{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SVPXW5TMMJVAJTJE7JPGOBGE6Q","short_pith_number":"pith:SVPXW5TM","canonical_record":{"source":{"id":"1210.6021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-10-22T19:57:17Z","cross_cats_sorted":[],"title_canon_sha256":"324190e080d0d7217af938f47aa83db6f46660ad2a1ff4a6a577cd0f20bf4000","abstract_canon_sha256":"084fc5261989ffdaad3918b40894d553f7f70716f70d3e562783f18cc38ff4f2"},"schema_version":"1.0"},"canonical_sha256":"955f7b766c626a04cd24fa5e6704c4f432762cc507c43006f362e662f17c4af2","source":{"kind":"arxiv","id":"1210.6021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6021","created_at":"2026-05-18T01:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6021v1","created_at":"2026-05-18T01:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6021","created_at":"2026-05-18T01:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"SVPXW5TMMJVA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SVPXW5TMMJVAJTJE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SVPXW5TM","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SVPXW5TMMJVAJTJE7JPGOBGE6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1210.6021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-10-22T19:57:17Z","cross_cats_sorted":[],"title_canon_sha256":"324190e080d0d7217af938f47aa83db6f46660ad2a1ff4a6a577cd0f20bf4000","abstract_canon_sha256":"084fc5261989ffdaad3918b40894d553f7f70716f70d3e562783f18cc38ff4f2"},"schema_version":"1.0"},"canonical_sha256":"955f7b766c626a04cd24fa5e6704c4f432762cc507c43006f362e662f17c4af2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:44.768788Z","signature_b64":"1hyuQulJ6Mkr2P7zZahzO2xUAsqE+nPGBJY4lEEQffI2SVTqoPI48C2aHbE9kHivuih/CYrzP/FnqLgL4O/FDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"955f7b766c626a04cd24fa5e6704c4f432762cc507c43006f362e662f17c4af2","last_reissued_at":"2026-05-18T01:53:44.768137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:44.768137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.6021","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":"2026-05-18T01:53:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PveFebWajaCjGqFn0cTKZjvNLH8JrieUAAdHI3+niwvu83BMPbE/WWdAUfM5PFFgAaG4MUKnGLh4c5YKkm4eAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:10:24.717303Z"},"content_sha256":"5d1e429521af7456891cebec8bf12993b60675faeb3639f854906f4f7f28fdec","schema_version":"1.0","event_id":"sha256:5d1e429521af7456891cebec8bf12993b60675faeb3639f854906f4f7f28fdec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SVPXW5TMMJVAJTJE7JPGOBGE6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order statistics applied to the most massive and most distant galaxy clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Jean-Claude Waizmann, Matthias Bartelmann, Stefano Ettori","submitted_at":"2012-10-22T19:57:17Z","abstract_excerpt":"In this work we present for the first time an analytic framework for calculating the individual and joint distributions of the n-th most massive or n-th highest redshift galaxy cluster for a given survey characteristic allowing to formulate LCDM exclusion criteria. We show that the cumulative distribution functions steepen with increasing order, giving them a higher constraining power with respect to the extreme value statistics. Additionally, we find that the order statistics in mass (being dominated by clusters at lower redshifts) is sensitive to the matter density and the normalisation of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6021","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":""},"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":"2026-05-18T01:53:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsB4oVxypP5y1F8mUYgnwlLegWF0yrgcxKRVukkFfoZM0i0AFoSOnzhq1M7fWnTMQL3IFmv6DsZGU08d3zlpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:10:24.717670Z"},"content_sha256":"33f5c212a4cc13a10616498ab35d0d649d638ab89488dd4b2f67304a94ca9687","schema_version":"1.0","event_id":"sha256:33f5c212a4cc13a10616498ab35d0d649d638ab89488dd4b2f67304a94ca9687"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SVPXW5TMMJVAJTJE7JPGOBGE6