{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5XDULTMF4MWO65BSG6HMAF76AA","short_pith_number":"pith:5XDULTMF","canonical_record":{"source":{"id":"2506.12655","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-14T22:50:54Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"4feb7099d3d5a0671b73a8bc80fc642fc370969bc417c22724820cc0a28802b5","abstract_canon_sha256":"37f91b1e506668b9acf598f77ea2cc0ea35035cbb2751c00e766fad50e3d8c35"},"schema_version":"1.0"},"canonical_sha256":"edc745cd85e32cef7432378ec017fe00117d1d36e6e94722fc4468fae7bb394c","source":{"kind":"arxiv","id":"2506.12655","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.12655","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"2506.12655v2","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.12655","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"5XDULTMF4MWO","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"pith_short_16","alias_value":"5XDULTMF4MWO65BS","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"pith_short_8","alias_value":"5XDULTMF","created_at":"2026-07-05T11:39:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5XDULTMF4MWO65BSG6HMAF76AA","target":"record","payload":{"canonical_record":{"source":{"id":"2506.12655","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-14T22:50:54Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"4feb7099d3d5a0671b73a8bc80fc642fc370969bc417c22724820cc0a28802b5","abstract_canon_sha256":"37f91b1e506668b9acf598f77ea2cc0ea35035cbb2751c00e766fad50e3d8c35"},"schema_version":"1.0"},"canonical_sha256":"edc745cd85e32cef7432378ec017fe00117d1d36e6e94722fc4468fae7bb394c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:55.155990Z","signature_b64":"rgQGOT0d9lAlegCzVfAMQcenHVllXFE2n2OUt2Y1EQt0ykhXSWlVY2h0SVQe261t8Hmb34K8yaqX71fLgNeEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edc745cd85e32cef7432378ec017fe00117d1d36e6e94722fc4468fae7bb394c","last_reissued_at":"2026-07-05T11:39:55.155585Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:55.155585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.12655","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":"2026-07-05T11:39:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BWlD5RXxNEo/zSqF65ZQn/J2gm7lIBPBN9PcvN8MasGXD3txycv1wLBkg34srq2QNKeYNBVjMxAXUjv2hDaRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:05:02.464151Z"},"content_sha256":"811b3445c01665be2c5762a1f3e65b7dd36fd89b3af2ce9d92465557f3db3b5a","schema_version":"1.0","event_id":"sha256:811b3445c01665be2c5762a1f3e65b7dd36fd89b3af2ce9d92465557f3db3b5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5XDULTMF4MWO65BSG6HMAF76AA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond Sin-Squared Error: Linear-Time Entrywise Uncertainty Quantification for Streaming PCA","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Purnamrita Sarkar, Shourya Pandey, Syamantak Kumar","submitted_at":"2025-06-14T22:50:54Z","abstract_excerpt":"We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja's algorithm, enabling the construction of confidence intervals for individual entries of the estimated eigenvector. Most existing works on streaming PCA focus on providing sharp sin-squared error guarantees. Recently, there has been some interest in uncertainty quantification for the sin-squared error. However, uncertainty quantification or sharp error guarantees for entries of the estimated eigenvector in the streaming setting remains largely unexplored. We derive a sharp Bernstein-ty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12655","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.12655/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:39:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRcu9ACnoscdWVMZ0seq08XvWsKCFA1niMLXsaXVI/IzmlPlV9hr362Wv1vpXxt2X8sFKwLzos1zjDNUBv6VBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:05:02.464670Z"},"content_sha256":"634ab60ae170604d6aca3d3f33e6cc4c7735b328f5e80726658906f32114dec3","schema_version":"1.0","event_id":"sha256:634ab60ae170604d6aca3d3f33e6cc4c7735b328f5e80726658906f32114dec3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XDULTMF4MWO65BSG6HMAF76AA/bundle.json","state_url":"https