{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QOMXIWPOEGUY6ZWHL76DQZ5KBT","short_pith_number":"pith:QOMXIWPO","canonical_record":{"source":{"id":"1105.5292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-26T14:03:28Z","cross_cats_sorted":[],"title_canon_sha256":"24d427a40089aea3cd21638cafbec0e3f9dff9fbf6ea2f180ae14104679a9b45","abstract_canon_sha256":"91279251f825dc241e671f2f64c5cfaf8aed0cfc7864a814632e9fb16e9822ff"},"schema_version":"1.0"},"canonical_sha256":"83997459ee21a98f66c75ffc3867aa0cf2a80eac5f1f6190057f4a91ff28e67c","source":{"kind":"arxiv","id":"1105.5292","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5292","created_at":"2026-05-18T04:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5292v2","created_at":"2026-05-18T04:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5292","created_at":"2026-05-18T04:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"QOMXIWPOEGUY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOMXIWPOEGUY6ZWH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOMXIWPO","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QOMXIWPOEGUY6ZWHL76DQZ5KBT","target":"record","payload":{"canonical_record":{"source":{"id":"1105.5292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-26T14:03:28Z","cross_cats_sorted":[],"title_canon_sha256":"24d427a40089aea3cd21638cafbec0e3f9dff9fbf6ea2f180ae14104679a9b45","abstract_canon_sha256":"91279251f825dc241e671f2f64c5cfaf8aed0cfc7864a814632e9fb16e9822ff"},"schema_version":"1.0"},"canonical_sha256":"83997459ee21a98f66c75ffc3867aa0cf2a80eac5f1f6190057f4a91ff28e67c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:56.313432Z","signature_b64":"C6bjxB+ZmPdklaWyB3/XPuU1Bx6HnxfDP92xHqCE4HFmaAe5jxC/yudgYnRoBlT4yNPL6CKmO4gkLnDKLfHPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83997459ee21a98f66c75ffc3867aa0cf2a80eac5f1f6190057f4a91ff28e67c","last_reissued_at":"2026-05-18T04:13:56.312968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:56.312968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.5292","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":"2026-05-18T04:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSW8t3YhKP8Nex+s3Af/xIfLTc+C699uJhYXrcFyoCg8qAeBRguf9WaoqvHL07tshqMf0i6zxHpfJ+Kpsh9+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:37:40.747685Z"},"content_sha256":"6c4bfcce986f3622b4d988ca740c34f085ac18cdc8f5d4604cb3dbeceebcaa6e","schema_version":"1.0","event_id":"sha256:6c4bfcce986f3622b4d988ca740c34f085ac18cdc8f5d4604cb3dbeceebcaa6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QOMXIWPOEGUY6ZWHL76DQZ5KBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The linear power spectrum of observed source number counts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Anthony Challinor, Antony Lewis","submitted_at":"2011-05-26T14:03:28Z","abstract_excerpt":"We relate the observable number of sources per solid angle and redshift to the underlying proper source density and velocity, background evolution and line-of-sight potentials. We give an exact result in the case of linearized perturbations assuming general relativity. This consistently includes contributions of the source density perturbations and redshift distortions, magnification, radial displacement, and various additional linear terms that are small on sub-horizon scales. In addition we calculate the effect on observed luminosities, and hence the result for sources observed as a function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5292","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":"2026-05-18T04:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YPnOiqbxVfvfvxxXxEcIkaeB8i/GldOOpOzbnUEtGMKzz9iQ3jpGVFs1qAZ1p7Qs8L+ncSS4iVDLKHYNTZUdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:37:40.748027Z"},"content_sha256":"20e44b44ca81008a3c246c199c7fb1d0a200051c432b2c316cbcdccc12b13f7b","schema_version":"1.0","event_id":"sha256:20e44b44ca81008a3c246c199c7fb1d0a200051c432b2c316cbcdccc12b13f7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QOMXIWPOEGUY6ZWHL76DQZ5KBT/bundle.json","state_url":"https://pith.science/pith