{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YZU6MXHOEOCJLY4RLXVUU3EXNV","short_pith_number":"pith:YZU6MXHO","canonical_record":{"source":{"id":"1511.01318","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-11-04T13:03:33Z","cross_cats_sorted":[],"title_canon_sha256":"079ade4e5a3673d706fc3e5d8f2228dceb128923e05fb0b82c21b2f27912eb6e","abstract_canon_sha256":"f461c0bd9f485ddf5f2fdc8b68ab49f66f8eaa43a4b3804436991ca7cfcd958c"},"schema_version":"1.0"},"canonical_sha256":"c669e65cee238495e3915deb4a6c976d4075b45275b68aa508382befa4c403f7","source":{"kind":"arxiv","id":"1511.01318","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01318","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01318v4","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01318","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"YZU6MXHOEOCJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YZU6MXHOEOCJLY4R","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YZU6MXHO","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YZU6MXHOEOCJLY4RLXVUU3EXNV","target":"record","payload":{"canonical_record":{"source":{"id":"1511.01318","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-11-04T13:03:33Z","cross_cats_sorted":[],"title_canon_sha256":"079ade4e5a3673d706fc3e5d8f2228dceb128923e05fb0b82c21b2f27912eb6e","abstract_canon_sha256":"f461c0bd9f485ddf5f2fdc8b68ab49f66f8eaa43a4b3804436991ca7cfcd958c"},"schema_version":"1.0"},"canonical_sha256":"c669e65cee238495e3915deb4a6c976d4075b45275b68aa508382befa4c403f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:58.763026Z","signature_b64":"7iNFbo2L+mm5oDhaJaahI9PoAapL79Vm8a5J/caiTFHgu6lua53d+gFkYZdEjHC1XdHds+MajgPqHaL2THNQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c669e65cee238495e3915deb4a6c976d4075b45275b68aa508382befa4c403f7","last_reissued_at":"2026-05-18T01:14:58.762459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:58.762459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.01318","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"foxLuv9JTvkLj42vQbIvbYJnNfJeWWfGF9lMBKH+dv9G/dgLjHpxdo5XiWgHCOzIZmwU+LlrtYKL7VjrJxJeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:09:40.269978Z"},"content_sha256":"aea630be3cae9bf2fc5358c9fc887b6db7f2dd63ab9940d4964c2dec17d09917","schema_version":"1.0","event_id":"sha256:aea630be3cae9bf2fc5358c9fc887b6db7f2dd63ab9940d4964c2dec17d09917"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YZU6MXHOEOCJLY4RLXVUU3EXNV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Distance Duality Relation from Strong Gravitational Lensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Kai Liao, Marek Biesiada, Shuo Cao, Xiaogang Zheng, Zhengxiang Li, Zong-Hong Zhu","submitted_at":"2015-11-04T13:03:33Z","abstract_excerpt":"Under very general assumptions of metric theory of spacetime, photons traveling along null geodesics and photon number conservation, two observable concepts of cosmic distance, i.e. the angular diameter and the luminosity distances are related to each other by the so-called distance duality relation (DDR) $D^L=D^A(1+z)^2$. Observational validation of this relation is quite important because any evidence of its violation could be a signal of new physics. In this paper we introduce a new method to test DDR based on strong gravitational lensing systems and type Ia supernovae under a flat universe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01318","kind":"arxiv","version":4},"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":"2026-05-18T01:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OK6G5N8iqztcSiNfdYwnIR1PEakzadFWVChvG8x3Mfdcj7DnirDCYW2gzjw7qxm2zzqCDh7xGQAvRmFFQdVfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:09:40.270338Z"},"content_sha256":"66f96ae8570ef8aefd1515ea498de993991885dd12de3bd260470a9acef5cf40","schema_version":"1.0","event_id":"sha256:66f96ae8570ef8aefd1515ea498de993991885dd12de3bd260470a9acef5cf40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZU6MXHOEOCJLY4RLXVUU3EXNV/bundle.json","state_url":"https://pith.science/pith/YZU6MXHOEOCJLY4RLXVUU3EXNV