{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:7Y6WMFJALQOKNMKIXPG7RBWVJU","short_pith_number":"pith:7Y6WMFJA","canonical_record":{"source":{"id":"1902.00104","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-31T22:24:21Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"fee918680c3801d22af34e32e66eeffa4ec95135e77a59c656095e1f8d4703b7","abstract_canon_sha256":"dc20e49fd50958910ba43ff5efd2181409342040f319ff1852dcc5b1a4d458a1"},"schema_version":"1.0"},"canonical_sha256":"fe3d6615205c1ca6b148bbcdf886d54d3d54a526b6336b8cd7b16ec41575a8e7","source":{"kind":"arxiv","id":"1902.00104","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00104","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00104v3","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00104","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"7Y6WMFJALQOK","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7Y6WMFJALQOKNMKI","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7Y6WMFJA","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:7Y6WMFJALQOKNMKIXPG7RBWVJU","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00104","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-31T22:24:21Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"fee918680c3801d22af34e32e66eeffa4ec95135e77a59c656095e1f8d4703b7","abstract_canon_sha256":"dc20e49fd50958910ba43ff5efd2181409342040f319ff1852dcc5b1a4d458a1"},"schema_version":"1.0"},"canonical_sha256":"fe3d6615205c1ca6b148bbcdf886d54d3d54a526b6336b8cd7b16ec41575a8e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:06.765225Z","signature_b64":"ElV+Ps9Jbp13J53/dFslo97EHr2hY+ElPnFikzbh94ev6r24kNjYres8eanpOVtKimbhTd5/ZCsUgXcn2XWRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3d6615205c1ca6b148bbcdf886d54d3d54a526b6336b8cd7b16ec41575a8e7","last_reissued_at":"2026-05-17T23:54:06.764735Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:06.764735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00104","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tny6Qm5iY+KsNjffRNcYhrCT4dIOuZV2brxFo00RWeUpf0C0iU+X17HoJzQ8HDnmGQo5vIeGP7kpJcVJPbOeCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:12:16.814864Z"},"content_sha256":"04533573fbf57a2cff489c8c559d96c1c490b30d38283a607b726a976b8abcea","schema_version":"1.0","event_id":"sha256:04533573fbf57a2cff489c8c559d96c1c490b30d38283a607b726a976b8abcea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:7Y6WMFJALQOKNMKIXPG7RBWVJU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase Transition in the Recovery of Rank One Matrices Corrupted by Gaussian Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Enrico Au-Yeung, Greg Zanotti","submitted_at":"2019-01-31T22:24:21Z","abstract_excerpt":"In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is comparable to the sample size, PCA can be misleading. A closely related problem is the following: is it possible to recover a rank-one matrix in the presence of a large amount of noise? In both situations, there is a phase transition in the eigen-structure of the matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00104","kind":"arxiv","version":3},"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":"2026-05-17T23:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOxhuYen1/dvLOtLKy/LYUGLTSgO+Fmor1I/Lc0Of33La1B57XOUlNKb6fyxJVbLw+vyChtxRBi7GTkQ/3aLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:12:16.815202Z"},"content_sha256":"0c9fc53b3227f7d08cf9db1da5ff6248a0728cfc7f60a8ce82f977400928924f","schema_version":"1.0","event_id":"sha256:0c9fc53b3227f7d08cf9db1da5ff6248a0728cfc7f60a8ce82f977400928924f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Y6WMFJALQOKNMKIXPG7RBWVJU/bundle.json","state_url":"https://pith.science/pith/7Y6WMFJALQOKNMKIXPG7RBWVJU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Y6WMFJALQOKNMKIXPG7RBWVJU/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":"2026-06-20T06:12:16Z","links":{"resolver":"https://pith.science/pith/7Y6WMFJALQOKNMKIXPG7RBWVJU","bundle":"https://pith.science/pith/7Y6WMFJALQOKNMKIXPG7RBWVJU/bundle.json","state":"https://pith.science/pith/7Y6WMFJALQOKNMKIXPG7RBWVJU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Y6WMFJALQOKNMKIXPG7RBWVJU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7Y6WMFJALQOKNMKIXPG7RBWVJU","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":"dc20e49fd50958910ba43ff5efd2181409342040f319ff1852dcc5b1a4d458a1","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-31T22:24:21Z","title_canon_sha256":"fee918680c3801d22af34e32e66eeffa4ec95135e77a59c656095e1f8d4703b7"},"schema_version":"1.0","source":{"id":"1902.00104","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00104","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00104v3","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00104","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"7Y6WMFJALQOK","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7Y6WMFJALQOKNMKI","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7Y6WMFJA","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:0c9fc53b3227f7d08cf9db1da5ff6248a0728cfc7f60a8ce82f977400928924f","target":"graph","created_at":"2026-05-17T23:54:06Z","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":"In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is comparable to the sample size, PCA can be misleading. A closely related problem is the following: is it possible to recover a rank-one matrix in the presence of a large amount of noise? In both situations, there is a phase transition in the eigen-structure of the matrix.","authors_text":"Enrico Au-Yeung, Greg Zanotti","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-31T22:24:21Z","title":"Phase Transition in the Recovery of Rank One Matrices Corrupted by Gaussian Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00104","kind":"arxiv","version":3},"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":"sha256:04533573fbf57a2cff489c8c559d96c1c490b30d38283a607b726a976b8abcea","target":"record","created_at":"2026-05-17T23:54:06Z","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":"dc20e49fd50958910ba43ff5efd2181409342040f319ff1852dcc5b1a4d458a1","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-31T22:24:21Z","title_canon_sha256":"fee918680c3801d22af34e32e66eeffa4ec95135e77a59c656095e1f8d4703b7"},"schema_version":"1.0","source":{"id":"1902.00104","kind":"arxiv","version":3}},"canonical_sha256":"fe3d6615205c1ca6b148bbcdf886d54d3d54a526b6336b8cd7b16ec41575a8e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe3d6615205c1ca6b148bbcdf886d54d3d54a526b6336b8cd7b16ec41575a8e7","first_computed_at":"2026-05-17T23:54:06.764735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:06.764735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ElV+Ps9Jbp13J53/dFslo97EHr2hY+ElPnFikzbh94ev6r24kNjYres8eanpOVtKimbhTd5/ZCsUgXcn2XWRCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:06.765225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00104","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04533573fbf57a2cff489c8c559d96c1c490b30d38283a607b726a976b8abcea","sha256:0c9fc53b3227f7d08cf9db1da5ff6248a0728cfc7f60a8ce82f977400928924f"],"state_sha256":"cf95307faa87d484c23dca9d8aa6bdf1c4d3c97ba3981d3b7f27f18f972177c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUZ+u+6XoaLkAbLQ53s5vvYzM1JXN8x5SH6OavBABq9DkDTeD3Wa5gGeXQxCI3aMcBog3qXFgXHYDkyZ1FibCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:12:16.817102Z","bundle_sha256":"daa98824c2de2ba6617ba85a54d5e272fbfd437f0df6fd0bd253a8ce00e5f55c"}}