/QOMXIWPOEGUY6ZWHL76DQZ5KBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QOMXIWPOEGUY6ZWHL76DQZ5KBT/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":"2026-06-07T11:37:40Z","links":{"resolver":"https://pith.science/pith/QOMXIWPOEGUY6ZWHL76DQZ5KBT","bundle":"https://pith.science/pith/QOMXIWPOEGUY6ZWHL76DQZ5KBT/bundle.json","state":"https://pith.science/pith/QOMXIWPOEGUY6ZWHL76DQZ5KBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QOMXIWPOEGUY6ZWHL76DQZ5KBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QOMXIWPOEGUY6ZWHL76DQZ5KBT","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":"91279251f825dc241e671f2f64c5cfaf8aed0cfc7864a814632e9fb16e9822ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-26T14:03:28Z","title_canon_sha256":"24d427a40089aea3cd21638cafbec0e3f9dff9fbf6ea2f180ae14104679a9b45"},"schema_version":"1.0","source":{"id":"1105.5292","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5292","created_at":"2026-05-18T04:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5292v2","created_at":"2026-05-18T04:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5292","created_at":"2026-05-18T04:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"QOMXIWPOEGUY","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOMXIWPOEGUY6ZWH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOMXIWPO","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:20e44b44ca81008a3c246c199c7fb1d0a200051c432b2c316cbcdccc12b13f7b","target":"graph","created_at":"2026-05-18T04:13:56Z","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":"We relate the observable number of sources per solid angle and redshift to the underlying proper source density and velocity, background evolution and line-of-sight potentials. We give an exact result in the case of linearized perturbations assuming general relativity. This consistently includes contributions of the source density perturbations and redshift distortions, magnification, radial displacement, and various additional linear terms that are small on sub-horizon scales. In addition we calculate the effect on observed luminosities, and hence the result for sources observed as a function","authors_text":"Anthony Challinor, Antony Lewis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-26T14:03:28Z","title":"The linear power spectrum of observed source number counts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5292","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":"sha256:6c4bfcce986f3622b4d988ca740c34f085ac18cdc8f5d4604cb3dbeceebcaa6e","target":"record","created_at":"2026-05-18T04:13:56Z","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":"91279251f825dc241e671f2f64c5cfaf8aed0cfc7864a814632e9fb16e9822ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-26T14:03:28Z","title_canon_sha256":"24d427a40089aea3cd21638cafbec0e3f9dff9fbf6ea2f180ae14104679a9b45"},"schema_version":"1.0","source":{"id":"1105.5292","kind":"arxiv","version":2}},"canonical_sha256":"83997459ee21a98f66c75ffc3867aa0cf2a80eac5f1f6190057f4a91ff28e67c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83997459ee21a98f66c75ffc3867aa0cf2a80eac5f1f6190057f4a91ff28e67c","first_computed_at":"2026-05-18T04:13:56.312968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:56.312968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C6bjxB+ZmPdklaWyB3/XPuU1Bx6HnxfDP92xHqCE4HFmaAe5jxC/yudgYnRoBlT4yNPL6CKmO4gkLnDKLfHPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:56.313432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5292","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c4bfcce986f3622b4d988ca740c34f085ac18cdc8f5d4604cb3dbeceebcaa6e","sha256:20e44b44ca81008a3c246c199c7fb1d0a200051c432b2c316cbcdccc12b13f7b"],"state_sha256":"30cafe7f2d80d8033d04942ede651e89ad1158b78b879d55e4ce2605750fef9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RIRpKxjIbNoMTrenAkX+tRGSBQLWRyB4R//Vki1vf6ZI8KuDiY1ATiEWFzrT+YROBaG71B03n1vA12eEwZwSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:37:40.749978Z","bundle_sha256":"edab83cb1ea36ea8ad91bc7b6c9a06c92824d26ab7a999c8257cc0634e8d93ef"}}