{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SAX2Z32XCN2UG2HTV6ZHUE6QZ7","short_pith_number":"pith:SAX2Z32X","canonical_record":{"source":{"id":"1808.02654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-08T08:12:09Z","cross_cats_sorted":[],"title_canon_sha256":"f34b1e7a61042312884ba33ed1f7e5e7a5085beb5643cf443d5341b1d03a9a32","abstract_canon_sha256":"727779dc5ec1e8b8c139bf7ffde20ecb39e2e02b3eec0638b87c348f9cd236ed"},"schema_version":"1.0"},"canonical_sha256":"902facef5713754368f3afb27a13d0cffe13fa538682a87632dc7bb7f9c8a32f","source":{"kind":"arxiv","id":"1808.02654","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02654","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02654v1","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02654","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"SAX2Z32XCN2U","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"SAX2Z32XCN2UG2HT","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"SAX2Z32X","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SAX2Z32XCN2UG2HTV6ZHUE6QZ7","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-08T08:12:09Z","cross_cats_sorted":[],"title_canon_sha256":"f34b1e7a61042312884ba33ed1f7e5e7a5085beb5643cf443d5341b1d03a9a32","abstract_canon_sha256":"727779dc5ec1e8b8c139bf7ffde20ecb39e2e02b3eec0638b87c348f9cd236ed"},"schema_version":"1.0"},"canonical_sha256":"902facef5713754368f3afb27a13d0cffe13fa538682a87632dc7bb7f9c8a32f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:34.742150Z","signature_b64":"IgToBDMyJ5/6sbVpU+aXYb8Rf0q4BrOXvC5kQfnSKLMQZ92x/uLJQTbFzgRRyMCYOVHxJ/auaW6bOJ4H+EtwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"902facef5713754368f3afb27a13d0cffe13fa538682a87632dc7bb7f9c8a32f","last_reissued_at":"2026-05-18T00:08:34.741448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:34.741448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02654","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":"2026-05-18T00:08:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Z4zi9wrliMyyoBj8ZwhpDwACb+9KOptYg+eFKQnX7u/oxlPDEvZ4pM7nqi5u0tGGoSefZD7MvRRTh+7HDiBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T05:06:12.244919Z"},"content_sha256":"788018bb26a85ac457d165f023e59dafb195c14176fcd25cecb11b94a6bb11e2","schema_version":"1.0","event_id":"sha256:788018bb26a85ac457d165f023e59dafb195c14176fcd25cecb11b94a6bb11e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SAX2Z32XCN2UG2HTV6ZHUE6QZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized Core Reduction for Discrete Ill-Posed Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Liping Zhang, Yimin Wei","submitted_at":"2018-08-08T08:12:09Z","abstract_excerpt":"In this paper, we apply randomized algorithms to approximate the total least squares (TLS) solution of the problem $Ax\\approx b$ in the large-scale discrete ill-posed problems. A regularization technique, based on the multiplicative randomization and the subspace iteration, is proposed to obtain the approximate core problem.In the error analysis, we provide upper bounds %in terms of the $(k\\!\\!+\\!\\!1)$-th singular value of $A$ for the errors of the solution and the residual of the randomized core reduction. Illustrative numerical examples and comparisons are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02654","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":""},"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":"2026-05-18T00:08:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3mUeyR42YpZu+cYsKTEChD1bc7+Oeyz1GxhvfvuLQlMntM2NTBfIivmsKNh1u//vM2Ge8dNEXzX0X97BpKoQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T05:06:12.245590Z"},"content_sha256":"bff82c37a9cdd6c6c80d91fdc0ad3bcf372a13e78976fdc4c7511195b7102c37","schema_version":"1.0","event_id":"sha256:bff82c37a9cdd6c6c80d91fdc0ad3bcf372a13e78976fdc4c7511195b7102c37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SAX2Z32XCN2UG2HTV6ZHUE6QZ7/bundle.json","state_url":"https://pith.science/pith/SAX2