{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JZJC6BW22IOCL42KD5RHJIQ3V7","short_pith_number":"pith:JZJC6BW2","schema_version":"1.0","canonical_sha256":"4e522f06dad21c25f34a1f6274a21bafec39c0687d2c7d994a3c4bc54e3f7cb9","source":{"kind":"arxiv","id":"1305.6989","version":2},"attestation_state":"computed","paper":{"title":"Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Hao-Ran Yu, Tong-Jie Zhang, Xi Yang","submitted_at":"2013-05-30T02:47:46Z","abstract_excerpt":"Our real universe is locally inhomogeneous. Dyer and Roeder introduced the smoothness parameter $\\alpha$ to describe the influence of local inhomogeneity on angular diameter distance, and they obtained the angular diameter distance-redshift approximate relation (Dyer-Roeder equation) for locally inhomogeneous universe. Furthermore, the Distance-Duality (DD) relation, $D_L(z)(1+z)^{-2}/D_A(z)=1$, should be valid for all cosmological models that are described by Riemannian geometry, where $D_L$ and $D_A$ are, respectively, the luminosity and angular distance distances. Therefore, it is necessary"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.6989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-05-30T02:47:46Z","cross_cats_sorted":[],"title_canon_sha256":"6e843e085b686433fbcd489bad1c661cf3644d97030188acec117bbcc8979392","abstract_canon_sha256":"57be672e2d954652025de1d3bb6077b72f705068f8d8dcfc4e0f603e53b0a02d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:58.113720Z","signature_b64":"LKAYxfSd3/zdO/XngExlFyMYhSG4Ujshqhfo0QSIRPGRj0ABvoKD6W71kb43/CzpmKOw1ko1rEL9klvKfwX6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e522f06dad21c25f34a1f6274a21bafec39c0687d2c7d994a3c4bc54e3f7cb9","last_reissued_at":"2026-05-18T03:20:58.113175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:58.113175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Hao-Ran Yu, Tong-Jie Zhang, Xi Yang","submitted_at":"2013-05-30T02:47:46Z","abstract_excerpt":"Our real universe is locally inhomogeneous. Dyer and Roeder introduced the smoothness parameter $\\alpha$ to describe the influence of local inhomogeneity on angular diameter distance, and they obtained the angular diameter distance-redshift approximate relation (Dyer-Roeder equation) for locally inhomogeneous universe. Furthermore, the Distance-Duality (DD) relation, $D_L(z)(1+z)^{-2}/D_A(z)=1$, should be valid for all cosmological models that are described by Riemannian geometry, where $D_L$ and $D_A$ are, respectively, the luminosity and angular distance distances. Therefore, it is necessary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6989","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.6989","created_at":"2026-05-18T03:20:58.113255+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6989v2","created_at":"2026-05-18T03:20:58.113255+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6989","created_at":"2026-05-18T03:20:58.113255+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZJC6BW22IOC","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZJC6BW22IOCL42K","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZJC6BW2","created_at":"2026-05-18T12:27:49.015174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7","json":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7.json","graph_json":"https://pith.science/api/pith-number/JZJC6BW22IOCL42KD5RHJIQ3V7/graph.json","events_json":"https://pith.science/api/pith-number/JZJC6BW22IOCL42KD5RHJIQ3V7/events.json","paper":"https://pith.science/paper/JZJC6BW2"},"agent_actions":{"view_html":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7","download_json":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7.json","view_paper":"https://pith.science/paper/JZJC6BW2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6989&json=true","fetch_graph":"https://pith.science/api/pith-number/JZJC6BW22IOCL42KD5RHJIQ3V7/graph.json","fetch_events":"https://pith.science/api/pith-number/JZJC6BW22IOCL42KD5RHJIQ3V7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7/action/storage_attestation","attest_author":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7/action/author_attestation","sign_citation":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7/action/citation_signature","submit_replication":"https://pith.science/pith/JZJC6BW22IOCL42KD5RHJIQ3V7/action/replication_record"}},"created_at":"2026-05-18T03:20:58.113255+00:00","updated_at":"2026-05-18T03:20:58.113255+00:00"}