{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:W3ER7FWQSB3765QYYENTYKAHKM","short_pith_number":"pith:W3ER7FWQ","canonical_record":{"source":{"id":"1603.04556","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-15T05:11:44Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c2e2ab745fabbd3ebb285250a82c1a9489d8bc918a6f804df8c56da60e69a504","abstract_canon_sha256":"cad3868195f395ac8dd853453652ce9a5d1445339cf5fb9692c301f94d2b6b94"},"schema_version":"1.0"},"canonical_sha256":"b6c91f96d09077ff7618c11b3c2807530f689db23745f4c0ce7ac29f5ec2828f","source":{"kind":"arxiv","id":"1603.04556","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04556","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04556v5","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04556","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"pith_short_12","alias_value":"W3ER7FWQSB37","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W3ER7FWQSB3765QY","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W3ER7FWQ","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:W3ER7FWQSB3765QYYENTYKAHKM","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04556","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-15T05:11:44Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c2e2ab745fabbd3ebb285250a82c1a9489d8bc918a6f804df8c56da60e69a504","abstract_canon_sha256":"cad3868195f395ac8dd853453652ce9a5d1445339cf5fb9692c301f94d2b6b94"},"schema_version":"1.0"},"canonical_sha256":"b6c91f96d09077ff7618c11b3c2807530f689db23745f4c0ce7ac29f5ec2828f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:44.201241Z","signature_b64":"IKe2jMooOCGFHN143UbOZ5CN82DeGulGkITDHwNvemyllJNHfQrPeaDKP81pbvPDRnQq7uw6Oyx7l+CS5NmgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6c91f96d09077ff7618c11b3c2807530f689db23745f4c0ce7ac29f5ec2828f","last_reissued_at":"2026-05-18T00:33:44.200630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:44.200630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04556","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lS7Q8SP4d/2JE2Cb9FdWGwAusc/um7rhSGORNW+tqpp5Yy5x0Fr8LKIdV63+DsHZPEWGNicRVkOcB2ppy4xnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:55:27.128923Z"},"content_sha256":"f22c5c587ddb542318d8d6bb445eab93ea9e4a2345a4c3a3c5fe9203e6767785","schema_version":"1.0","event_id":"sha256:f22c5c587ddb542318d8d6bb445eab93ea9e4a2345a4c3a3c5fe9203e6767785"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:W3ER7FWQSB3765QYYENTYKAHKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Estimation in Tournaments and Graphs under Monotonicity Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Sabyasachi Chatterjee, Sumit Mukherjee","submitted_at":"2016-03-15T05:11:44Z","abstract_excerpt":"We consider the problem of estimating the probability matrix governing a tournament or linkage in graphs from incomplete observations, under the assumption that the probability matrix satisfies natural monotonicity constraints after being permuted in both rows and columns by some latent permutation. This condition is classical in the social sciences literature (see Fishburn(1973)) and has been studied in the statistics literature in recent work (see Chatterjee (2015) and Shah et al. (2016)). In this paper, we investigate in detail a natural estimator which bypasses the need to search over all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04556","kind":"arxiv","version":5},"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":"2026-05-18T00:33:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tgRYlY6ec3GSxqMh3ibcwWWpEmiN2k0+EKNWQtpOJ6WLoaPzhw2bJVAoKHSv+K8HAXFTQ8awbT+u30k4Gs4+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:55:27.129666Z"},"content_sha256":"e6b1e581cfbedf371ca465571bc7538a5dc168860e6793cedbcbe44591f4869e","schema_version":"1.0","event_id":"sha256:e6b1e581cfbedf371ca465571bc7538a5dc168860e6793cedbcbe44591f4869e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3ER7FWQSB3765QYYENTYKAHKM/bundle.json","state_url":"https://pith.science/pith/W3ER7FWQSB3765QYYENTYKAHKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3ER7FWQSB3765QYYENTYKAHKM/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":"2026-05-27T00:55:27Z","links":{"resolver":"https://pith.science/pith/W3ER7FWQSB3765QYYENTYKAHKM","bundle":"https://pith.science/pith/W3ER7FWQSB3765QYYENTYKAHKM/bundle.json","state":"https://pith.science/pith/W3ER7FWQSB3765QYYENTYKAHKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3ER7FWQSB3765QYYENTYKAHKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W3ER7FWQSB3765QYYENTYKAHKM","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":"cad3868195f395ac8dd853453652ce9a5d1445339cf5fb9692c301f94d2b6b94","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-15T05:11:44Z","title_canon_sha256":"c2e2ab745fabbd3ebb285250a82c1a9489d8bc918a6f804df8c56da60e69a504"},"schema_version":"1.0","source":{"id":"1603.04556","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04556","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04556v5","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04556","created_at":"2026-05-18T00:33:44Z"},{"alias_kind":"pith_short_12","alias_value":"W3ER7FWQSB37","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W3ER7FWQSB3765QY","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W3ER7FWQ","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:e6b1e581cfbedf371ca465571bc7538a5dc168860e6793cedbcbe44591f4869e","target":"graph","created_at":"2026-05-18T00:33:44Z","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":"We consider the problem of estimating the probability matrix governing a tournament or linkage in graphs from incomplete observations, under the assumption that the probability matrix satisfies natural monotonicity constraints after being permuted in both rows and columns by some latent permutation. This condition is classical in the social sciences literature (see Fishburn(1973)) and has been studied in the statistics literature in recent work (see Chatterjee (2015) and Shah et al. (2016)). In this paper, we investigate in detail a natural estimator which bypasses the need to search over all ","authors_text":"Sabyasachi Chatterjee, Sumit Mukherjee","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-15T05:11:44Z","title":"On Estimation in Tournaments and Graphs under Monotonicity Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04556","kind":"arxiv","version":5},"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:f22c5c587ddb542318d8d6bb445eab93ea9e4a2345a4c3a3c5fe9203e6767785","target":"record","created_at":"2026-05-18T00:33:44Z","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":"cad3868195f395ac8dd853453652ce9a5d1445339cf5fb9692c301f94d2b6b94","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-15T05:11:44Z","title_canon_sha256":"c2e2ab745fabbd3ebb285250a82c1a9489d8bc918a6f804df8c56da60e69a504"},"schema_version":"1.0","source":{"id":"1603.04556","kind":"arxiv","version":5}},"canonical_sha256":"b6c91f96d09077ff7618c11b3c2807530f689db23745f4c0ce7ac29f5ec2828f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6c91f96d09077ff7618c11b3c2807530f689db23745f4c0ce7ac29f5ec2828f","first_computed_at":"2026-05-18T00:33:44.200630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:44.200630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IKe2jMooOCGFHN143UbOZ5CN82DeGulGkITDHwNvemyllJNHfQrPeaDKP81pbvPDRnQq7uw6Oyx7l+CS5NmgAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:44.201241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04556","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f22c5c587ddb542318d8d6bb445eab93ea9e4a2345a4c3a3c5fe9203e6767785","sha256:e6b1e581cfbedf371ca465571bc7538a5dc168860e6793cedbcbe44591f4869e"],"state_sha256":"b522ea6532ee9a4923e38ba791281c00a63bcfb001004011ac18a233caf5be91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n7AECbeMh2ZFc8k4TnUSS3+UAUc7GexG+iEj+KFNd8H5ykXhAamcEcgNa1vs5FMtUoXdLQojOHeQZQLHVcJRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:55:27.133163Z","bundle_sha256":"f14efb7d6c805c8f58d79b0d283675d7dbe01ca8caa68446c518a0ab2545cb81"}}