{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DSYQFOCXTGUT5B5T2GW7V6UTLA","short_pith_number":"pith:DSYQFOCX","canonical_record":{"source":{"id":"1812.02337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-06T03:46:11Z","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"title_canon_sha256":"c6cba2f8732dd2602668945497459997a342d7a55282be616840b964bcca22ce","abstract_canon_sha256":"22f1dd83a672eb79f1424ebe20f5d3f2a0f96786c5436c0fdf6f0133b8b22b2a"},"schema_version":"1.0"},"canonical_sha256":"1cb102b85799a93e87b3d1adfafa93583d0d10b015b47a9dc74d8b80887f4868","source":{"kind":"arxiv","id":"1812.02337","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02337","created_at":"2026-05-17T23:50:33Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02337v2","created_at":"2026-05-17T23:50:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02337","created_at":"2026-05-17T23:50:33Z"},{"alias_kind":"pith_short_12","alias_value":"DSYQFOCXTGUT","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DSYQFOCXTGUT5B5T","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DSYQFOCX","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DSYQFOCXTGUT5B5T2GW7V6UTLA","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-06T03:46:11Z","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"title_canon_sha256":"c6cba2f8732dd2602668945497459997a342d7a55282be616840b964bcca22ce","abstract_canon_sha256":"22f1dd83a672eb79f1424ebe20f5d3f2a0f96786c5436c0fdf6f0133b8b22b2a"},"schema_version":"1.0"},"canonical_sha256":"1cb102b85799a93e87b3d1adfafa93583d0d10b015b47a9dc74d8b80887f4868","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:33.525199Z","signature_b64":"7gWlkg+CKLcGNUeQHhUeYGkDKf76PS7qtqJDnl4GC2BLt3CUrsXBJBm/c7BspenxuQOK9W9uQeenuT9H2HVcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cb102b85799a93e87b3d1adfafa93583d0d10b015b47a9dc74d8b80887f4868","last_reissued_at":"2026-05-17T23:50:33.524539Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:33.524539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02337","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":"2026-05-17T23:50:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"brbXba+hNHDx4u4vqYciO/PIjsTlzIRu403xvJjcH7gAAXU2YIDR1QXyNb2gqAg0nK60ZX3MPIC42MWc5t5hAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:23:40.541411Z"},"content_sha256":"05928137530ae9659bf112e24ac859fee59d2a98631ac66c22dc514b848eaad6","schema_version":"1.0","event_id":"sha256:05928137530ae9659bf112e24ac859fee59d2a98631ac66c22dc514b848eaad6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DSYQFOCXTGUT5B5T2GW7V6UTLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Inference on the Rank of a Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ME","stat.TH"],"primary_cat":"econ.EM","authors_text":"Qihui Chen, Zheng Fang","submitted_at":"2018-12-06T03:46:11Z","abstract_excerpt":"This paper develops a general framework for conducting inference on the rank of an unknown matrix $\\Pi_0$. A defining feature of our setup is the null hypothesis of the form $\\mathrm H_0: \\mathrm{rank}(\\Pi_0)\\le r$. The problem is of first order importance because the previous literature focuses on $\\mathrm H_0': \\mathrm{rank}(\\Pi_0)= r$ by implicitly assuming away $\\mathrm{rank}(\\Pi_0)<r$, which may lead to invalid rank tests due to over-rejections. In particular, we show that limiting distributions of test statistics under $\\mathrm H_0'$ may not stochastically dominate those under $\\mathrm{r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02337","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":"2026-05-17T23:50:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1rc+hS5ClL+hVw4hpfesTgYL+nIIUlqGp2wdb91i0A1gNtIBtbRt+XazJikVfIa13rdo+axRS2jy5w4mguhFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:23:40.542132Z"},"content_sha256":"1b20631cf1a5315d2c6d9cf61ed686d490e21703e8ae102c37929fb59b8fab9b","schema_version":"1.0","event_id":"sha256:1b20631cf1a5315d2c6d9cf61ed686d490e21703e8ae102c37929fb59b8fab9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DSYQFOCXTGUT5B5T2GW7V6UTLA/bundle.json","state_url":"https://pith.science