Z32XCN2UG2HTV6ZHUE6QZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SAX2Z32XCN2UG2HTV6ZHUE6QZ7/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":"2026-05-23T05:06:12Z","links":{"resolver":"https://pith.science/pith/SAX2Z32XCN2UG2HTV6ZHUE6QZ7","bundle":"https://pith.science/pith/SAX2Z32XCN2UG2HTV6ZHUE6QZ7/bundle.json","state":"https://pith.science/pith/SAX2Z32XCN2UG2HTV6ZHUE6QZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SAX2Z32XCN2UG2HTV6ZHUE6QZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SAX2Z32XCN2UG2HTV6ZHUE6QZ7","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":"727779dc5ec1e8b8c139bf7ffde20ecb39e2e02b3eec0638b87c348f9cd236ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-08T08:12:09Z","title_canon_sha256":"f34b1e7a61042312884ba33ed1f7e5e7a5085beb5643cf443d5341b1d03a9a32"},"schema_version":"1.0","source":{"id":"1808.02654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02654","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02654v1","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02654","created_at":"2026-05-18T00:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"SAX2Z32XCN2U","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"SAX2Z32XCN2UG2HT","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"SAX2Z32X","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:bff82c37a9cdd6c6c80d91fdc0ad3bcf372a13e78976fdc4c7511195b7102c37","target":"graph","created_at":"2026-05-18T00:08:34Z","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"},"paper":{"abstract_excerpt":"In this paper, we apply randomized algorithms to approximate the total least squares (TLS) solution of the problem $Ax\\approx b$ in the large-scale discrete ill-posed problems. A regularization technique, based on the multiplicative randomization and the subspace iteration, is proposed to obtain the approximate core problem.In the error analysis, we provide upper bounds %in terms of the $(k\\!\\!+\\!\\!1)$-th singular value of $A$ for the errors of the solution and the residual of the randomized core reduction. Illustrative numerical examples and comparisons are presented.","authors_text":"Liping Zhang, Yimin Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-08T08:12:09Z","title":"Randomized Core Reduction for Discrete Ill-Posed Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02654","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":"sha256:788018bb26a85ac457d165f023e59dafb195c14176fcd25cecb11b94a6bb11e2","target":"record","created_at":"2026-05-18T00:08:34Z","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":"727779dc5ec1e8b8c139bf7ffde20ecb39e2e02b3eec0638b87c348f9cd236ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-08T08:12:09Z","title_canon_sha256":"f34b1e7a61042312884ba33ed1f7e5e7a5085beb5643cf443d5341b1d03a9a32"},"schema_version":"1.0","source":{"id":"1808.02654","kind":"arxiv","version":1}},"canonical_sha256":"902facef5713754368f3afb27a13d0cffe13fa538682a87632dc7bb7f9c8a32f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"902facef5713754368f3afb27a13d0cffe13fa538682a87632dc7bb7f9c8a32f","first_computed_at":"2026-05-18T00:08:34.741448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:34.741448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IgToBDMyJ5/6sbVpU+aXYb8Rf0q4BrOXvC5kQfnSKLMQZ92x/uLJQTbFzgRRyMCYOVHxJ/auaW6bOJ4H+EtwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:34.742150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:788018bb26a85ac457d165f023e59dafb195c14176fcd25cecb11b94a6bb11e2","sha256:bff82c37a9cdd6c6c80d91fdc0ad3bcf372a13e78976fdc4c7511195b7102c37"],"state_sha256":"a7011605864bd920bda1e140d69d99dc57bc70ea4ba7a61bf637b3a4b037aefe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RhHVzCqYCsSNEsmaZwSLWgkL+hJASa2anW/SRNss4SL86gv9wixnHO3EAacC35hMleM7CLA6rGDNcyyepcJZBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T05:06:12.249080Z","bundle_sha256":"f304cfe223c994a3a00dcd737e63be29df69fe26612ee2c9a90b2c738ff5eb26"}}