{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:TIUM3BPKX4V4AAAVV5WPIBHOBU","short_pith_number":"pith:TIUM3BPK","canonical_record":{"source":{"id":"2010.02482","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2020-10-06T05:18:24Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.CO","stat.ME","stat.TH"],"title_canon_sha256":"5f5ebd1ff9ac5428ebb0c9f93aef075ef5b6fffdd2b879ffd5102e1a0190a107","abstract_canon_sha256":"32a9b93360afc34061ca1f3f7f518d8f44a8fc2c90c298e6a090a9abf135db59"},"schema_version":"1.0"},"canonical_sha256":"9a28cd85eabf2bc00015af6cf404ee0d326b5ee89d646b61d057456a517ce89f","source":{"kind":"arxiv","id":"2010.02482","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.02482","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"arxiv_version","alias_value":"2010.02482v2","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.02482","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"pith_short_12","alias_value":"TIUM3BPKX4V4","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"pith_short_16","alias_value":"TIUM3BPKX4V4AAAV","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"pith_short_8","alias_value":"TIUM3BPK","created_at":"2026-07-05T03:51:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:TIUM3BPKX4V4AAAVV5WPIBHOBU","target":"record","payload":{"canonical_record":{"source":{"id":"2010.02482","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2020-10-06T05:18:24Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.CO","stat.ME","stat.TH"],"title_canon_sha256":"5f5ebd1ff9ac5428ebb0c9f93aef075ef5b6fffdd2b879ffd5102e1a0190a107","abstract_canon_sha256":"32a9b93360afc34061ca1f3f7f518d8f44a8fc2c90c298e6a090a9abf135db59"},"schema_version":"1.0"},"canonical_sha256":"9a28cd85eabf2bc00015af6cf404ee0d326b5ee89d646b61d057456a517ce89f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:51:04.796128Z","signature_b64":"DJ/j7pybGjrFnD6FsjhjJNqyxalxjL4NsVC8UjxgDm5YSmgzvK4jfFZp17bra3GC+ElET8vM/BLHheU1QPuLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a28cd85eabf2bc00015af6cf404ee0d326b5ee89d646b61d057456a517ce89f","last_reissued_at":"2026-07-05T03:51:04.795787Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:51:04.795787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.02482","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":"2026-07-05T03:51:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hV2ZmFvno2+6SEOrOW+jtl3jsHJ56wF8ZhvF30ArLOyUBhoCDArwvv5T6li2bE1DKJV3uu/ht67bKCwCh+8gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T13:43:20.077564Z"},"content_sha256":"342a159e8d6c837668caba6f87a72614c4cc28060084bf05fc7ebdaaf3d32a80","schema_version":"1.0","event_id":"sha256:342a159e8d6c837668caba6f87a72614c4cc28060084bf05fc7ebdaaf3d32a80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:TIUM3BPKX4V4AAAVV5WPIBHOBU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","stat.CO","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Anru R. Zhang, Lili Zheng, Yazhen Wang, Yuchen Zhou","submitted_at":"2020-10-06T05:18:24Z","abstract_excerpt":"This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estimate the low tensor-train rank structure from the noisy high-order tensor observation. The proposed TTOI consists of initialization via TT-SVD (Oseledets, 2011) and new iterative backward/forward updates. We develop the general upper bound on estimation error for TTOI with the support of several new representation lemmas on tensor matricizations. By developing a matching information-theoretic lower bound, we also prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.02482","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/2010.02482/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":"2026-07-05T03:51:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WhItSmvi4wDHvrfTciiOpw0FQwgwZyoLghfmnX2v0HI4rgrFS1MzbN9WSl0np7bnp7XWaJFJuwcez3DVQzOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T13:43:20.078200Z"},"content_sha256":"21bfd599d7ff8bf7b81282504bb43fc6d3e97d0c8b8ca12013c0cc82fa972f3c","schema_version":"1.0","event_id":"sha256:21bfd599d7ff8bf7b81282504bb43fc6d3e97d0c8b8ca12013c0cc82fa972f3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIUM3BPKX4V4AAAVV5WPIBHOBU/bundle.json","state_url":"https://pith.science/pith/TIUM3BPKX4V4AAAVV5WPIBHOBU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIUM3BPKX4V4AAAVV5WPIBHOBU/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":"2026-08-11T13:43:20Z","links":{"resolver":"https://pith.science/pith/TIUM3BPKX4V4AAAVV5WPIBHOBU","bundle":"https://pith.science/pith/TIUM3BPKX4V4AAAVV5WPIBHOBU/bundle.json","state":"https://pith.science/pith/TIUM3BPKX4V4AAAVV5WPIBHOBU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIUM3BPKX4V4AAAVV5WPIBHOBU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:TIUM3BPKX4V4AAAVV5WPIBHOBU","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":"32a9b93360afc34061ca1f3f7f518d8f44a8fc2c90c298e6a090a9abf135db59","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.CO","stat.ME","stat.TH"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2020-10-06T05:18:24Z","title_canon_sha256":"5f5ebd1ff9ac5428ebb0c9f93aef075ef5b6fffdd2b879ffd5102e1a0190a107"},"schema_version":"1.0","source":{"id":"2010.02482","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.02482","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"arxiv_version","alias_value":"2010.02482v2","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.02482","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"pith_short_12","alias_value":"TIUM3BPKX4V4","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"pith_short_16","alias_value":"TIUM3BPKX4V4AAAV","created_at":"2026-07-05T03:51:04Z"},{"alias_kind":"pith_short_8","alias_value":"TIUM3BPK","created_at":"2026-07-05T03:51:04Z"}],"graph_snapshots":[{"event_id":"sha256:21bfd599d7ff8bf7b81282504bb43fc6d3e97d0c8b8ca12013c0cc82fa972f3c","target":"graph","created_at":"2026-07-05T03:51:04Z","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/2010.02482/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estimate the low tensor-train rank structure from the noisy high-order tensor observation. The proposed TTOI consists of initialization via TT-SVD (Oseledets, 2011) and new iterative backward/forward updates. We develop the general upper bound on estimation error for TTOI with the support of several new representation lemmas on tensor matricizations. By developing a matching information-theoretic lower bound, we also prov","authors_text":"Anru R. Zhang, Lili Zheng, Yazhen Wang, Yuchen Zhou","cross_cats":["cs.LG","cs.NA","math.NA","stat.CO","stat.ME","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2020-10-06T05:18:24Z","title":"Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.02482","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":"sha256:342a159e8d6c837668caba6f87a72614c4cc28060084bf05fc7ebdaaf3d32a80","target":"record","created_at":"2026-07-05T03:51:04Z","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":"32a9b93360afc34061ca1f3f7f518d8f44a8fc2c90c298e6a090a9abf135db59","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.CO","stat.ME","stat.TH"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.ST","submitted_at":"2020-10-06T05:18:24Z","title_canon_sha256":"5f5ebd1ff9ac5428ebb0c9f93aef075ef5b6fffdd2b879ffd5102e1a0190a107"},"schema_version":"1.0","source":{"id":"2010.02482","kind":"arxiv","version":2}},"canonical_sha256":"9a28cd85eabf2bc00015af6cf404ee0d326b5ee89d646b61d057456a517ce89f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a28cd85eabf2bc00015af6cf404ee0d326b5ee89d646b61d057456a517ce89f","first_computed_at":"2026-07-05T03:51:04.795787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:51:04.795787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DJ/j7pybGjrFnD6FsjhjJNqyxalxjL4NsVC8UjxgDm5YSmgzvK4jfFZp17bra3GC+ElET8vM/BLHheU1QPuLBw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:51:04.796128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.02482","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:342a159e8d6c837668caba6f87a72614c4cc28060084bf05fc7ebdaaf3d32a80","sha256:21bfd599d7ff8bf7b81282504bb43fc6d3e97d0c8b8ca12013c0cc82fa972f3c"],"state_sha256":"4ad0b9b7d6d53cbf9d7e3a51f91c52b200c4b852c3fbc2f556ef24e155bc4deb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d6OnsFAoJRqCSdJSsg2Ept5VWcOHz2Ym0BOOmP+sQ2qGCs8T9HpSqkj8w1KCplxBLAjLMi17f+aue40U4bRQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T13:43:20.086188Z","bundle_sha256":"cc5b518bbb572fc33a19a561c59ecd31825909d43ef090e9dc89b2266b4ea9a4"}}