Q/bundle.json","state_url":"https://pith.science/pith/SVPXW5TMMJVAJTJE7JPGOBGE6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SVPXW5TMMJVAJTJE7JPGOBGE6Q/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":"2026-06-03T14:10:24Z","links":{"resolver":"https://pith.science/pith/SVPXW5TMMJVAJTJE7JPGOBGE6Q","bundle":"https://pith.science/pith/SVPXW5TMMJVAJTJE7JPGOBGE6Q/bundle.json","state":"https://pith.science/pith/SVPXW5TMMJVAJTJE7JPGOBGE6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SVPXW5TMMJVAJTJE7JPGOBGE6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SVPXW5TMMJVAJTJE7JPGOBGE6Q","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":"084fc5261989ffdaad3918b40894d553f7f70716f70d3e562783f18cc38ff4f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-10-22T19:57:17Z","title_canon_sha256":"324190e080d0d7217af938f47aa83db6f46660ad2a1ff4a6a577cd0f20bf4000"},"schema_version":"1.0","source":{"id":"1210.6021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6021","created_at":"2026-05-18T01:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6021v1","created_at":"2026-05-18T01:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6021","created_at":"2026-05-18T01:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"SVPXW5TMMJVA","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SVPXW5TMMJVAJTJE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SVPXW5TM","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:33f5c212a4cc13a10616498ab35d0d649d638ab89488dd4b2f67304a94ca9687","target":"graph","created_at":"2026-05-18T01:53:44Z","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":"In this work we present for the first time an analytic framework for calculating the individual and joint distributions of the n-th most massive or n-th highest redshift galaxy cluster for a given survey characteristic allowing to formulate LCDM exclusion criteria. We show that the cumulative distribution functions steepen with increasing order, giving them a higher constraining power with respect to the extreme value statistics. Additionally, we find that the order statistics in mass (being dominated by clusters at lower redshifts) is sensitive to the matter density and the normalisation of t","authors_text":"Jean-Claude Waizmann, Matthias Bartelmann, Stefano Ettori","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-10-22T19:57:17Z","title":"Order statistics applied to the most massive and most distant galaxy clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6021","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":"sha256:5d1e429521af7456891cebec8bf12993b60675faeb3639f854906f4f7f28fdec","target":"record","created_at":"2026-05-18T01:53:44Z","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":"084fc5261989ffdaad3918b40894d553f7f70716f70d3e562783f18cc38ff4f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-10-22T19:57:17Z","title_canon_sha256":"324190e080d0d7217af938f47aa83db6f46660ad2a1ff4a6a577cd0f20bf4000"},"schema_version":"1.0","source":{"id":"1210.6021","kind":"arxiv","version":1}},"canonical_sha256":"955f7b766c626a04cd24fa5e6704c4f432762cc507c43006f362e662f17c4af2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"955f7b766c626a04cd24fa5e6704c4f432762cc507c43006f362e662f17c4af2","first_computed_at":"2026-05-18T01:53:44.768137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:44.768137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1hyuQulJ6Mkr2P7zZahzO2xUAsqE+nPGBJY4lEEQffI2SVTqoPI48C2aHbE9kHivuih/CYrzP/FnqLgL4O/FDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:44.768788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d1e429521af7456891cebec8bf12993b60675faeb3639f854906f4f7f28fdec","sha256:33f5c212a4cc13a10616498ab35d0d649d638ab89488dd4b2f67304a94ca9687"],"state_sha256":"cf16fa93f12935a2f064a47c1870a069e9db2e1c90b0959308b1632e42351d6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQLvScbTdWbIaefYZifuZURXBq++XVDFNkmdXdOYryZSOOx8Y3zU2np96rkU/z+HeR0GL8nxIGJaEHTxOq7LDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:10:24.719904Z","bundle_sha256":"270e57e3239df5098a9b30833fbce5ff97c4c56171015a8abc63ad251ba47588"}}