{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VNSS4LR2COK722AQHZQN47F4FQ","short_pith_number":"pith:VNSS4LR2","canonical_record":{"source":{"id":"2505.23046","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-29T03:42:03Z","cross_cats_sorted":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"04632a4fac78f804e61635a0988259b7058e01437ed2ae740652bc57c947cd09","abstract_canon_sha256":"9758b340cb50492a14f08dcef8eb409d4c39cd4ee104c76ee17d679acaffbae2"},"schema_version":"1.0"},"canonical_sha256":"ab652e2e3a1395fd68103e60de7cbc2c12eb5939314e2a55f96425b35bdeafe7","source":{"kind":"arxiv","id":"2505.23046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.23046","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"2505.23046v1","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23046","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"VNSS4LR2COK7","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"pith_short_16","alias_value":"VNSS4LR2COK722AQ","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"pith_short_8","alias_value":"VNSS4LR2","created_at":"2026-07-05T11:11:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VNSS4LR2COK722AQHZQN47F4FQ","target":"record","payload":{"canonical_record":{"source":{"id":"2505.23046","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-29T03:42:03Z","cross_cats_sorted":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"04632a4fac78f804e61635a0988259b7058e01437ed2ae740652bc57c947cd09","abstract_canon_sha256":"9758b340cb50492a14f08dcef8eb409d4c39cd4ee104c76ee17d679acaffbae2"},"schema_version":"1.0"},"canonical_sha256":"ab652e2e3a1395fd68103e60de7cbc2c12eb5939314e2a55f96425b35bdeafe7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:54.320409Z","signature_b64":"fb5yv7ydXrdWAWbpeVl5Fk+JT81kpl83Q7Wiwfeo+SUaSKOZyiIJZOa3cuxdVcgeMGDIIqYm26qZaylmeLTNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab652e2e3a1395fd68103e60de7cbc2c12eb5939314e2a55f96425b35bdeafe7","last_reissued_at":"2026-07-05T11:11:54.319805Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:54.319805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.23046","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":"2026-07-05T11:11:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ii8zqHgYzMA2e6TaTokVQ2zWVDofCJqBZA+KkpNxZ0LJUEVILOzHLcvZNDSkaLXBpHueJ1ZsLbdBSY/T1JO6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:42:47.141102Z"},"content_sha256":"106a9d0ce8957355928fc3ea1516b7f20a76f39ca8550694ff55f27e053b39f9","schema_version":"1.0","event_id":"sha256:106a9d0ce8957355928fc3ea1516b7f20a76f39ca8550694ff55f27e053b39f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VNSS4LR2COK722AQHZQN47F4FQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Revisit CP Tensor Decomposition: Statistical Optimality and Fast Convergence","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"primary_cat":"stat.ME","authors_text":"Anru R. Zhang, Julien Chhor, Olga Klopp, Runshi Tang","submitted_at":"2025-05-29T03:42:03Z","abstract_excerpt":"Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and empirical success, its theoretical foundation, particularly regarding statistical optimality and convergence behavior, remain underdeveloped, especially in noisy, non-orthogonal, and higher-rank settings.\n  In this work, we revisit CP tensor decomposition from a statistical perspective and provide a comprehensive theoretical analysis of ALS under a signal-pl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23046","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/2505.23046/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":"2026-07-05T11:11:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDeWaB/wZbco5Nup2Xxu+BUZIkftHzORzrsnCtZ1SnSGr00X0ObaKFatrcdOpSDkhQjM0I26FU6I0gAiV44SCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:42:47.141629Z"},"content_sha256":"97a9f60a50e1bf75086778c7f01a6e04280b18e06e338ea3bebb077833fc773b","schema_version":"1.0","event_id":"sha256:97a9f60a50e1bf75086778c7f01a6e04280b18e06e338ea3bebb077833fc773b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/bundle.json","state_url":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNSS4LR2COK722AQHZQN47F4FQ/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":"2026-08-04T02:42:47Z","links":{"resolver":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ","bundle":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/bundle.json","state":"https://pith.science/pith/VNSS4LR2COK722AQHZQN47F4FQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNSS4LR2COK722AQHZQN47F4FQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VNSS4LR2COK722AQHZQN47F4FQ","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":"9758b340cb50492a14f08dcef8eb409d4c39cd4ee104c76ee17d679acaffbae2","cross_cats_sorted":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-29T03:42:03Z","title_canon_sha256":"04632a4fac78f804e61635a0988259b7058e01437ed2ae740652bc57c947cd09"},"schema_version":"1.0","source":{"id":"2505.23046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.23046","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"arxiv_version","alias_value":"2505.23046v1","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23046","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"pith_short_12","alias_value":"VNSS4LR2COK7","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"pith_short_16","alias_value":"VNSS4LR2COK722AQ","created_at":"2026-07-05T11:11:54Z"},{"alias_kind":"pith_short_8","alias_value":"VNSS4LR2","created_at":"2026-07-05T11:11:54Z"}],"graph_snapshots":[{"event_id":"sha256:97a9f60a50e1bf75086778c7f01a6e04280b18e06e338ea3bebb077833fc773b","target":"graph","created_at":"2026-07-05T11:11:54Z","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/2505.23046/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and empirical success, its theoretical foundation, particularly regarding statistical optimality and convergence behavior, remain underdeveloped, especially in noisy, non-orthogonal, and higher-rank settings.\n  In this work, we revisit CP tensor decomposition from a statistical perspective and provide a comprehensive theoretical analysis of ALS under a signal-pl","authors_text":"Anru R. Zhang, Julien Chhor, Olga Klopp, Runshi Tang","cross_cats":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-29T03:42:03Z","title":"Revisit CP Tensor Decomposition: Statistical Optimality and Fast Convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23046","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":"sha256:106a9d0ce8957355928fc3ea1516b7f20a76f39ca8550694ff55f27e053b39f9","target":"record","created_at":"2026-07-05T11:11:54Z","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":"9758b340cb50492a14f08dcef8eb409d4c39cd4ee104c76ee17d679acaffbae2","cross_cats_sorted":["cs.NA","math.NA","math.ST","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-29T03:42:03Z","title_canon_sha256":"04632a4fac78f804e61635a0988259b7058e01437ed2ae740652bc57c947cd09"},"schema_version":"1.0","source":{"id":"2505.23046","kind":"arxiv","version":1}},"canonical_sha256":"ab652e2e3a1395fd68103e60de7cbc2c12eb5939314e2a55f96425b35bdeafe7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab652e2e3a1395fd68103e60de7cbc2c12eb5939314e2a55f96425b35bdeafe7","first_computed_at":"2026-07-05T11:11:54.319805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:54.319805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fb5yv7ydXrdWAWbpeVl5Fk+JT81kpl83Q7Wiwfeo+SUaSKOZyiIJZOa3cuxdVcgeMGDIIqYm26qZaylmeLTNAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:54.320409Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.23046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:106a9d0ce8957355928fc3ea1516b7f20a76f39ca8550694ff55f27e053b39f9","sha256:97a9f60a50e1bf75086778c7f01a6e04280b18e06e338ea3bebb077833fc773b"],"state_sha256":"46515e9ede429e9c9cf9969436ed7932756fa7d1b37afde4044931387c2d07e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PFgdxFOWIPJFwjAW4hIukfnAgTrqWTLWGtGY+CS6+oOgqK79QSTLQZzOiai6SF2M77PtaJGz+mLRGaQit76IBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T02:42:47.145340Z","bundle_sha256":"c7e5737743f4480dd902a88020431c284ac0b7eed15206a6d289e033f215e3b0"}}