{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6NPQI3TCL7DHVXXTF6KEPIMOV5","short_pith_number":"pith:6NPQI3TC","canonical_record":{"source":{"id":"1902.03056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-08T12:33:08Z","cross_cats_sorted":["cs.NA","math.NA","math.OC","stat.TH"],"title_canon_sha256":"cf3b300277a268e451915da840815e71d3c4324559b87482d6ccc8123abb9ba0","abstract_canon_sha256":"8f59e4e92456d0717b0505e13723451186377f6f21f53645599d2eec1963bc0b"},"schema_version":"1.0"},"canonical_sha256":"f35f046e625fc67adef32f9447a18eaf4b844f7e343bfbb89aaf5972fbcdfe01","source":{"kind":"arxiv","id":"1902.03056","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03056","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03056v1","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03056","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"pith_short_12","alias_value":"6NPQI3TCL7DH","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"pith_short_16","alias_value":"6NPQI3TCL7DHVXXT","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"pith_short_8","alias_value":"6NPQI3TC","created_at":"2026-06-04T20:13:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6NPQI3TCL7DHVXXTF6KEPIMOV5","target":"record","payload":{"canonical_record":{"source":{"id":"1902.03056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-08T12:33:08Z","cross_cats_sorted":["cs.NA","math.NA","math.OC","stat.TH"],"title_canon_sha256":"cf3b300277a268e451915da840815e71d3c4324559b87482d6ccc8123abb9ba0","abstract_canon_sha256":"8f59e4e92456d0717b0505e13723451186377f6f21f53645599d2eec1963bc0b"},"schema_version":"1.0"},"canonical_sha256":"f35f046e625fc67adef32f9447a18eaf4b844f7e343bfbb89aaf5972fbcdfe01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:52.668110Z","signature_b64":"LW2BP36zRrfJL7nGIhvbEdDWJb61xaOKNnrfcJkp/xNpeJrDG9FyUxVpcwXYGo6td9fVhYN5hYpI4Hu/1H4cDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f35f046e625fc67adef32f9447a18eaf4b844f7e343bfbb89aaf5972fbcdfe01","last_reissued_at":"2026-06-04T20:13:52.667610Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:52.667610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.03056","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":"2026-06-04T20:13:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxEGxWO96saa6JvW5K8JIGezUOHcOF2WREdkwwauBGY+kiSg8+g9Yg33agmiRdTBH/CdHwatW/rZACxHwkPjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:54:17.441421Z"},"content_sha256":"19a3c30dfcdc573433a8c8877e2c7ee6ef3a14991c990da56d9e320b8bd684e7","schema_version":"1.0","event_id":"sha256:19a3c30dfcdc573433a8c8877e2c7ee6ef3a14991c990da56d9e320b8bd684e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6NPQI3TCL7DHVXXTF6KEPIMOV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bernstein Concentration Inequalities for Tensors via Einstein Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"L. Qi, Ph. L. Toint, Z. Luo","submitted_at":"2019-02-08T12:33:08Z","abstract_excerpt":"A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established between matrices and tensors, in turn allowing exploitation of existing results for the former."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03056","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/1902.03056/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":"2026-06-04T20:13:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KjrEUmsrQyaoxtL3BY9L0UXkQeH+tTDO9hd1MFkzQvp2Mo6fbRJ1PcOMlMe+G+Al4AKrjtG/pN1Mi/uzGHZ4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:54:17.441812Z"},"content_sha256":"d7f6907fa0c61157ea89fff71b4bf2adb6533ada9ee07bcdc329118ab57c6219","schema_version":"1.0","event_id":"sha256:d7f6907fa0c61157ea89fff71b4bf2adb6533ada9ee07bcdc329118ab57c6219"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NPQI3TCL7DHVXXTF6KEPIMOV5/bundle.json","state