{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:G4Y62YTJ4WBIM5GMSR7UX2GNXK","short_pith_number":"pith:G4Y62YTJ","canonical_record":{"source":{"id":"2607.23914","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-27T01:06:31Z","cross_cats_sorted":["eess.SP","math.PR","stat.ML","stat.TH"],"title_canon_sha256":"bafa5ee5adf4c5d3e05a7af09215fa038e854e94410112c373314337e33373bb","abstract_canon_sha256":"9e66752f50f65846385961cdd6ae14860bcd0591ad89f994afc0f998a1ab2506"},"schema_version":"1.0"},"canonical_sha256":"3731ed6269e5828674cc947f4be8cdbab464b2e4fb9819833fda4c4733359d9a","source":{"kind":"arxiv","id":"2607.23914","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23914","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23914v1","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23914","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"G4Y62YTJ4WBI","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"pith_short_16","alias_value":"G4Y62YTJ4WBIM5GM","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"pith_short_8","alias_value":"G4Y62YTJ","created_at":"2026-07-28T01:23:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:G4Y62YTJ4WBIM5GMSR7UX2GNXK","target":"record","payload":{"canonical_record":{"source":{"id":"2607.23914","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-27T01:06:31Z","cross_cats_sorted":["eess.SP","math.PR","stat.ML","stat.TH"],"title_canon_sha256":"bafa5ee5adf4c5d3e05a7af09215fa038e854e94410112c373314337e33373bb","abstract_canon_sha256":"9e66752f50f65846385961cdd6ae14860bcd0591ad89f994afc0f998a1ab2506"},"schema_version":"1.0"},"canonical_sha256":"3731ed6269e5828674cc947f4be8cdbab464b2e4fb9819833fda4c4733359d9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:23:17.508353Z","signature_b64":"iWUXet0QA4TR6KdLK1pC5Ef9Q34R94imqwUDuv2eqR/RqC8jv+n1oJiWiCxbjrceMiE34jd2lQqTguC12763Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3731ed6269e5828674cc947f4be8cdbab464b2e4fb9819833fda4c4733359d9a","last_reissued_at":"2026-07-28T01:23:17.507506Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:23:17.507506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.23914","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-28T01:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tw1fN3Aer1WsxIAHg1sVt5zz7FW1tCtLTQQSg2Pi1YKh4ZCGGvSvYYxPi9xMiW6MkTWsi2LJF18ipb8sKd4kBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:10:12.899333Z"},"content_sha256":"17840090c974462e81f28dc68a4c696aeb5cfcb216623beb0be580623f849f4e","schema_version":"1.0","event_id":"sha256:17840090c974462e81f28dc68a4c696aeb5cfcb216623beb0be580623f849f4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:G4Y62YTJ4WBIM5GMSR7UX2GNXK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Phase Transition in Online PCA Depends on $n/d\\log(d)$, not $n/d$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["eess.SP","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Apratim Dey","submitted_at":"2026-07-27T01:06:31Z","abstract_excerpt":"High dimensional statistical theory has established the importance of constant aspect ratio, when the number of dimensions ($d$) and samples ($n$) satisfy $n,d\\to\\infty$ with $n/d\\to \\gamma\\in(0,\\infty)$, in understanding the limits of canonical estimation problems. In particular, for estimating the top eigenvector of a $d\\times d$ population covariance matrix from $n$ iid samples, the BBP phase transition gives a precise threshold -- a simple functional of the aspect ratio -- such that the top sample principal component attains nonzero asymptotic correlation with the truth only when the leadi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23914","kind":"arxiv","version":1},"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/2607.23914/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":"2026-07-28T01:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xZCtL7rpmxvqTK9/B2ORkb0ap/EWxu6/jR9OrcwA3hXlMgoPwXDCaFQzoZFamRFXROnREuz3wFSUMsB0ZQnZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:10:12.899893Z"},"content_sha256":"9c2f5beabc6363588695f3476ac7a244b2d06e23789b139601a835b4db99658b","schema_version":"1.0","event_id":"sha256:9c2f5beabc6363588695f3476ac7a244b2d06e23789b139601a835b4db99658b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4Y62YTJ4WBIM5GMSR7UX2GNXK/bundle.json","state_url":"https://pith.science