{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FO6ZDHK3GAHF3SFHSYKHDAY6B5","short_pith_number":"pith:FO6ZDHK3","canonical_record":{"source":{"id":"1906.01774","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-06-05T01:16:45Z","cross_cats_sorted":["cs.NA","math.IT","math.NA"],"title_canon_sha256":"1c78093825676430e1769268c920227c75dcf73e4e2f1fc0256b8f78fef2e8ad","abstract_canon_sha256":"7f5805cb4b170d34ceae2c47c9e632e36a676fd5236ce2739a77afeb39d55ebe"},"schema_version":"1.0"},"canonical_sha256":"2bbd919d5b300e5dc8a7961471831e0f430ac88d4774c5850a8b092e51a93ebc","source":{"kind":"arxiv","id":"1906.01774","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01774","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01774v2","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01774","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"FO6ZDHK3GAHF","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"FO6ZDHK3GAHF3SFH","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"FO6ZDHK3","created_at":"2026-06-03T21:05:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FO6ZDHK3GAHF3SFHSYKHDAY6B5","target":"record","payload":{"canonical_record":{"source":{"id":"1906.01774","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-06-05T01:16:45Z","cross_cats_sorted":["cs.NA","math.IT","math.NA"],"title_canon_sha256":"1c78093825676430e1769268c920227c75dcf73e4e2f1fc0256b8f78fef2e8ad","abstract_canon_sha256":"7f5805cb4b170d34ceae2c47c9e632e36a676fd5236ce2739a77afeb39d55ebe"},"schema_version":"1.0"},"canonical_sha256":"2bbd919d5b300e5dc8a7961471831e0f430ac88d4774c5850a8b092e51a93ebc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T21:05:57.661462Z","signature_b64":"Izsp2POwdiNaNwQ+eP5XwK0jo8qSPrp4s0IHJLtTCkBy4gojoix8sEjjkBXRUq+DKny8WMwtiytXE+vVTZM9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bbd919d5b300e5dc8a7961471831e0f430ac88d4774c5850a8b092e51a93ebc","last_reissued_at":"2026-06-03T21:05:57.659976Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T21:05:57.659976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.01774","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":"2026-06-03T21:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rjaz+UQCFwXAw71fqJWwan53MlUY3yx6mfOuzmwEtIIGv2BYliIpi1761JzG4ejBQMZ9yxXi4zzqIbCSwlysDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:09:42.173034Z"},"content_sha256":"ff2a7f4a465be1a22ea61964e0c1e114cadba4788888f09a205f3ed61d262108","schema_version":"1.0","event_id":"sha256:ff2a7f4a465be1a22ea61964e0c1e114cadba4788888f09a205f3ed61d262108"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FO6ZDHK3GAHF3SFHSYKHDAY6B5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"RIP-based performance guarantee for low-tubal-rank tensor recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Feng Zhang, Jianjun Wang, Jianwen Huang, Wendong Wang, Yao Wang","submitted_at":"2019-06-05T01:16:45Z","abstract_excerpt":"The essential task of tensor data analysis focuses on the tensor decomposition and the corresponding notion of rank. In this paper, by introducing the notion of tensor Singular Value Decomposition (t-SVD), we establish a Regularized Tensor Nuclear Norm Minimization (RTNNM) model for low-tubal-rank tensor recovery. As we know that many variants of the Restricted Isometry Property (RIP) have proven to be crucial analysis tools for sparse recovery. In the t-SVD framework, we initiatively define a novel tensor Restricted Isometry Property (t-RIP). Furthermore, we show that any third-order tensor $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01774","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/1906.01774/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":"2026-06-03T21:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OqXN9qNNys7P5XqfftP6CBDI9H39dyJh62OKfeEDz3+10Yj0RIKjhZrnsczSlKguODnH/Rybur5MgFD0Q4GJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:09:42.173424Z"},"content_sha256":"86e4c9e1bcc14e16fabac1ba8adbfc1d6eaba95022914f67bd8f2c938ee52070","schema_version":"1.0","event_id":"sha256:86e4c9e1bcc14e16fabac1ba8adbfc1d6eaba95022914f67bd8f2c938ee52070"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FO6ZDHK3GAHF3SFHSYKHDAY6B5/bundle.json","state_url":"https://pith.science/pith/FO6ZDHK3GAHF3SFHSYKHDAY6B5