{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2X4AYN32XHZB73SK7MX7QP6GCW","short_pith_number":"pith:2X4AYN32","canonical_record":{"source":{"id":"1211.0287","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-11-01T20:00:16Z","cross_cats_sorted":[],"title_canon_sha256":"bb8cdcb2817afb126efc2a779df7789e1bca5686d77b7998b1eec9b7d19b74fe","abstract_canon_sha256":"2e7aca554f344c95ea084554f2a20d27ccb6faa3ffce0208aa9b2718fccf9ffa"},"schema_version":"1.0"},"canonical_sha256":"d5f80c377ab9f21fee4afb2ff83fc6158ac59027ca1dc373a729a21dde9ef9c9","source":{"kind":"arxiv","id":"1211.0287","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0287","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0287v2","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0287","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"pith_short_12","alias_value":"2X4AYN32XHZB","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2X4AYN32XHZB73SK","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2X4AYN32","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2X4AYN32XHZB73SK7MX7QP6GCW","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0287","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-11-01T20:00:16Z","cross_cats_sorted":[],"title_canon_sha256":"bb8cdcb2817afb126efc2a779df7789e1bca5686d77b7998b1eec9b7d19b74fe","abstract_canon_sha256":"2e7aca554f344c95ea084554f2a20d27ccb6faa3ffce0208aa9b2718fccf9ffa"},"schema_version":"1.0"},"canonical_sha256":"d5f80c377ab9f21fee4afb2ff83fc6158ac59027ca1dc373a729a21dde9ef9c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:13.536264Z","signature_b64":"4HIAIAdgXoKCOTqA5iV41IfPc25ypQZWQQ5OkoKGKlhIlatzGeT7Y/wwR9GIwOyBzJVcqbv/cbQX9axrucYWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5f80c377ab9f21fee4afb2ff83fc6158ac59027ca1dc373a729a21dde9ef9c9","last_reissued_at":"2026-05-18T03:35:13.535629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:13.535629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0287","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":"2026-05-18T03:35:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7PUccMM7jSuWiikPorGnjZqkGO/ta7OfttW45O4prjCfxie7AahfbSFM+kuScZhhh3v4YrJdYYHNMgzsfg9JBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:44:16.677653Z"},"content_sha256":"38136f58d117f64b0e45cf26b4f4ae844c135d8a0003cdb34943c92667788c84","schema_version":"1.0","event_id":"sha256:38136f58d117f64b0e45cf26b4f4ae844c135d8a0003cdb34943c92667788c84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2X4AYN32XHZB73SK7MX7QP6GCW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measures of galaxy environment -- II. Rank-ordered mark correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Darren J. Croton, Frazer R. Pearce, Genevieve M. Shattow, Ramin A. Skibba, Ravi K. Sheth, Stuart I. Muldrew, Ummi Abbas","submitted_at":"2012-11-01T20:00:16Z","abstract_excerpt":"We analyze environmental correlations using mark clustering statistics with the mock galaxy catalogue constructed by Muldrew et al. (Paper I). We find that mark correlation functions are able to detect even a small dependence of galaxy properties on the environment, quantified by the overdensity $1+\\delta$, while such a small dependence would be difficult to detect by traditional methods. We then show that rank ordering the marks and using the rank as a weight is a simple way of comparing the correlation signals for different marks. With this we quantify to what extent fixed-aperture overdensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0287","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":"2026-05-18T03:35:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZbJXr+bGHTIjew5vb6CmRShqhy8ieMcOUiZnXkxDHAbwRjWXKROlyTALwXCxdVd9ysdnnC+Kj2gbDNJp/4NBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:44:16.677997Z"},"content_sha256":"7ad85c4920fa21a60b893e61cf5003a738e9d0dbe265ab3b92385c0db6217a63","schema_version":"1.0","event_id":"sha256:7ad85c4920fa21a60b893e61cf5003a738e9d0dbe265ab3b92385c0db6217a63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2X4AYN32XHZB73SK7MX7QP6GCW/bundle.json","state_url":"https://pith.science/pith/2X4AYN32XHZB73SK7MX7QP6GCW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2X4AYN32XHZB73SK7MX7QP6GCW/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":"2026-06-01T09:44:16Z","links":{"resolver":"https://pith.science/pith/2X4AYN32XHZB73SK7MX7QP6GCW","bundle":"https://pith.science/pith/2X4AYN32XHZB73SK7MX7QP6GCW/bundle.json","state":"https://pith.science/pith/2X4AYN32XHZB73SK7MX7QP6GCW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2X4AYN32XHZB73SK7MX7QP6GCW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2X4AYN32XHZB73SK7MX7QP6GCW","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":"2e7aca554f344c95ea084554f2a20d27ccb6faa3ffce0208aa9b2718fccf9ffa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-11-01T20:00:16Z","title_canon_sha256":"bb8cdcb2817afb126efc2a779df7789e1bca5686d77b7998b1eec9b7d19b74fe"},"schema_version":"1.0","source":{"id":"1211.0287","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0287","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0287v2","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0287","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"pith_short_12","alias_value":"2X4AYN32XHZB","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2X4AYN32XHZB73SK","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2X4AYN32","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:7ad85c4920fa21a60b893e61cf5003a738e9d0dbe265ab3b92385c0db6217a63","target":"graph","created_at":"2026-05-18T03:35:13Z","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 analyze environmental correlations using mark clustering statistics with the mock galaxy catalogue constructed by Muldrew et al. (Paper I). We find that mark correlation functions are able to detect even a small dependence of galaxy properties on the environment, quantified by the overdensity $1+\\delta$, while such a small dependence would be difficult to detect by traditional methods. We then show that rank ordering the marks and using the rank as a weight is a simple way of comparing the correlation signals for different marks. With this we quantify to what extent fixed-aperture overdensi","authors_text":"Darren J. Croton, Frazer R. Pearce, Genevieve M. Shattow, Ramin A. Skibba, Ravi K. Sheth, Stuart I. Muldrew, Ummi Abbas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-11-01T20:00:16Z","title":"Measures of galaxy environment -- II. Rank-ordered mark correlations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0287","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":"sha256:38136f58d117f64b0e45cf26b4f4ae844c135d8a0003cdb34943c92667788c84","target":"record","created_at":"2026-05-18T03:35:13Z","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":"2e7aca554f344c95ea084554f2a20d27ccb6faa3ffce0208aa9b2718fccf9ffa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-11-01T20:00:16Z","title_canon_sha256":"bb8cdcb2817afb126efc2a779df7789e1bca5686d77b7998b1eec9b7d19b74fe"},"schema_version":"1.0","source":{"id":"1211.0287","kind":"arxiv","version":2}},"canonical_sha256":"d5f80c377ab9f21fee4afb2ff83fc6158ac59027ca1dc373a729a21dde9ef9c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5f80c377ab9f21fee4afb2ff83fc6158ac59027ca1dc373a729a21dde9ef9c9","first_computed_at":"2026-05-18T03:35:13.535629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:13.535629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4HIAIAdgXoKCOTqA5iV41IfPc25ypQZWQQ5OkoKGKlhIlatzGeT7Y/wwR9GIwOyBzJVcqbv/cbQX9axrucYWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:13.536264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0287","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38136f58d117f64b0e45cf26b4f4ae844c135d8a0003cdb34943c92667788c84","sha256:7ad85c4920fa21a60b893e61cf5003a738e9d0dbe265ab3b92385c0db6217a63"],"state_sha256":"ffc234b00d0e63454db3637c8597be6b0607b1189392b0cbf06d57577f92be7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lre9QzviVV8zC+VwtN4n598/T5jGr07nTfFveS7Dtb49a9SFBYyH5TaHr6jRzD1rM12SUI/BzK1NA1gqJ0lfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:44:16.679908Z","bundle_sha256":"4a79a6e6447e251a9221ada531c3484326c2d3953b637213afac2700ab591984"}}