{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NHC2IXAUP3UVRD3RGD2JW3HKG2","short_pith_number":"pith:NHC2IXAU","canonical_record":{"source":{"id":"1502.04491","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-02-16T11:01:06Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"f41d0f1ca2c2be2b9efe37965d843980efa97fb5866f33cab369168d850ee757","abstract_canon_sha256":"f4cad0782314e708f5f76314a1d09fa53366dbaf3fde8baf0151cea6f75fa025"},"schema_version":"1.0"},"canonical_sha256":"69c5a45c147ee9588f7130f49b6cea36bf5a46edaeb7b08c1c0080586a145dfe","source":{"kind":"arxiv","id":"1502.04491","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04491","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04491v2","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04491","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"NHC2IXAUP3UV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NHC2IXAUP3UVRD3R","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NHC2IXAU","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NHC2IXAUP3UVRD3RGD2JW3HKG2","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04491","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-02-16T11:01:06Z","cross_cats_sorted":["stat.AP"],"title_canon_sha256":"f41d0f1ca2c2be2b9efe37965d843980efa97fb5866f33cab369168d850ee757","abstract_canon_sha256":"f4cad0782314e708f5f76314a1d09fa53366dbaf3fde8baf0151cea6f75fa025"},"schema_version":"1.0"},"canonical_sha256":"69c5a45c147ee9588f7130f49b6cea36bf5a46edaeb7b08c1c0080586a145dfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:46.463756Z","signature_b64":"0fcLSkSUxNpcMRXQwAtJQ55tQybR0xtZmhEOO6Zr4qNCFjN6xUwA+tT4tYHQFuCLvLsJ7i1xgICc6g6XImNcCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69c5a45c147ee9588f7130f49b6cea36bf5a46edaeb7b08c1c0080586a145dfe","last_reissued_at":"2026-05-18T01:29:46.463192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:46.463192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04491","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":"2026-05-18T01:29:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XcZnr0JHVXJL3DTtA5qJszEso0X0273AUezAzDJvZceUnSbm4BICRcTKHvCkvnfBuY3dM3tysdybVyHxQqTlCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:25:03.613345Z"},"content_sha256":"f82aae99dfbeecc67abdc0fd3e4ae6247d4b5c3d78cd809e8c3c9de26d5342b6","schema_version":"1.0","event_id":"sha256:f82aae99dfbeecc67abdc0fd3e4ae6247d4b5c3d78cd809e8c3c9de26d5342b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NHC2IXAUP3UVRD3RGD2JW3HKG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constrained correlation functions from the Millennium Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP"],"primary_cat":"astro-ph.CO","authors_text":"Peter Schneider, Philipp Wilking, Randolf R\\\"oseler","submitted_at":"2015-02-16T11:01:06Z","abstract_excerpt":"Context. In previous work, we developed a quasi-Gaussian approximation for the likelihood of correlation functions, which, in contrast to the usual Gaussian approach, incorporates fundamental mathematical constraints on correlation functions. The analytical computation of these constraints is only feasible in the case of correlation functions of one-dimensional random fields.\n  Aims. In this work, we aim to obtain corresponding constraints in the case of higher-dimensional random fields and test them in a more realistic context.\n  Methods. We develop numerical methods to compute the constraint"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04491","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":"2026-05-18T01:29:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dRAk1howJkp2uV3kxxI7HDJdG/SnD1Q9FQqgklr7gAF7CZpXOS+NVusG2o1NpKJ+xFyodZ2EDvf5flsuCoyXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:25:03.613693Z"},"content_sha256":"dcac902bd34d2d922192b2865924b6301c327ff282d1a55b0a300a42f6ca8728","schema_version":"1.0","event_id":"sha256:dcac902bd34d2d922192b2865924b6301c327ff282d1a55b0a300a42f6ca8728"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NHC2IXAUP3UVRD3RGD2JW3HKG2/bundle.json","state_url":"https://pith.science/pith/NHC2IXAUP3UVRD3RGD