/pith/G4Y62YTJ4WBIM5GMSR7UX2GNXK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4Y62YTJ4WBIM5GMSR7UX2GNXK/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":"2026-08-10T09:10:12Z","links":{"resolver":"https://pith.science/pith/G4Y62YTJ4WBIM5GMSR7UX2GNXK","bundle":"https://pith.science/pith/G4Y62YTJ4WBIM5GMSR7UX2GNXK/bundle.json","state":"https://pith.science/pith/G4Y62YTJ4WBIM5GMSR7UX2GNXK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4Y62YTJ4WBIM5GMSR7UX2GNXK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:G4Y62YTJ4WBIM5GMSR7UX2GNXK","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":"9e66752f50f65846385961cdd6ae14860bcd0591ad89f994afc0f998a1ab2506","cross_cats_sorted":["eess.SP","math.PR","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-27T01:06:31Z","title_canon_sha256":"bafa5ee5adf4c5d3e05a7af09215fa038e854e94410112c373314337e33373bb"},"schema_version":"1.0","source":{"id":"2607.23914","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23914","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23914v1","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23914","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"G4Y62YTJ4WBI","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"pith_short_16","alias_value":"G4Y62YTJ4WBIM5GM","created_at":"2026-07-28T01:23:17Z"},{"alias_kind":"pith_short_8","alias_value":"G4Y62YTJ","created_at":"2026-07-28T01:23:17Z"}],"graph_snapshots":[{"event_id":"sha256:9c2f5beabc6363588695f3476ac7a244b2d06e23789b139601a835b4db99658b","target":"graph","created_at":"2026-07-28T01:23:17Z","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/2607.23914/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"High dimensional statistical theory has established the importance of constant aspect ratio, when the number of dimensions ($d$) and samples ($n$) satisfy $n,d\\to\\infty$ with $n/d\\to \\gamma\\in(0,\\infty)$, in understanding the limits of canonical estimation problems. In particular, for estimating the top eigenvector of a $d\\times d$ population covariance matrix from $n$ iid samples, the BBP phase transition gives a precise threshold -- a simple functional of the aspect ratio -- such that the top sample principal component attains nonzero asymptotic correlation with the truth only when the leadi","authors_text":"Apratim Dey","cross_cats":["eess.SP","math.PR","stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-27T01:06:31Z","title":"The Phase Transition in Online PCA Depends on $n/d\\log(d)$, not $n/d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23914","kind":"arxiv","version":1},"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":"sha256:17840090c974462e81f28dc68a4c696aeb5cfcb216623beb0be580623f849f4e","target":"record","created_at":"2026-07-28T01:23:17Z","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":"9e66752f50f65846385961cdd6ae14860bcd0591ad89f994afc0f998a1ab2506","cross_cats_sorted":["eess.SP","math.PR","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-27T01:06:31Z","title_canon_sha256":"bafa5ee5adf4c5d3e05a7af09215fa038e854e94410112c373314337e33373bb"},"schema_version":"1.0","source":{"id":"2607.23914","kind":"arxiv","version":1}},"canonical_sha256":"3731ed6269e5828674cc947f4be8cdbab464b2e4fb9819833fda4c4733359d9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3731ed6269e5828674cc947f4be8cdbab464b2e4fb9819833fda4c4733359d9a","first_computed_at":"2026-07-28T01:23:17.507506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:23:17.507506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iWUXet0QA4TR6KdLK1pC5Ef9Q34R94imqwUDuv2eqR/RqC8jv+n1oJiWiCxbjrceMiE34jd2lQqTguC12763Bg==","signature_status":"signed_v1","signed_at":"2026-07-28T01:23:17.508353Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23914","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17840090c974462e81f28dc68a4c696aeb5cfcb216623beb0be580623f849f4e","sha256:9c2f5beabc6363588695f3476ac7a244b2d06e23789b139601a835b4db99658b"],"state_sha256":"fe6ec7c17cb34c08ed5e2e74ac8c5d6d6e287d9c1bbef7aca967f1ffc24ee439"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wa6Ws9QAzN1OGSLWzXoVVOgiUUwi4BZ6L8LvNlRIu1Ox2neW7Gs59R68tmQKNm6ya2mY0TcYSDtmMc+v1cxJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T09:10:12.903580Z","bundle_sha256":"28455e0677faaa9e578bfbf5862e17055447d90b4bedb954fe5839c4453dfb0e"}}