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZU6MXHOEOCJLY4RLXVUU3EXNV/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":"2026-06-03T00:09:40Z","links":{"resolver":"https://pith.science/pith/YZU6MXHOEOCJLY4RLXVUU3EXNV","bundle":"https://pith.science/pith/YZU6MXHOEOCJLY4RLXVUU3EXNV/bundle.json","state":"https://pith.science/pith/YZU6MXHOEOCJLY4RLXVUU3EXNV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZU6MXHOEOCJLY4RLXVUU3EXNV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YZU6MXHOEOCJLY4RLXVUU3EXNV","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":"f461c0bd9f485ddf5f2fdc8b68ab49f66f8eaa43a4b3804436991ca7cfcd958c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-11-04T13:03:33Z","title_canon_sha256":"079ade4e5a3673d706fc3e5d8f2228dceb128923e05fb0b82c21b2f27912eb6e"},"schema_version":"1.0","source":{"id":"1511.01318","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01318","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01318v4","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01318","created_at":"2026-05-18T01:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"YZU6MXHOEOCJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YZU6MXHOEOCJLY4R","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YZU6MXHO","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:66f96ae8570ef8aefd1515ea498de993991885dd12de3bd260470a9acef5cf40","target":"graph","created_at":"2026-05-18T01:14:58Z","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":"Under very general assumptions of metric theory of spacetime, photons traveling along null geodesics and photon number conservation, two observable concepts of cosmic distance, i.e. the angular diameter and the luminosity distances are related to each other by the so-called distance duality relation (DDR) $D^L=D^A(1+z)^2$. Observational validation of this relation is quite important because any evidence of its violation could be a signal of new physics. In this paper we introduce a new method to test DDR based on strong gravitational lensing systems and type Ia supernovae under a flat universe","authors_text":"Kai Liao, Marek Biesiada, Shuo Cao, Xiaogang Zheng, Zhengxiang Li, Zong-Hong Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-11-04T13:03:33Z","title":"The Distance Duality Relation from Strong Gravitational Lensing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01318","kind":"arxiv","version":4},"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:aea630be3cae9bf2fc5358c9fc887b6db7f2dd63ab9940d4964c2dec17d09917","target":"record","created_at":"2026-05-18T01:14:58Z","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":"f461c0bd9f485ddf5f2fdc8b68ab49f66f8eaa43a4b3804436991ca7cfcd958c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-11-04T13:03:33Z","title_canon_sha256":"079ade4e5a3673d706fc3e5d8f2228dceb128923e05fb0b82c21b2f27912eb6e"},"schema_version":"1.0","source":{"id":"1511.01318","kind":"arxiv","version":4}},"canonical_sha256":"c669e65cee238495e3915deb4a6c976d4075b45275b68aa508382befa4c403f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c669e65cee238495e3915deb4a6c976d4075b45275b68aa508382befa4c403f7","first_computed_at":"2026-05-18T01:14:58.762459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:58.762459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7iNFbo2L+mm5oDhaJaahI9PoAapL79Vm8a5J/caiTFHgu6lua53d+gFkYZdEjHC1XdHds+MajgPqHaL2THNQAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:58.763026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01318","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aea630be3cae9bf2fc5358c9fc887b6db7f2dd63ab9940d4964c2dec17d09917","sha256:66f96ae8570ef8aefd1515ea498de993991885dd12de3bd260470a9acef5cf40"],"state_sha256":"4ebf28644ba6cdd8de6352d7cf5beb0ce4e1f2dabd03c6adeb17b24d53c32770"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sUbBtWBNMD50rvqafz4N2y5kHskq/zr3Jr9M4Baz7Da1PNLH65+iY938BRI8Hyd9g8Y59VFE1vsU41W65KquBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:09:40.272543Z","bundle_sha256":"206121eca64a6fcefbecaa1b85512e281f5eb5f4e218665bc1a29fa55bfd23c7"}}