{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QQORAXNKVCVUVO2GMJLIR2BVNH","short_pith_number":"pith:QQORAXNK","canonical_record":{"source":{"id":"2401.11940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-22T13:30:11Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"507a3f914685a5f4005beb4cbec22c0394c04cf2fd919a5ba347cb8ee902bf83","abstract_canon_sha256":"5ee99ea80ffaa0190b256ccd1650e6682393737e157267e720d6e977ae734afc"},"schema_version":"1.0"},"canonical_sha256":"841d105daaa8ab4abb46625688e83569e75d4d51f9e3ec6eedf508b2fddb2aa9","source":{"kind":"arxiv","id":"2401.11940","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.11940","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"arxiv_version","alias_value":"2401.11940v3","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.11940","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"pith_short_12","alias_value":"QQORAXNKVCVU","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"pith_short_16","alias_value":"QQORAXNKVCVUVO2G","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"pith_short_8","alias_value":"QQORAXNK","created_at":"2026-07-05T09:59:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QQORAXNKVCVUVO2GMJLIR2BVNH","target":"record","payload":{"canonical_record":{"source":{"id":"2401.11940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-22T13:30:11Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"507a3f914685a5f4005beb4cbec22c0394c04cf2fd919a5ba347cb8ee902bf83","abstract_canon_sha256":"5ee99ea80ffaa0190b256ccd1650e6682393737e157267e720d6e977ae734afc"},"schema_version":"1.0"},"canonical_sha256":"841d105daaa8ab4abb46625688e83569e75d4d51f9e3ec6eedf508b2fddb2aa9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:14.076155Z","signature_b64":"LbJsFUwE+2bO7LXZQ0id4XPiiwtEMaL5+WoxRS/TFszu4oDf/JMW5MD12icJYIhQLzUhN6HWaoXRs2RSN2SpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"841d105daaa8ab4abb46625688e83569e75d4d51f9e3ec6eedf508b2fddb2aa9","last_reissued_at":"2026-07-05T09:59:14.075668Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:14.075668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.11940","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:59:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1DKktCdk/YSF9dOX5/H/BGc5xSayx+JcG21VVi+hjnG1VjquUwHcr7XWZ4lvYdR3d5kamjbzOdjXofGKzUhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T16:54:20.252561Z"},"content_sha256":"7c5bbd5cf5a68dc753fb3678c3dca8fcfa597a103607b9ff103d10cb77323ea3","schema_version":"1.0","event_id":"sha256:7c5bbd5cf5a68dc753fb3678c3dca8fcfa597a103607b9ff103d10cb77323ea3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QQORAXNKVCVUVO2GMJLIR2BVNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Xi-Le Zhao, Yandong Tang, Yao Wang, Zhi Han, Zhiyu Liu","submitted_at":"2024-01-22T13:30:11Z","abstract_excerpt":"This paper considers the problem of recovering a tensor with an underlying low-tubal-rank structure from a small number of corrupted linear measurements. Traditional approaches tackling such a problem require the computation of tensor Singular Value Decomposition (t-SVD), that is a computationally intensive process, rendering them impractical for dealing with large-scale tensors. Aim to address this challenge, we propose an efficient and effective low-tubal-rank tensor recovery method based on a factorization procedure akin to the Burer-Monteiro (BM) method. Precisely, our fundamental approach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.11940","kind":"arxiv","version":3},"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/2401.11940/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":"2026-07-05T09:59:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q5ZJDQybXyCKXFF31rQWQ2fESwXbB7d5f7JUIaBhIJDjvPkQMJP7aojMP1TSFgfEiV3x88aAvshT5UJp6JdrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T16:54:20.253222Z"},"content_sha256":"67022cc5ecfece93d23d661c7db69197cca04f5141cbf592888f50d79e47bba6","schema_version":"1.0","event_id":"sha256:67022cc5ecfece93d23d661c7db69197cca04f5141cbf592888f50d79e47bba6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQORAXNKVCVUVO2GMJLIR2BVNH/bundle.json","state_url":"https://pith.science/pith/QQORAXNKVCVUVO2GMJLIR2BVNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQORAXNKVCVUVO2GMJLIR2BVNH/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":"2026-08-16T16:54:20Z","links":{"resolver":"https://pith.science/pith/QQORAXNKVCVUVO2GMJLIR2BVNH","bundle":"https://pith.science/pith/QQORAXNKVCVUVO2GMJLIR2BVNH/bundle.json","state":"https://pith.science/pith/QQORAXNKVCVUVO2GMJLIR2BVNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQORAXNKVCVUVO2GMJLIR2BVNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QQORAXNKVCVUVO2GMJLIR2BVNH","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":"5ee99ea80ffaa0190b256ccd1650e6682393737e157267e720d6e977ae734afc","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-22T13:30:11Z","title_canon_sha256":"507a3f914685a5f4005beb4cbec22c0394c04cf2fd919a5ba347cb8ee902bf83"},"schema_version":"1.0","source":{"id":"2401.11940","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.11940","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"arxiv_version","alias_value":"2401.11940v3","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.11940","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"pith_short_12","alias_value":"QQORAXNKVCVU","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"pith_short_16","alias_value":"QQORAXNKVCVUVO2G","created_at":"2026-07-05T09:59:14Z"},{"alias_kind":"pith_short_8","alias_value":"QQORAXNK","created_at":"2026-07-05T09:59:14Z"}],"graph_snapshots":[{"event_id":"sha256:67022cc5ecfece93d23d661c7db69197cca04f5141cbf592888f50d79e47bba6","target":"graph","created_at":"2026-07-05T09:59:14Z","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/2401.11940/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper considers the problem of recovering a tensor with an underlying low-tubal-rank structure from a small number of corrupted linear measurements. Traditional approaches tackling such a problem require the computation of tensor Singular Value Decomposition (t-SVD), that is a computationally intensive process, rendering them impractical for dealing with large-scale tensors. Aim to address this challenge, we propose an efficient and effective low-tubal-rank tensor recovery method based on a factorization procedure akin to the Burer-Monteiro (BM) method. Precisely, our fundamental approach","authors_text":"Xi-Le Zhao, Yandong Tang, Yao Wang, Zhi Han, Zhiyu Liu","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-22T13:30:11Z","title":"Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.11940","kind":"arxiv","version":3},"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":"sha256:7c5bbd5cf5a68dc753fb3678c3dca8fcfa597a103607b9ff103d10cb77323ea3","target":"record","created_at":"2026-07-05T09:59:14Z","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":"5ee99ea80ffaa0190b256ccd1650e6682393737e157267e720d6e977ae734afc","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-22T13:30:11Z","title_canon_sha256":"507a3f914685a5f4005beb4cbec22c0394c04cf2fd919a5ba347cb8ee902bf83"},"schema_version":"1.0","source":{"id":"2401.11940","kind":"arxiv","version":3}},"canonical_sha256":"841d105daaa8ab4abb46625688e83569e75d4d51f9e3ec6eedf508b2fddb2aa9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"841d105daaa8ab4abb46625688e83569e75d4d51f9e3ec6eedf508b2fddb2aa9","first_computed_at":"2026-07-05T09:59:14.075668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:59:14.075668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LbJsFUwE+2bO7LXZQ0id4XPiiwtEMaL5+WoxRS/TFszu4oDf/JMW5MD12icJYIhQLzUhN6HWaoXRs2RSN2SpAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:59:14.076155Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.11940","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c5bbd5cf5a68dc753fb3678c3dca8fcfa597a103607b9ff103d10cb77323ea3","sha256:67022cc5ecfece93d23d661c7db69197cca04f5141cbf592888f50d79e47bba6"],"state_sha256":"576a194f7dd72b51ed9300d106858a5fdef42033dd121096fdc5993b2f7094bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNvA7szdYarV0eEnCYJtnvR0+0DD397sYaSNscjos8fsey8YhKtnpJ3Cr33tN0SamrvKcH5Ir34olLImhUJTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T16:54:20.257981Z","bundle_sha256":"91815b5b55ec0acae9f98fe5f53fc34cef2780399df2fccd7d7dcc49bf92c1ee"}}