabcdc29f311"},"schema_version":"1.0"},"canonical_sha256":"856d44bb353ad0f6f39413a06bc936393159d0f2205edd7833561c9a646c240f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:39:06.604328Z","signature_b64":"QokoBcmIClNg0un8kgeaAH+iQ4NAfFsp4k9ZrZ9DifxbMjtA9CRaCuYHYtz2cMFN3PDqHjGeZQWJMwMi0OnABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"856d44bb353ad0f6f39413a06bc936393159d0f2205edd7833561c9a646c240f","last_reissued_at":"2026-07-05T03:39:06.603954Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:39:06.603954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.04149","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxiWQjMKytQ7NyMDRuujVZI3wOtP1hPC+VXT0vsUCwR9LJyTJZ/YNRCFce0dP9KWYN3k88qfelRIbOHZZDICBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:08:55.368111Z"},"content_sha256":"5372f66be0cfc52240298d7142ec3875e3df7d8d9b5616f4df44d0c47b4bdd6c","schema_version":"1.0","event_id":"sha256:5372f66be0cfc52240298d7142ec3875e3df7d8d9b5616f4df44d0c47b4bdd6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:QVWUJOZVHLIPN44UCOQGXSJWHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometrization of light bending and its application to SdSw spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Zhen Zhang","submitted_at":"2021-12-08T07:34:28Z","abstract_excerpt":"The mysterious dark energy remains one of the greatest puzzles of modern science. Current detections for it are mostly indirect. The spacetime effects of dark energy can be locally described by the SdSw metric. Understanding these local effects exactly is an essential step towards the direct probe of dark energy. From first principles, we prove that dark energy can exert a repulsive dark force on astrophysical scales, different from the Newtonian attraction of both visible and dark matter. One way of measuring local effects of dark energy is through the gravitational deflection of light. We ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04149","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.04149/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:39:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ReYR7499REFOQU7oniRVbZ0nZmArLvUmfKWAHn5EAqXUfm5SYEG5RcklysMTZxgFVi7/f/HjE25+Mrx8+6y8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:08:55.369202Z"},"content_sha256":"46722ca44667d0c992b2efec610afbbd0cf949e439d4a3166f22020d39b04a10","schema_version":"1.0","event_id":"sha256:46722ca44667d0c992b2efec610afbbd0cf949e439d4a3166f22020d39b04a10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVWUJOZVHLIPN44UCOQGXSJWHE/bundle.json","state_url":"https://pith.science/pith/QVWUJOZVHLIPN44UCOQGXSJWHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVWUJOZVHLIPN44UCOQGXSJWHE/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":"2026-08-17T14:08:55Z","links":{"resolver":"https://pith.science/pith/QVWUJOZVHLIPN44UCOQGXSJWHE","bundle":"https://pith.science/pith/QVWUJOZVHLIPN44UCOQGXSJWHE/bundle.json","state":"https://pith.science/pith/QVWUJOZVHLIPN44UCOQGXSJWHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVWUJOZVHLIPN44UCOQGXSJWHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:QVWUJOZVHLIPN44UCOQGXSJWHE","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":"0b13f8e249747193e2fdb9819171bc560fa168ec7a9827eccecdbabcdc29f311","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-12-08T07:34:28Z","title_canon_sha256":"d49e4b060318728a1226f73788c688c169585ff60fe433219cc0f42c7373031b"},"schema_version":"1.0","source":{"id":"2112.04149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.04149","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"arxiv_version","alias_value":"2112.04149v1","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04149","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"pith_short_12","alias_value":"QVWUJOZVHLIP","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"pith_short_16","alias_value":"QVWUJOZVHLIPN44U","created_at":"2026-07-05T03:39:06Z"},{"alias_kind":"pith_short_8","alias_value":"QVWUJOZV","created_at":"2026-07-05T03:39:06Z"}],"graph_snapshots":[{"event_id":"sha256:46722ca44667d0c992b2efec610afbbd0cf949e439d4a3166f22020d39b04a10","target":"graph","created_at":"2026-07-05T03:39:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.04149/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The mysterious dark energy remains one of the greatest puzzles of modern science. Current detections for it are mostly indirect. The spacetime effects of dark energy can be locally described by the SdSw metric. Understanding these local effects exactly is an essential step towards the direct probe of dark energy. From first principles, we prove that dark energy can exert a repulsive dark force on astrophysical scales, different from the Newtonian attraction of both visible and dark matter. One way of measuring local effects of dark energy is through the gravitational deflection of light. We ge","authors_text":"Zhen Zhang","cross_cats":["astro-ph.CO","hep-ph","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-12-08T07:34:28Z","title":"Geometrization of light bending and its application to SdSw spacetime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04149","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":"sha256:5372f66be0cfc52240298d7142ec3875e3df7d8d9b5616f4df44d0c47b4bdd6c","target":"record","created_at":"2026-07-05T03:39:06Z","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":"0b13f8e249747193e2fdb9819171bc560fa168ec7a9827eccecdbabcdc29f311","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-12-08T07:34:28Z","title_canon_sha256":"d49e4b060318728a1226f73788c688c169585ff60fe433219cc0f42c7373031b"},"schema_version":"1.0","source":{"id":"2112.04149","kind":"arxiv","version":1}},"canonical_sha256":"856d44bb353ad0f6f39413a06bc936393159d0f2205edd7833561c9a646c240f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"856d44bb353ad0f6f39413a06bc936393159d0f2205edd7833561c9a646c240f","first_computed_at":"2026-07-05T03:39:06.603954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:39:06.603954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QokoBcmIClNg0un8kgeaAH+iQ4NAfFsp4k9ZrZ9DifxbMjtA9CRaCuYHYtz2cMFN3PDqHjGeZQWJMwMi0OnABw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:39:06.604328Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.04149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5372f66be0cfc52240298d7142ec3875e3df7d8d9b5616f4df44d0c47b4bdd6c","sha256:46722ca44667d0c992b2efec610afbbd0cf949e439d4a3166f22020d39b04a10"],"state_sha256":"65bc799d4e8b722657e6d0208377ba09309f55bdc32f2398c653bc9bfdfc7620"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IV13FtJvmxTOjBILZskv89MNP1RMIoIBKmwNn/pe+FEY2auCsWsQ/8A+qkrhB6y+K5wolhBv1zObGr9VPCSVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T14:08:55.444976Z","bundle_sha256":"ecc4a56c246dc8c05e3e5fde243931465c2c17a18a7786911f60e7cb2f94605d"}}