{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QRS3EBEBGECP7PXJC5T52FRNV6","short_pith_number":"pith:QRS3EBEB","canonical_record":{"source":{"id":"2508.07553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-11T02:26:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1e4edb29e0a012d61320f83635d13d1d42cb903a549f5dbac84c2298398f7f31","abstract_canon_sha256":"b334905e2d9b9fbd666df010e10a72c1d0548ed3a02bc66235b92dea59b6d115"},"schema_version":"1.0"},"canonical_sha256":"8465b204813104ffbee91767dd162daf97fe4c820130863e4c949e57e28d5790","source":{"kind":"arxiv","id":"2508.07553","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07553","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07553v1","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07553","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"QRS3EBEBGECP","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"pith_short_16","alias_value":"QRS3EBEBGECP7PXJ","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"pith_short_8","alias_value":"QRS3EBEB","created_at":"2026-07-05T11:51:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QRS3EBEBGECP7PXJC5T52FRNV6","target":"record","payload":{"canonical_record":{"source":{"id":"2508.07553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-11T02:26:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1e4edb29e0a012d61320f83635d13d1d42cb903a549f5dbac84c2298398f7f31","abstract_canon_sha256":"b334905e2d9b9fbd666df010e10a72c1d0548ed3a02bc66235b92dea59b6d115"},"schema_version":"1.0"},"canonical_sha256":"8465b204813104ffbee91767dd162daf97fe4c820130863e4c949e57e28d5790","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:51:48.224267Z","signature_b64":"2geE+yMP6LFlo9j4zGNgK8za3slWFIKMXXi3RcgXi+sExczC22ZIAmFg0OWIeHDYh+AlgpcfonG0Gyq6CHK+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8465b204813104ffbee91767dd162daf97fe4c820130863e4c949e57e28d5790","last_reissued_at":"2026-07-05T11:51:48.223827Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:51:48.223827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.07553","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":"2026-07-05T11:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vd2g8WDpvr3Eo9w1cbJmE+yCIfPxN+lfHx+uysnB1IocWJKWj9trM5JdKqoravve9owivY3o5+tGflmPOafMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:49:40.100389Z"},"content_sha256":"371d1b1f3e45be8bd9cd74f9628572c239be16778edd5f77763a5fa7fdab5141","schema_version":"1.0","event_id":"sha256:371d1b1f3e45be8bd9cd74f9628572c239be16778edd5f77763a5fa7fdab5141"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QRS3EBEBGECP7PXJC5T52FRNV6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient adaptive randomized algorithms for fixed-threshold low-rank matrix approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Qiaohua Liu, Yuejuan Yu","submitted_at":"2025-08-11T02:26:29Z","abstract_excerpt":"The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized rank-revealing algorithm of the data matrix $A$, in which the basis matrix $Q$ of the approximate range space is adaptively built block by block, through a recursive deflation procedure on $A$. Detailed analysis of randomized projection schemes are provided to analyze the numerical rank reduce during the deflation. The provable spectral and Frobenius error $(I-QQ^T)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07553","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/2508.07553/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":"2026-07-05T11:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"weztn5cV4bHNg6sOCegwFZJUhWcgHCGKpvvlrjc4WBUsY347OkbPE/77a84Ko4Kj6NQzuTyCXMzxF6xc5YDeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:49:40.100764Z"},"content_sha256":"2bc1e6eda6eaff4c3aa176fcf1a9df5fe05f3c731689f35fbec998691d1525f8","schema_version":"1.0","event_id":"sha256:2bc1e6eda6eaff4c3aa176fcf1a9df5fe05f3c731689f35fbec998691d1525f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QRS3EBEBGECP7PXJC5T52FRNV6/bundle.json","state_url":"https://pith.science/pith/QRS3EBEBGECP7PXJC5T52FRNV6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QRS3EBEBGECP7PXJC5T52FRNV6/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":"2026-07-07T14:49:40Z","links":{"resolver":"https://pith.science/pith/QRS3EBEBGECP7PXJC5T52FRNV6","bundle":"https://pith.science/pith/QRS3EBEBGECP7PXJC5T52FRNV6/bundle.json","state":"https://pith.science/pith/QRS3EBEBGECP7PXJC5T52FRNV6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QRS3EBEBGECP7PXJC5T52FRNV6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QRS3EBEBGECP7PXJC5T52FRNV6","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":"b334905e2d9b9fbd666df010e10a72c1d0548ed3a02bc66235b92dea59b6d115","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-11T02:26:29Z","title_canon_sha256":"1e4edb29e0a012d61320f83635d13d1d42cb903a549f5dbac84c2298398f7f31"},"schema_version":"1.0","source":{"id":"2508.07553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.07553","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"2508.07553v1","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.07553","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"QRS3EBEBGECP","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"pith_short_16","alias_value":"QRS3EBEBGECP7PXJ","created_at":"2026-07-05T11:51:48Z"},{"alias_kind":"pith_short_8","alias_value":"QRS3EBEB","created_at":"2026-07-05T11:51:48Z"}],"graph_snapshots":[{"event_id":"sha256:2bc1e6eda6eaff4c3aa176fcf1a9df5fe05f3c731689f35fbec998691d1525f8","target":"graph","created_at":"2026-07-05T11:51:48Z","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/2508.07553/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized rank-revealing algorithm of the data matrix $A$, in which the basis matrix $Q$ of the approximate range space is adaptively built block by block, through a recursive deflation procedure on $A$. Detailed analysis of randomized projection schemes are provided to analyze the numerical rank reduce during the deflation. The provable spectral and Frobenius error $(I-QQ^T)","authors_text":"Qiaohua Liu, Yuejuan Yu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-11T02:26:29Z","title":"Efficient adaptive randomized algorithms for fixed-threshold low-rank matrix approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.07553","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":"sha256:371d1b1f3e45be8bd9cd74f9628572c239be16778edd5f77763a5fa7fdab5141","target":"record","created_at":"2026-07-05T11:51:48Z","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":"b334905e2d9b9fbd666df010e10a72c1d0548ed3a02bc66235b92dea59b6d115","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-11T02:26:29Z","title_canon_sha256":"1e4edb29e0a012d61320f83635d13d1d42cb903a549f5dbac84c2298398f7f31"},"schema_version":"1.0","source":{"id":"2508.07553","kind":"arxiv","version":1}},"canonical_sha256":"8465b204813104ffbee91767dd162daf97fe4c820130863e4c949e57e28d5790","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8465b204813104ffbee91767dd162daf97fe4c820130863e4c949e57e28d5790","first_computed_at":"2026-07-05T11:51:48.223827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:51:48.223827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2geE+yMP6LFlo9j4zGNgK8za3slWFIKMXXi3RcgXi+sExczC22ZIAmFg0OWIeHDYh+AlgpcfonG0Gyq6CHK+Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:51:48.224267Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.07553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:371d1b1f3e45be8bd9cd74f9628572c239be16778edd5f77763a5fa7fdab5141","sha256:2bc1e6eda6eaff4c3aa176fcf1a9df5fe05f3c731689f35fbec998691d1525f8"],"state_sha256":"b98777defe0d0ef5e82496e2ac802cc79fc67c389e524f801eec023a8c4b691c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/5OOEFHrTRHKxgRSdC2Z7C7kfNCWRgmZu2GK6cVdGLssx8gdAi5+5iM/kZruyAyvDZX5djLqu4dbuVVYkgaSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:49:40.102692Z","bundle_sha256":"df4c86ed8171807f15761dba248dfc43f21cce63a8bafd8110da267975e935fb"}}