{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:B2E77A5WXTJHJ6IHMQWE7VFC2R","short_pith_number":"pith:B2E77A5W","canonical_record":{"source":{"id":"1807.00891","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-02T21:11:57Z","cross_cats_sorted":["cs.DS","cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"title_canon_sha256":"f90596bb38104d50da3ef73e18c7b7ddd9f051738bd54726405dd045f68c1b3e","abstract_canon_sha256":"5013e2d176e5c186f53ebc422846cc44664e4e0c8b7507a769c270786644dbc0"},"schema_version":"1.0"},"canonical_sha256":"0e89ff83b6bcd274f907642c4fd4a2d47c7047bdd47a33f73544495be8877794","source":{"kind":"arxiv","id":"1807.00891","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00891","created_at":"2026-05-18T00:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00891v2","created_at":"2026-05-18T00:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00891","created_at":"2026-05-18T00:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"B2E77A5WXTJH","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B2E77A5WXTJHJ6IH","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B2E77A5W","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:B2E77A5WXTJHJ6IHMQWE7VFC2R","target":"record","payload":{"canonical_record":{"source":{"id":"1807.00891","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-02T21:11:57Z","cross_cats_sorted":["cs.DS","cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"title_canon_sha256":"f90596bb38104d50da3ef73e18c7b7ddd9f051738bd54726405dd045f68c1b3e","abstract_canon_sha256":"5013e2d176e5c186f53ebc422846cc44664e4e0c8b7507a769c270786644dbc0"},"schema_version":"1.0"},"canonical_sha256":"0e89ff83b6bcd274f907642c4fd4a2d47c7047bdd47a33f73544495be8877794","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:06.450578Z","signature_b64":"yvHd+ALwByGiunMiPzRzGigVymJ+u83hqZdJ7TgMD/WZbCQMvNVnGRP3B3ebfM/aVZv3YFgvqMMwbvb21HAUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e89ff83b6bcd274f907642c4fd4a2d47c7047bdd47a33f73544495be8877794","last_reissued_at":"2026-05-18T00:07:06.449798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:06.449798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.00891","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":"2026-05-18T00:07:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Hw39PrasGJcEd9J1ZnwimOMgc4QFg5ECvGUosqIWYK+T6SlDXEMMTgLiezVqTpovFh0qmcEStpPinghfXC2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:45:34.613438Z"},"content_sha256":"13bc0a289b381dea5fdfd80dde833bb14d1278d703821578b69a8a8b415dcc01","schema_version":"1.0","event_id":"sha256:13bc0a289b381dea5fdfd80dde833bb14d1278d703821578b69a8a8b415dcc01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:B2E77A5WXTJHJ6IHMQWE7VFC2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Afonso S. Bandeira, Alexander S. Wein, Amelia Perry, Ankur Moitra","submitted_at":"2018-07-02T21:11:57Z","abstract_excerpt":"A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or \"spike\") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Peche showed that the spiked Wishart ensemble exhibits a sharp phase transition asymptotically: when the spike strength is above a critical threshold, it is possible to detect the presence of a spike based on the top eigenvalue, and below the t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00891","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":"2026-05-18T00:07:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYpzJpi9KTHCH1aSmcutUiMJfn6xEKK8ZrNi26qRwS6FeJEMxDy6d0UBuZc00Ef25Qo/Re0WIZuqT0IQHJxXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:45:34.614698Z"},"content_sha256":"6921ea111249e86e20bd65c96bc850705a3f87f6a3ad33e3551ef7f7c75621df","schema_version":"1.0","event_id":"sha256:6921ea111249e86e20bd65c96bc850705a3f87f6a3ad33e3551ef7f7c75621df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2E77A5WXTJHJ6IHMQWE7VFC2R/bundle.json","state_url":"https://pith.science/pith/B2E77A5WXTJHJ6IHMQWE7VFC2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2E77A5WXTJHJ6IHMQWE7VFC2R/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":"2026-05-28T20:45:34Z","links":{"resolver":"https://pith.science/pith/B2E77A5WXTJHJ6IHMQWE7VFC2R","bundle":"https://pith.science/pith/B2E77A5WXTJHJ6IHMQWE7VFC2R/bundle.json","state":"https://pith.science/pith/B2E77A5WXTJHJ6IHMQWE7VFC2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2E77A5WXTJHJ6IHMQWE7VFC2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B2E77A5WXTJHJ6IHMQWE7VFC2R","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":"5013e2d176e5c186f53ebc422846cc44664e4e0c8b7507a769c270786644dbc0","cross_cats_sorted":["cs.DS","cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-02T21:11:57Z","title_canon_sha256":"f90596bb38104d50da3ef73e18c7b7ddd9f051738bd54726405dd045f68c1b3e"},"schema_version":"1.0","source":{"id":"1807.00891","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00891","created_at":"2026-05-18T00:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00891v2","created_at":"2026-05-18T00:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00891","created_at":"2026-05-18T00:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"B2E77A5WXTJH","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B2E77A5WXTJHJ6IH","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B2E77A5W","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:6921ea111249e86e20bd65c96bc850705a3f87f6a3ad33e3551ef7f7c75621df","target":"graph","created_at":"2026-05-18T00:07:06Z","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":"A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or \"spike\") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Peche showed that the spiked Wishart ensemble exhibits a sharp phase transition asymptotically: when the spike strength is above a critical threshold, it is possible to detect the presence of a spike based on the top eigenvalue, and below the t","authors_text":"Afonso S. Bandeira, Alexander S. Wein, Amelia Perry, Ankur Moitra","cross_cats":["cs.DS","cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-02T21:11:57Z","title":"Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00891","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":"sha256:13bc0a289b381dea5fdfd80dde833bb14d1278d703821578b69a8a8b415dcc01","target":"record","created_at":"2026-05-18T00:07:06Z","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":"5013e2d176e5c186f53ebc422846cc44664e4e0c8b7507a769c270786644dbc0","cross_cats_sorted":["cs.DS","cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-07-02T21:11:57Z","title_canon_sha256":"f90596bb38104d50da3ef73e18c7b7ddd9f051738bd54726405dd045f68c1b3e"},"schema_version":"1.0","source":{"id":"1807.00891","kind":"arxiv","version":2}},"canonical_sha256":"0e89ff83b6bcd274f907642c4fd4a2d47c7047bdd47a33f73544495be8877794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e89ff83b6bcd274f907642c4fd4a2d47c7047bdd47a33f73544495be8877794","first_computed_at":"2026-05-18T00:07:06.449798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:06.449798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yvHd+ALwByGiunMiPzRzGigVymJ+u83hqZdJ7TgMD/WZbCQMvNVnGRP3B3ebfM/aVZv3YFgvqMMwbvb21HAUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:06.450578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00891","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13bc0a289b381dea5fdfd80dde833bb14d1278d703821578b69a8a8b415dcc01","sha256:6921ea111249e86e20bd65c96bc850705a3f87f6a3ad33e3551ef7f7c75621df"],"state_sha256":"ca63e145267b16a7703d8233667105ed731e65530bdf8dc6298608ad05ad181d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cky65O1J6VH9wb785P0hpB8kPKek5Hn3oHmtoFvrdrcrxx3MSV8KecY+mCZx/CduBt6C+3rtO4kDXk7H9a6FCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:45:34.618335Z","bundle_sha256":"9590e2ab0dfcd849b13b8de4de106ea7af679262550a5d568657fd795f6ec711"}}