{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MVQRKMXCHEQG3MCKF2X6EBUQRU","short_pith_number":"pith:MVQRKMXC","canonical_record":{"source":{"id":"1003.5906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-30T19:36:41Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0603ab7a57274e43abd24448ecaabc53a972705e12bf797dedfeeb856b8360cb","abstract_canon_sha256":"17f6b7930bc61ef4f92665daec2168a3344c69513f366ee26c642f50a0f72c4e"},"schema_version":"1.0"},"canonical_sha256":"65611532e239206db04a2eafe206908d20ac7e00e1aacb7435cad18f9f1efedd","source":{"kind":"arxiv","id":"1003.5906","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5906","created_at":"2026-05-18T02:24:25Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5906v2","created_at":"2026-05-18T02:24:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5906","created_at":"2026-05-18T02:24:25Z"},{"alias_kind":"pith_short_12","alias_value":"MVQRKMXCHEQG","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MVQRKMXCHEQG3MCK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MVQRKMXC","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MVQRKMXCHEQG3MCKF2X6EBUQRU","target":"record","payload":{"canonical_record":{"source":{"id":"1003.5906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-30T19:36:41Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0603ab7a57274e43abd24448ecaabc53a972705e12bf797dedfeeb856b8360cb","abstract_canon_sha256":"17f6b7930bc61ef4f92665daec2168a3344c69513f366ee26c642f50a0f72c4e"},"schema_version":"1.0"},"canonical_sha256":"65611532e239206db04a2eafe206908d20ac7e00e1aacb7435cad18f9f1efedd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:25.997754Z","signature_b64":"OdlZYqaJ6EwdkrepbHhKhnQzMU/jRe5iekvh31iZHOcqVajAv/JSHGgkw1sxusbtXk13dngTiRFDF1OUpB2HCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65611532e239206db04a2eafe206908d20ac7e00e1aacb7435cad18f9f1efedd","last_reissued_at":"2026-05-18T02:24:25.996935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:25.996935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.5906","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":"2026-05-18T02:24:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97a71u+ptjNQ+Bzgb27D8oq3HuFSS0E+FHFC4bYzPKvnNFbKKr9PyL7HvydlvhEn/+6ZMXe/9+2Yo94Ox47RDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:39:57.756542Z"},"content_sha256":"297822542a50fbdc1118fe34c84b76a445f5cdce22cc1ad733a807d62e879b55","schema_version":"1.0","event_id":"sha256:297822542a50fbdc1118fe34c84b76a445f5cdce22cc1ad733a807d62e879b55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MVQRKMXCHEQG3MCKF2X6EBUQRU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cosmic Distance Duality Relation and the Shape of Galaxy Clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph.CO","authors_text":"J. A. S. Lima, M. B. Ribeiro, R. F. L. Holanda","submitted_at":"2010-03-30T19:36:41Z","abstract_excerpt":"Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, D_L(z) (1 + z)^{2}/D_{A}(z) = 1, an exact result required by the Etherington reciprocity theorem where D_L(z) and D_A(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D_A(z) = D_L(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D_A(z)from galaxy clusters. This combination offers the possibility of testing th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5906","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":"2026-05-18T02:24:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dI6nsuEh72lFYhxnGBNSjz3f/8NkUXfd3mNzhcRCotuY+cBPyxd9XqsjJFwXmYy8aULouQMrEFDMQZlnKfm6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:39:57.756886Z"},"content_sha256":"c68be99dac9b5bfc84ca15512e13220e7a5ddce79b36cf2bfd3ff1fba501bb09","schema_version":"1.0","event_id":"sha256:c68be99dac9b5bfc84ca15512e13220e7a5ddce79b36cf2bfd3ff1fba501bb09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVQRKMXCHEQG3MCKF2X6EBUQRU/bundle.json","state_url":"https://pith.science/pith/MVQRKMXCHEQG3MCKF2X6EBUQRU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVQRKMXCHEQG3MCKF2X6EBUQRU/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":"2026-05-28T02:39:57Z","links":{"resolver":"https://pith.science/pith/MVQRKMXCHEQG3MCKF2X6EBUQRU","bundle":"https://pith.science/pith/MVQRKMXCHEQG3MCKF2X6EBUQRU/bundle.json","state":"https://pith.science/pith/MVQRKMXCHEQG3MCKF2X6EBUQRU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVQRKMXCHEQG3MCKF2X6EBUQRU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MVQRKMXCHEQG3MCKF2X6EBUQRU","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":"17f6b7930bc61ef4f92665daec2168a3344c69513f366ee26c642f50a0f72c4e","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-30T19:36:41Z","title_canon_sha256":"0603ab7a57274e43abd24448ecaabc53a972705e12bf797dedfeeb856b8360cb"},"schema_version":"1.0","source":{"id":"1003.5906","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5906","created_at":"2026-05-18T02:24:25Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5906v2","created_at":"2026-05-18T02:24:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5906","created_at":"2026-05-18T02:24:25Z"},{"alias_kind":"pith_short_12","alias_value":"MVQRKMXCHEQG","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MVQRKMXCHEQG3MCK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MVQRKMXC","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:c68be99dac9b5bfc84ca15512e13220e7a5ddce79b36cf2bfd3ff1fba501bb09","target":"graph","created_at":"2026-05-18T02:24:25Z","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":"Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, D_L(z) (1 + z)^{2}/D_{A}(z) = 1, an exact result required by the Etherington reciprocity theorem where D_L(z) and D_A(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D_A(z) = D_L(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D_A(z)from galaxy clusters. This combination offers the possibility of testing th","authors_text":"J. A. S. Lima, M. B. Ribeiro, R. F. L. Holanda","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-30T19:36:41Z","title":"Cosmic Distance Duality Relation and the Shape of Galaxy Clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5906","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":"sha256:297822542a50fbdc1118fe34c84b76a445f5cdce22cc1ad733a807d62e879b55","target":"record","created_at":"2026-05-18T02:24:25Z","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":"17f6b7930bc61ef4f92665daec2168a3344c69513f366ee26c642f50a0f72c4e","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-30T19:36:41Z","title_canon_sha256":"0603ab7a57274e43abd24448ecaabc53a972705e12bf797dedfeeb856b8360cb"},"schema_version":"1.0","source":{"id":"1003.5906","kind":"arxiv","version":2}},"canonical_sha256":"65611532e239206db04a2eafe206908d20ac7e00e1aacb7435cad18f9f1efedd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65611532e239206db04a2eafe206908d20ac7e00e1aacb7435cad18f9f1efedd","first_computed_at":"2026-05-18T02:24:25.996935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:25.996935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OdlZYqaJ6EwdkrepbHhKhnQzMU/jRe5iekvh31iZHOcqVajAv/JSHGgkw1sxusbtXk13dngTiRFDF1OUpB2HCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:25.997754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5906","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:297822542a50fbdc1118fe34c84b76a445f5cdce22cc1ad733a807d62e879b55","sha256:c68be99dac9b5bfc84ca15512e13220e7a5ddce79b36cf2bfd3ff1fba501bb09"],"state_sha256":"66402f943da461d37cdbcaf240e794cd941c8429c95a06e354a79fe7eeb1e028"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0R//EzTdI3AsUcWHxDRXzdUQJr7Je4cpYOHC7qRP+6siFUS3FVcLri55GC98/fhx3PaIE8y1wVoVI7gjsVFiDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:39:57.758785Z","bundle_sha256":"e9d77b81d86cc3c39f0f98cbe9dc1cdf91d790323022fca266c2427f66a759e8"}}