{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZD5WMC7E5YB2LKPMGSRGHMEEFJ","short_pith_number":"pith:ZD5WMC7E","canonical_record":{"source":{"id":"2606.09153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T07:46:09Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"864d192f48ed4e64b5f53829fe88d5e4958fe424dbdcf3fbc83fbc0e024abe73","abstract_canon_sha256":"5c2b69194871d725d0589cda2caa6773e442f842368dc691afa907c06daf9bdd"},"schema_version":"1.0"},"canonical_sha256":"c8fb660be4ee03a5a9ec34a263b0842a7c3af8401651aba42014ad1a73bd1735","source":{"kind":"arxiv","id":"2606.09153","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09153","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09153v1","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09153","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZD5WMC7E5YB2","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZD5WMC7E5YB2LKPM","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZD5WMC7E","created_at":"2026-06-09T02:08:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZD5WMC7E5YB2LKPMGSRGHMEEFJ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.09153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T07:46:09Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"864d192f48ed4e64b5f53829fe88d5e4958fe424dbdcf3fbc83fbc0e024abe73","abstract_canon_sha256":"5c2b69194871d725d0589cda2caa6773e442f842368dc691afa907c06daf9bdd"},"schema_version":"1.0"},"canonical_sha256":"c8fb660be4ee03a5a9ec34a263b0842a7c3af8401651aba42014ad1a73bd1735","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:03.299117Z","signature_b64":"+NL9mGWAsfWO+dgiWvn2MGQg0J1pQuPttsv0dYwpkUd5eocXsp4Kw7imkFGMRkdqXXY5RoywCwZBKkJaH9jBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8fb660be4ee03a5a9ec34a263b0842a7c3af8401651aba42014ad1a73bd1735","last_reissued_at":"2026-06-09T02:08:03.298209Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:03.298209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.09153","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":"2026-06-09T02:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"70sNC56HB577oNmKa0N/XNP+ig0cQBLQy1p1tJmq9T+9PuhTIWzihSDAm82zSvVmXv/ce44lEXS35021JINNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:14:37.649735Z"},"content_sha256":"dbb25cdc74f3043743cecab3c2b0bdd0a7ef95b2b0f99d9c57437e9204e02726","schema_version":"1.0","event_id":"sha256:dbb25cdc74f3043743cecab3c2b0bdd0a7ef95b2b0f99d9c57437e9204e02726"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZD5WMC7E5YB2LKPMGSRGHMEEFJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Asymptotic Distribution of Sample Canonical Directions in Gaussian Spiked High-dimensional CCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Jiang Hu, Zhangni Pu, Zhangxiao Zhuo","submitted_at":"2026-06-08T07:46:09Z","abstract_excerpt":"This paper studies the asymptotic behavior of sample canonical directions in a finite-rank spiked high-dimensional canonical correlation analysis model under a Gaussian population assumption. Under the asymptotic regime in which the dimensions of the two data blocks grow proportionally with the sample size, sample canonical directions are generally not consistent estimators of their population counterparts, even when the corresponding sample canonical correlations separate from the bulk spectrum. To quantify directional recovery, we investigate the squared alignment between a sample canonical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09153","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/2606.09153/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":"2026-06-09T02:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RMqrOfB7rlIet63gpVUerM2ASLKKtFNPTISrlJZXu+5Ncn5zP6y2xn6ugfe7P1WTIfa0BwzyBghqA6CDFpcyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:14:37.650200Z"},"content_sha256":"1592d5938f36d3d5df49256d8cdc5b0da9834a6ff22953bf04417eabeae2d966","schema_version":"1.0","event_id":"sha256:1592d5938f36d3d5df49256d8cdc5b0da9834a6ff22953bf04417eabeae2d966"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZD5WMC7E5YB2LKPMGSRGHMEEFJ/bundle.json","state_url":"