://pith.science/pith/5XDULTMF4MWO65BSG6HMAF76AA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XDULTMF4MWO65BSG6HMAF76AA/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":"2026-08-09T20:05:02Z","links":{"resolver":"https://pith.science/pith/5XDULTMF4MWO65BSG6HMAF76AA","bundle":"https://pith.science/pith/5XDULTMF4MWO65BSG6HMAF76AA/bundle.json","state":"https://pith.science/pith/5XDULTMF4MWO65BSG6HMAF76AA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XDULTMF4MWO65BSG6HMAF76AA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5XDULTMF4MWO65BSG6HMAF76AA","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":"37f91b1e506668b9acf598f77ea2cc0ea35035cbb2751c00e766fad50e3d8c35","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-14T22:50:54Z","title_canon_sha256":"4feb7099d3d5a0671b73a8bc80fc642fc370969bc417c22724820cc0a28802b5"},"schema_version":"1.0","source":{"id":"2506.12655","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.12655","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"2506.12655v2","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.12655","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"5XDULTMF4MWO","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"pith_short_16","alias_value":"5XDULTMF4MWO65BS","created_at":"2026-07-05T11:39:55Z"},{"alias_kind":"pith_short_8","alias_value":"5XDULTMF","created_at":"2026-07-05T11:39:55Z"}],"graph_snapshots":[{"event_id":"sha256:634ab60ae170604d6aca3d3f33e6cc4c7735b328f5e80726658906f32114dec3","target":"graph","created_at":"2026-07-05T11:39:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.12655/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja's algorithm, enabling the construction of confidence intervals for individual entries of the estimated eigenvector. Most existing works on streaming PCA focus on providing sharp sin-squared error guarantees. Recently, there has been some interest in uncertainty quantification for the sin-squared error. However, uncertainty quantification or sharp error guarantees for entries of the estimated eigenvector in the streaming setting remains largely unexplored. We derive a sharp Bernstein-ty","authors_text":"Purnamrita Sarkar, Shourya Pandey, Syamantak Kumar","cross_cats":["cs.LG","stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-14T22:50:54Z","title":"Beyond Sin-Squared Error: Linear-Time Entrywise Uncertainty Quantification for Streaming PCA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12655","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":"sha256:811b3445c01665be2c5762a1f3e65b7dd36fd89b3af2ce9d92465557f3db3b5a","target":"record","created_at":"2026-07-05T11:39:55Z","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":"37f91b1e506668b9acf598f77ea2cc0ea35035cbb2751c00e766fad50e3d8c35","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-14T22:50:54Z","title_canon_sha256":"4feb7099d3d5a0671b73a8bc80fc642fc370969bc417c22724820cc0a28802b5"},"schema_version":"1.0","source":{"id":"2506.12655","kind":"arxiv","version":2}},"canonical_sha256":"edc745cd85e32cef7432378ec017fe00117d1d36e6e94722fc4468fae7bb394c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edc745cd85e32cef7432378ec017fe00117d1d36e6e94722fc4468fae7bb394c","first_computed_at":"2026-07-05T11:39:55.155585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:55.155585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgQGOT0d9lAlegCzVfAMQcenHVllXFE2n2OUt2Y1EQt0ykhXSWlVY2h0SVQe261t8Hmb34K8yaqX71fLgNeEAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:55.155990Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.12655","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:811b3445c01665be2c5762a1f3e65b7dd36fd89b3af2ce9d92465557f3db3b5a","sha256:634ab60ae170604d6aca3d3f33e6cc4c7735b328f5e80726658906f32114dec3"],"state_sha256":"fb31ebf9464399d1b71062d1246b60099ecad93fe13a359962c556836508df43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4SNsiURb3XcYKBCIOYuyFjSAHdowWo3o0NuiE3gF1oIwaE5tNTLenpbrWV3/4Ap2ZVjRSdKueLm17mRi5PirBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:05:02.468857Z","bundle_sha256":"56b9fb44e7d7cea3830208d5ad4e3771d76d72ac499f922577bd9b1307a0c90d"}}