_url":"https://pith.science/pith/6NPQI3TCL7DHVXXTF6KEPIMOV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NPQI3TCL7DHVXXTF6KEPIMOV5/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":"2026-06-06T18:54:17Z","links":{"resolver":"https://pith.science/pith/6NPQI3TCL7DHVXXTF6KEPIMOV5","bundle":"https://pith.science/pith/6NPQI3TCL7DHVXXTF6KEPIMOV5/bundle.json","state":"https://pith.science/pith/6NPQI3TCL7DHVXXTF6KEPIMOV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NPQI3TCL7DHVXXTF6KEPIMOV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6NPQI3TCL7DHVXXTF6KEPIMOV5","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":"8f59e4e92456d0717b0505e13723451186377f6f21f53645599d2eec1963bc0b","cross_cats_sorted":["cs.NA","math.NA","math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-08T12:33:08Z","title_canon_sha256":"cf3b300277a268e451915da840815e71d3c4324559b87482d6ccc8123abb9ba0"},"schema_version":"1.0","source":{"id":"1902.03056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03056","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03056v1","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03056","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"pith_short_12","alias_value":"6NPQI3TCL7DH","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"pith_short_16","alias_value":"6NPQI3TCL7DHVXXT","created_at":"2026-06-04T20:13:52Z"},{"alias_kind":"pith_short_8","alias_value":"6NPQI3TC","created_at":"2026-06-04T20:13:52Z"}],"graph_snapshots":[{"event_id":"sha256:d7f6907fa0c61157ea89fff71b4bf2adb6533ada9ee07bcdc329118ab57c6219","target":"graph","created_at":"2026-06-04T20:13:52Z","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/1902.03056/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established between matrices and tensors, in turn allowing exploitation of existing results for the former.","authors_text":"L. Qi, Ph. L. Toint, Z. Luo","cross_cats":["cs.NA","math.NA","math.OC","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-08T12:33:08Z","title":"Bernstein Concentration Inequalities for Tensors via Einstein Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03056","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":"sha256:19a3c30dfcdc573433a8c8877e2c7ee6ef3a14991c990da56d9e320b8bd684e7","target":"record","created_at":"2026-06-04T20:13:52Z","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":"8f59e4e92456d0717b0505e13723451186377f6f21f53645599d2eec1963bc0b","cross_cats_sorted":["cs.NA","math.NA","math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-08T12:33:08Z","title_canon_sha256":"cf3b300277a268e451915da840815e71d3c4324559b87482d6ccc8123abb9ba0"},"schema_version":"1.0","source":{"id":"1902.03056","kind":"arxiv","version":1}},"canonical_sha256":"f35f046e625fc67adef32f9447a18eaf4b844f7e343bfbb89aaf5972fbcdfe01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f35f046e625fc67adef32f9447a18eaf4b844f7e343bfbb89aaf5972fbcdfe01","first_computed_at":"2026-06-04T20:13:52.667610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:13:52.667610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LW2BP36zRrfJL7nGIhvbEdDWJb61xaOKNnrfcJkp/xNpeJrDG9FyUxVpcwXYGo6td9fVhYN5hYpI4Hu/1H4cDQ==","signature_status":"signed_v1","signed_at":"2026-06-04T20:13:52.668110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19a3c30dfcdc573433a8c8877e2c7ee6ef3a14991c990da56d9e320b8bd684e7","sha256:d7f6907fa0c61157ea89fff71b4bf2adb6533ada9ee07bcdc329118ab57c6219"],"state_sha256":"eb9a5a925c3e418a5ef71276844ea37e94b5b36b1f05f61620c005041634afa8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AZAXJTVBNcebGx0BOIi6dELc65oEz5vUnVnqlf9w2mYshhkRE8Kkr/QzXAbwT3xbXZPARITNlNr7vcxU1BOxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:54:17.443987Z","bundle_sha256":"b51d7b28d08ae1d079010cb23d79ab3066993e6f30a1fa1be40abc1e20d67b23"}}