{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PU36HITX5JGHQ7RWEDCOZ35SLD","short_pith_number":"pith:PU36HITX","canonical_record":{"source":{"id":"1109.3701","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-09-16T19:35:13Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"title_canon_sha256":"5f8063a16a9ab161a0d90ea0f51c226c37d1fbfbf4239a164486dfeea3bf81b6","abstract_canon_sha256":"8c2b7df85177d20fed72223c3f2ebc91e7d9d57e6cb204fa32f0f08158fc3cd0"},"schema_version":"1.0"},"canonical_sha256":"7d37e3a277ea4c787e3620c4ecefb258c42500dace90b3749762528d768efe48","source":{"kind":"arxiv","id":"1109.3701","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3701","created_at":"2026-05-18T04:06:35Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3701v2","created_at":"2026-05-18T04:06:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3701","created_at":"2026-05-18T04:06:35Z"},{"alias_kind":"pith_short_12","alias_value":"PU36HITX5JGH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PU36HITX5JGHQ7RW","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PU36HITX","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PU36HITX5JGHQ7RWEDCOZ35SLD","target":"record","payload":{"canonical_record":{"source":{"id":"1109.3701","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-09-16T19:35:13Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"title_canon_sha256":"5f8063a16a9ab161a0d90ea0f51c226c37d1fbfbf4239a164486dfeea3bf81b6","abstract_canon_sha256":"8c2b7df85177d20fed72223c3f2ebc91e7d9d57e6cb204fa32f0f08158fc3cd0"},"schema_version":"1.0"},"canonical_sha256":"7d37e3a277ea4c787e3620c4ecefb258c42500dace90b3749762528d768efe48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:35.459093Z","signature_b64":"Cr0obCRWHTXLVCOe7IhCqHMJqM9cBzLnujXGvX6EuXc49lMKvB2Z/1zKuZ7+fDWVc6f645xQfLZXtXdqvu/eAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d37e3a277ea4c787e3620c4ecefb258c42500dace90b3749762528d768efe48","last_reissued_at":"2026-05-18T04:06:35.458488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:35.458488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.3701","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":"2026-05-18T04:06:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D+TiX65vcTz8IihcDj4bFM1wXBzx4gu5+tCPXR8iCl/yqrmSu5j3tTBS7phWYX5DVe6jXK11Bp3izUfM4OFcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:23:23.082566Z"},"content_sha256":"0432851baa025426bf733006c4b78379cd230969151afc9f988e4dc7cf705cc6","schema_version":"1.0","event_id":"sha256:0432851baa025426bf733006c4b78379cd230969151afc9f988e4dc7cf705cc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PU36HITX5JGHQ7RWEDCOZ35SLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Active Ranking using Pairwise Comparisons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Kevin G. Jamieson, Robert D. Nowak","submitted_at":"2011-09-16T19:35:13Z","abstract_excerpt":"This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise comparisons. We are interested in natural situations in which relationships among the objects may allow for ranking using far fewer pairwise comparisons. Specifically, we assume that the objects can be embedded into a $d$-dimensional Euclidean space and that the rankings reflect their relative distances from a common reference point in $R^d$. We show that under thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3701","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":"2026-05-18T04:06:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUYY94vG07P8EMJfqOCVVMJy4/jaaO5dxHWlOrjDg9G6hPSqXHnTvY3GvKCYGgLsyjuDgxYOcJFkI03V8oZ7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:23:23.083289Z"},"content_sha256":"fabfd83b1a43d22d8301662ca10738af9ce007ac8223e993979d6b1e8fdd62bf","schema_version":"1.0","event_id":"sha256:fabfd83b1a43d22d8301662ca10738af9ce007ac8223e993979d6b1e8fdd62bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PU36HITX5JGHQ7RWEDCOZ35SLD/bundle.json","state_url":"https://pith.science/pith/PU36HITX5JGHQ7RWEDCOZ35SLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PU36HITX5JGHQ7RWEDCOZ35SLD/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":"2026-05-26T23:23:23Z","links":{"resolver":"https://pith.science/pith/PU36HITX5JGHQ7RWEDCOZ35SLD","bundle":"https://pith.science/pith/PU36HITX5JGHQ7RWEDCOZ35SLD/bundle.json","state":"https://pith.science/pith/PU36HITX5JGHQ7RWEDCOZ35SLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PU36HITX5JGHQ7RWEDCOZ35SLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PU36HITX5JGHQ7RWEDCOZ35SLD","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":"8c2b7df85177d20fed72223c3f2ebc91e7d9d57e6cb204fa32f0f08158fc3cd0","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-09-16T19:35:13Z","title_canon_sha256":"5f8063a16a9ab161a0d90ea0f51c226c37d1fbfbf4239a164486dfeea3bf81b6"},"schema_version":"1.0","source":{"id":"1109.3701","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3701","created_at":"2026-05-18T04:06:35Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3701v2","created_at":"2026-05-18T04:06:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3701","created_at":"2026-05-18T04:06:35Z"},{"alias_kind":"pith_short_12","alias_value":"PU36HITX5JGH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PU36HITX5JGHQ7RW","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PU36HITX","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:fabfd83b1a43d22d8301662ca10738af9ce007ac8223e993979d6b1e8fdd62bf","target":"graph","created_at":"2026-05-18T04:06:35Z","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":"This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise comparisons. We are interested in natural situations in which relationships among the objects may allow for ranking using far fewer pairwise comparisons. Specifically, we assume that the objects can be embedded into a $d$-dimensional Euclidean space and that the rankings reflect their relative distances from a common reference point in $R^d$. We show that under thi","authors_text":"Kevin G. Jamieson, Robert D. Nowak","cross_cats":["cs.IT","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-09-16T19:35:13Z","title":"Active Ranking using Pairwise Comparisons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3701","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":"sha256:0432851baa025426bf733006c4b78379cd230969151afc9f988e4dc7cf705cc6","target":"record","created_at":"2026-05-18T04:06:35Z","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":"8c2b7df85177d20fed72223c3f2ebc91e7d9d57e6cb204fa32f0f08158fc3cd0","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2011-09-16T19:35:13Z","title_canon_sha256":"5f8063a16a9ab161a0d90ea0f51c226c37d1fbfbf4239a164486dfeea3bf81b6"},"schema_version":"1.0","source":{"id":"1109.3701","kind":"arxiv","version":2}},"canonical_sha256":"7d37e3a277ea4c787e3620c4ecefb258c42500dace90b3749762528d768efe48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d37e3a277ea4c787e3620c4ecefb258c42500dace90b3749762528d768efe48","first_computed_at":"2026-05-18T04:06:35.458488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:35.458488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cr0obCRWHTXLVCOe7IhCqHMJqM9cBzLnujXGvX6EuXc49lMKvB2Z/1zKuZ7+fDWVc6f645xQfLZXtXdqvu/eAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:35.459093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3701","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0432851baa025426bf733006c4b78379cd230969151afc9f988e4dc7cf705cc6","sha256:fabfd83b1a43d22d8301662ca10738af9ce007ac8223e993979d6b1e8fdd62bf"],"state_sha256":"174f33997989f968523c6bafc7507e1699fd9d3e6e6ad2af2d6f9ea4a9fac08e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QdomzQzX59eRzMNmprw/l5JfRwmv/pDAtf2c5gTpF71GwJjyMlrMcg7w/j6hLGEtAbZYnlTh77DkLcFZuofyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:23:23.087912Z","bundle_sha256":"d7ffe53e8080793933deb786b4adeed98efd52d2b60633651fbaceaa523b1a34"}}