2JW3HKG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NHC2IXAUP3UVRD3RGD2JW3HKG2/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":"2026-06-01T10:25:03Z","links":{"resolver":"https://pith.science/pith/NHC2IXAUP3UVRD3RGD2JW3HKG2","bundle":"https://pith.science/pith/NHC2IXAUP3UVRD3RGD2JW3HKG2/bundle.json","state":"https://pith.science/pith/NHC2IXAUP3UVRD3RGD2JW3HKG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NHC2IXAUP3UVRD3RGD2JW3HKG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NHC2IXAUP3UVRD3RGD2JW3HKG2","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":"f4cad0782314e708f5f76314a1d09fa53366dbaf3fde8baf0151cea6f75fa025","cross_cats_sorted":["stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-02-16T11:01:06Z","title_canon_sha256":"f41d0f1ca2c2be2b9efe37965d843980efa97fb5866f33cab369168d850ee757"},"schema_version":"1.0","source":{"id":"1502.04491","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04491","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04491v2","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04491","created_at":"2026-05-18T01:29:46Z"},{"alias_kind":"pith_short_12","alias_value":"NHC2IXAUP3UV","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NHC2IXAUP3UVRD3R","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NHC2IXAU","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:dcac902bd34d2d922192b2865924b6301c327ff282d1a55b0a300a42f6ca8728","target":"graph","created_at":"2026-05-18T01:29:46Z","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":"Context. In previous work, we developed a quasi-Gaussian approximation for the likelihood of correlation functions, which, in contrast to the usual Gaussian approach, incorporates fundamental mathematical constraints on correlation functions. The analytical computation of these constraints is only feasible in the case of correlation functions of one-dimensional random fields.\n  Aims. In this work, we aim to obtain corresponding constraints in the case of higher-dimensional random fields and test them in a more realistic context.\n  Methods. We develop numerical methods to compute the constraint","authors_text":"Peter Schneider, Philipp Wilking, Randolf R\\\"oseler","cross_cats":["stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-02-16T11:01:06Z","title":"Constrained correlation functions from the Millennium Simulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04491","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:f82aae99dfbeecc67abdc0fd3e4ae6247d4b5c3d78cd809e8c3c9de26d5342b6","target":"record","created_at":"2026-05-18T01:29:46Z","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":"f4cad0782314e708f5f76314a1d09fa53366dbaf3fde8baf0151cea6f75fa025","cross_cats_sorted":["stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-02-16T11:01:06Z","title_canon_sha256":"f41d0f1ca2c2be2b9efe37965d843980efa97fb5866f33cab369168d850ee757"},"schema_version":"1.0","source":{"id":"1502.04491","kind":"arxiv","version":2}},"canonical_sha256":"69c5a45c147ee9588f7130f49b6cea36bf5a46edaeb7b08c1c0080586a145dfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69c5a45c147ee9588f7130f49b6cea36bf5a46edaeb7b08c1c0080586a145dfe","first_computed_at":"2026-05-18T01:29:46.463192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:46.463192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0fcLSkSUxNpcMRXQwAtJQ55tQybR0xtZmhEOO6Zr4qNCFjN6xUwA+tT4tYHQFuCLvLsJ7i1xgICc6g6XImNcCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:46.463756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04491","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f82aae99dfbeecc67abdc0fd3e4ae6247d4b5c3d78cd809e8c3c9de26d5342b6","sha256:dcac902bd34d2d922192b2865924b6301c327ff282d1a55b0a300a42f6ca8728"],"state_sha256":"1b64864e92621460d555de9667ee2fec9c0398834113ad9a9fd3a31d0ce042ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cvRjMHkJe7Yix/85bDa499rYCDPwuxyiQNKkFHnj7qxzrYVqCY1iNyyq6jy58GLq1H6y7bGtnsG3Fsg7zDInAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:25:03.615641Z","bundle_sha256":"458630a9bcfbaf0c69198f2c6a67eb6162473f96351d4a76a2134062cb98bfcb"}}