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FO6ZDHK3GAHF3SFHSYKHDAY6B5/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":"2026-07-02T06:09:42Z","links":{"resolver":"https://pith.science/pith/FO6ZDHK3GAHF3SFHSYKHDAY6B5","bundle":"https://pith.science/pith/FO6ZDHK3GAHF3SFHSYKHDAY6B5/bundle.json","state":"https://pith.science/pith/FO6ZDHK3GAHF3SFHSYKHDAY6B5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FO6ZDHK3GAHF3SFHSYKHDAY6B5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FO6ZDHK3GAHF3SFHSYKHDAY6B5","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":"7f5805cb4b170d34ceae2c47c9e632e36a676fd5236ce2739a77afeb39d55ebe","cross_cats_sorted":["cs.NA","math.IT","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-06-05T01:16:45Z","title_canon_sha256":"1c78093825676430e1769268c920227c75dcf73e4e2f1fc0256b8f78fef2e8ad"},"schema_version":"1.0","source":{"id":"1906.01774","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01774","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01774v2","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01774","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"FO6ZDHK3GAHF","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"FO6ZDHK3GAHF3SFH","created_at":"2026-06-03T21:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"FO6ZDHK3","created_at":"2026-06-03T21:05:57Z"}],"graph_snapshots":[{"event_id":"sha256:86e4c9e1bcc14e16fabac1ba8adbfc1d6eaba95022914f67bd8f2c938ee52070","target":"graph","created_at":"2026-06-03T21:05:57Z","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/1906.01774/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The essential task of tensor data analysis focuses on the tensor decomposition and the corresponding notion of rank. In this paper, by introducing the notion of tensor Singular Value Decomposition (t-SVD), we establish a Regularized Tensor Nuclear Norm Minimization (RTNNM) model for low-tubal-rank tensor recovery. As we know that many variants of the Restricted Isometry Property (RIP) have proven to be crucial analysis tools for sparse recovery. In the t-SVD framework, we initiatively define a novel tensor Restricted Isometry Property (t-RIP). Furthermore, we show that any third-order tensor $","authors_text":"Feng Zhang, Jianjun Wang, Jianwen Huang, Wendong Wang, Yao Wang","cross_cats":["cs.NA","math.IT","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-06-05T01:16:45Z","title":"RIP-based performance guarantee for low-tubal-rank tensor recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01774","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:ff2a7f4a465be1a22ea61964e0c1e114cadba4788888f09a205f3ed61d262108","target":"record","created_at":"2026-06-03T21:05:57Z","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":"7f5805cb4b170d34ceae2c47c9e632e36a676fd5236ce2739a77afeb39d55ebe","cross_cats_sorted":["cs.NA","math.IT","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-06-05T01:16:45Z","title_canon_sha256":"1c78093825676430e1769268c920227c75dcf73e4e2f1fc0256b8f78fef2e8ad"},"schema_version":"1.0","source":{"id":"1906.01774","kind":"arxiv","version":2}},"canonical_sha256":"2bbd919d5b300e5dc8a7961471831e0f430ac88d4774c5850a8b092e51a93ebc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bbd919d5b300e5dc8a7961471831e0f430ac88d4774c5850a8b092e51a93ebc","first_computed_at":"2026-06-03T21:05:57.659976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T21:05:57.659976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Izsp2POwdiNaNwQ+eP5XwK0jo8qSPrp4s0IHJLtTCkBy4gojoix8sEjjkBXRUq+DKny8WMwtiytXE+vVTZM9Bw==","signature_status":"signed_v1","signed_at":"2026-06-03T21:05:57.661462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01774","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff2a7f4a465be1a22ea61964e0c1e114cadba4788888f09a205f3ed61d262108","sha256:86e4c9e1bcc14e16fabac1ba8adbfc1d6eaba95022914f67bd8f2c938ee52070"],"state_sha256":"3e916a8743071cd38a184f55898101767f24d9aa4a78b0b92f8c617a8e78ee0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oXuOv1GHe9mxNtoSfPMNEIPvb1DL9Ugd7ZO0C7HGCmoEQXSKjGfIfobzFyI7tQhWYA47RPe9nlYTE+bAcxYjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T06:09:42.175462Z","bundle_sha256":"3271337e320e16d12d46dfdf0dc5f8204f611e374ca95b6495937b72c89b6977"}}