https://pith.science/pith/ZD5WMC7E5YB2LKPMGSRGHMEEFJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZD5WMC7E5YB2LKPMGSRGHMEEFJ/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":"2026-07-04T18:14:37Z","links":{"resolver":"https://pith.science/pith/ZD5WMC7E5YB2LKPMGSRGHMEEFJ","bundle":"https://pith.science/pith/ZD5WMC7E5YB2LKPMGSRGHMEEFJ/bundle.json","state":"https://pith.science/pith/ZD5WMC7E5YB2LKPMGSRGHMEEFJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZD5WMC7E5YB2LKPMGSRGHMEEFJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZD5WMC7E5YB2LKPMGSRGHMEEFJ","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":"5c2b69194871d725d0589cda2caa6773e442f842368dc691afa907c06daf9bdd","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T07:46:09Z","title_canon_sha256":"864d192f48ed4e64b5f53829fe88d5e4958fe424dbdcf3fbc83fbc0e024abe73"},"schema_version":"1.0","source":{"id":"2606.09153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09153","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09153v1","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09153","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZD5WMC7E5YB2","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZD5WMC7E5YB2LKPM","created_at":"2026-06-09T02:08:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZD5WMC7E","created_at":"2026-06-09T02:08:03Z"}],"graph_snapshots":[{"event_id":"sha256:1592d5938f36d3d5df49256d8cdc5b0da9834a6ff22953bf04417eabeae2d966","target":"graph","created_at":"2026-06-09T02:08:03Z","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/2606.09153/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the asymptotic behavior of sample canonical directions in a finite-rank spiked high-dimensional canonical correlation analysis model under a Gaussian population assumption. Under the asymptotic regime in which the dimensions of the two data blocks grow proportionally with the sample size, sample canonical directions are generally not consistent estimators of their population counterparts, even when the corresponding sample canonical correlations separate from the bulk spectrum. To quantify directional recovery, we investigate the squared alignment between a sample canonical ","authors_text":"Jiang Hu, Zhangni Pu, Zhangxiao Zhuo","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T07:46:09Z","title":"The Asymptotic Distribution of Sample Canonical Directions in Gaussian Spiked High-dimensional CCA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09153","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:dbb25cdc74f3043743cecab3c2b0bdd0a7ef95b2b0f99d9c57437e9204e02726","target":"record","created_at":"2026-06-09T02:08:03Z","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":"5c2b69194871d725d0589cda2caa6773e442f842368dc691afa907c06daf9bdd","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-08T07:46:09Z","title_canon_sha256":"864d192f48ed4e64b5f53829fe88d5e4958fe424dbdcf3fbc83fbc0e024abe73"},"schema_version":"1.0","source":{"id":"2606.09153","kind":"arxiv","version":1}},"canonical_sha256":"c8fb660be4ee03a5a9ec34a263b0842a7c3af8401651aba42014ad1a73bd1735","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8fb660be4ee03a5a9ec34a263b0842a7c3af8401651aba42014ad1a73bd1735","first_computed_at":"2026-06-09T02:08:03.298209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:03.298209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+NL9mGWAsfWO+dgiWvn2MGQg0J1pQuPttsv0dYwpkUd5eocXsp4Kw7imkFGMRkdqXXY5RoywCwZBKkJaH9jBAw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:03.299117Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbb25cdc74f3043743cecab3c2b0bdd0a7ef95b2b0f99d9c57437e9204e02726","sha256:1592d5938f36d3d5df49256d8cdc5b0da9834a6ff22953bf04417eabeae2d966"],"state_sha256":"bfdec1b713eb664ed2c2955ac4596cec9f2a2ddba62813513652b85a39656730"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tms6J6uCGGWehLqFtaH+kRQQZjWjEGmIXplRoeP+c+nW0LEXpkuNlNMH9Y0Y/UrR4upizz+FFbQtnGFvf4vuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T18:14:37.652658Z","bundle_sha256":"a9389f9f0e66ec5a71de98cd3c83588b3c95bf7b9a405df80d7186471a4ebc98"}}