/pith/DSYQFOCXTGUT5B5T2GW7V6UTLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DSYQFOCXTGUT5B5T2GW7V6UTLA/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":"2026-05-31T23:23:40Z","links":{"resolver":"https://pith.science/pith/DSYQFOCXTGUT5B5T2GW7V6UTLA","bundle":"https://pith.science/pith/DSYQFOCXTGUT5B5T2GW7V6UTLA/bundle.json","state":"https://pith.science/pith/DSYQFOCXTGUT5B5T2GW7V6UTLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DSYQFOCXTGUT5B5T2GW7V6UTLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DSYQFOCXTGUT5B5T2GW7V6UTLA","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":"22f1dd83a672eb79f1424ebe20f5d3f2a0f96786c5436c0fdf6f0133b8b22b2a","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-06T03:46:11Z","title_canon_sha256":"c6cba2f8732dd2602668945497459997a342d7a55282be616840b964bcca22ce"},"schema_version":"1.0","source":{"id":"1812.02337","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02337","created_at":"2026-05-17T23:50:33Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02337v2","created_at":"2026-05-17T23:50:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02337","created_at":"2026-05-17T23:50:33Z"},{"alias_kind":"pith_short_12","alias_value":"DSYQFOCXTGUT","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DSYQFOCXTGUT5B5T","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DSYQFOCX","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:1b20631cf1a5315d2c6d9cf61ed686d490e21703e8ae102c37929fb59b8fab9b","target":"graph","created_at":"2026-05-17T23:50:33Z","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 develops a general framework for conducting inference on the rank of an unknown matrix $\\Pi_0$. A defining feature of our setup is the null hypothesis of the form $\\mathrm H_0: \\mathrm{rank}(\\Pi_0)\\le r$. The problem is of first order importance because the previous literature focuses on $\\mathrm H_0': \\mathrm{rank}(\\Pi_0)= r$ by implicitly assuming away $\\mathrm{rank}(\\Pi_0)<r$, which may lead to invalid rank tests due to over-rejections. In particular, we show that limiting distributions of test statistics under $\\mathrm H_0'$ may not stochastically dominate those under $\\mathrm{r","authors_text":"Qihui Chen, Zheng Fang","cross_cats":["math.ST","stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-06T03:46:11Z","title":"Improved Inference on the Rank of a Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02337","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":"sha256:05928137530ae9659bf112e24ac859fee59d2a98631ac66c22dc514b848eaad6","target":"record","created_at":"2026-05-17T23:50:33Z","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":"22f1dd83a672eb79f1424ebe20f5d3f2a0f96786c5436c0fdf6f0133b8b22b2a","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2018-12-06T03:46:11Z","title_canon_sha256":"c6cba2f8732dd2602668945497459997a342d7a55282be616840b964bcca22ce"},"schema_version":"1.0","source":{"id":"1812.02337","kind":"arxiv","version":2}},"canonical_sha256":"1cb102b85799a93e87b3d1adfafa93583d0d10b015b47a9dc74d8b80887f4868","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cb102b85799a93e87b3d1adfafa93583d0d10b015b47a9dc74d8b80887f4868","first_computed_at":"2026-05-17T23:50:33.524539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:33.524539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7gWlkg+CKLcGNUeQHhUeYGkDKf76PS7qtqJDnl4GC2BLt3CUrsXBJBm/c7BspenxuQOK9W9uQeenuT9H2HVcCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:33.525199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02337","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05928137530ae9659bf112e24ac859fee59d2a98631ac66c22dc514b848eaad6","sha256:1b20631cf1a5315d2c6d9cf61ed686d490e21703e8ae102c37929fb59b8fab9b"],"state_sha256":"98732ba12ff3a91ad29cd610133ab4ff00f347430490d9a831b4f9f9e9355da0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aUwi4j6vrnoRBxEeoaL9s+sklO9TVF70qp6pApiEnkDQF73M3JiA6iETT64u8kYa3Z/d4xHRo+KBZsDRNgSlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:23:40.545825Z","bundle_sha256":"a41312ecd1ae46cbd31efab29e272b567c59fe6033bdd1eb34578ba92d7555b5"}}