{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:URMHP6QZEQYYFXMBHYPYKLDFQB","short_pith_number":"pith:URMHP6QZ","canonical_record":{"source":{"id":"1710.02812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-10-08T09:28:07Z","cross_cats_sorted":[],"title_canon_sha256":"cab73482bcd0e94db03d351f1c81921cfd0a27bc9a8e53e44a7252dc11d9f846","abstract_canon_sha256":"0eb69cadf1a0c66a5f5abcc9e40712e4e0b7e72f9b86398a2d467820bb4dce5e"},"schema_version":"1.0"},"canonical_sha256":"a45877fa19243182dd813e1f852c658064be077d65706ca546e18b800804de25","source":{"kind":"arxiv","id":"1710.02812","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02812","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02812v2","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02812","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"pith_short_12","alias_value":"URMHP6QZEQYY","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"URMHP6QZEQYYFXMB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"URMHP6QZ","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:URMHP6QZEQYYFXMBHYPYKLDFQB","target":"record","payload":{"canonical_record":{"source":{"id":"1710.02812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-10-08T09:28:07Z","cross_cats_sorted":[],"title_canon_sha256":"cab73482bcd0e94db03d351f1c81921cfd0a27bc9a8e53e44a7252dc11d9f846","abstract_canon_sha256":"0eb69cadf1a0c66a5f5abcc9e40712e4e0b7e72f9b86398a2d467820bb4dce5e"},"schema_version":"1.0"},"canonical_sha256":"a45877fa19243182dd813e1f852c658064be077d65706ca546e18b800804de25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:36.500341Z","signature_b64":"+RBsoXlUhZhM+mwtKicTJOZIeJUnrze6ou97xFRNucAJfB8U6Lw2eT4kgznc69pULZomojLoAgjES1GkvWaNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a45877fa19243182dd813e1f852c658064be077d65706ca546e18b800804de25","last_reissued_at":"2026-05-17T23:46:36.499665Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:36.499665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.02812","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":"2026-05-17T23:46:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HCvCuEzA2w2yESRljI7NYFQNGB8JRvP0lDjXu1OL8R8RsaJhvoqRorggIJ8ZS2Ka4pHgnSEdo/Tsahtixp7pAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:02:31.362290Z"},"content_sha256":"c90234d07a94e876a2978abb209abac96ca7e7571ac171dcf4577750aaa1d4df","schema_version":"1.0","event_id":"sha256:c90234d07a94e876a2978abb209abac96ca7e7571ac171dcf4577750aaa1d4df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:URMHP6QZEQYYFXMBHYPYKLDFQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Hierarchical Singular Value Decomposition Algorithm for Low Rank Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"M. Ramakrishna, Vinita Vasudevan","submitted_at":"2017-10-08T09:28:07Z","abstract_excerpt":"Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank matrices. In these cases, a truncated SVD corresponding to the most significant singular values is sufficient. In this paper, we propose a tree based merge-and-truncate algorithm to obtain an approximate truncated SVD of the matrix. Unlike previous methods, our technique is not limited to \"tall and skinny\" or \"short and fat\" matrices and it can be used for matric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02812","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":""},"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":"2026-05-17T23:46:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWKdoiBWSkRI+itcoxQ8rfohmQ5XJz7t3z9TjRR/UqIT9z7yU5lLFgKB/WSuKxWTUWtrJqX2kLGC6ODUMXkPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:02:31.362840Z"},"content_sha256":"31ed47f7a2cb1241e06fb47dcf1aaa14b67e0f5fb79b0d6dd4e0a60ef1b36fb6","schema_version":"1.0","event_id":"sha256:31ed47f7a2cb1241e06fb47dcf1aaa14b67e0f5fb79b0d6dd4e0a60ef1b36fb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/URMHP6QZEQYYFXMBHYPYKLDFQB/bundle.json","state_url":"https://pith.science/pith/URMHP6QZEQYYFXMBHYPYKLDFQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/URMHP6QZEQYYFXMBHYPYKLDFQB/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":"2026-06-11T10:02:31Z","links":{"resolver":"https://pith.science/pith/URMHP6QZEQYYFXMBHYPYKLDFQB","bundle":"https://pith.science/pith/URMHP6QZEQYYFXMBHYPYKLDFQB/bundle.json","state":"https://pith.science/pith/URMHP6QZEQYYFXMBHYPYKLDFQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/URMHP6QZEQYYFXMBHYPYKLDFQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:URMHP6QZEQYYFXMBHYPYKLDFQB","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":"0eb69cadf1a0c66a5f5abcc9e40712e4e0b7e72f9b86398a2d467820bb4dce5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-10-08T09:28:07Z","title_canon_sha256":"cab73482bcd0e94db03d351f1c81921cfd0a27bc9a8e53e44a7252dc11d9f846"},"schema_version":"1.0","source":{"id":"1710.02812","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02812","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02812v2","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02812","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"pith_short_12","alias_value":"URMHP6QZEQYY","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"URMHP6QZEQYYFXMB","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"URMHP6QZ","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:31ed47f7a2cb1241e06fb47dcf1aaa14b67e0f5fb79b0d6dd4e0a60ef1b36fb6","target":"graph","created_at":"2026-05-17T23:46:36Z","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":"Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank matrices. In these cases, a truncated SVD corresponding to the most significant singular values is sufficient. In this paper, we propose a tree based merge-and-truncate algorithm to obtain an approximate truncated SVD of the matrix. Unlike previous methods, our technique is not limited to \"tall and skinny\" or \"short and fat\" matrices and it can be used for matric","authors_text":"M. Ramakrishna, Vinita Vasudevan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-10-08T09:28:07Z","title":"A Hierarchical Singular Value Decomposition Algorithm for Low Rank Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02812","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:c90234d07a94e876a2978abb209abac96ca7e7571ac171dcf4577750aaa1d4df","target":"record","created_at":"2026-05-17T23:46:36Z","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":"0eb69cadf1a0c66a5f5abcc9e40712e4e0b7e72f9b86398a2d467820bb4dce5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2017-10-08T09:28:07Z","title_canon_sha256":"cab73482bcd0e94db03d351f1c81921cfd0a27bc9a8e53e44a7252dc11d9f846"},"schema_version":"1.0","source":{"id":"1710.02812","kind":"arxiv","version":2}},"canonical_sha256":"a45877fa19243182dd813e1f852c658064be077d65706ca546e18b800804de25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a45877fa19243182dd813e1f852c658064be077d65706ca546e18b800804de25","first_computed_at":"2026-05-17T23:46:36.499665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:36.499665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+RBsoXlUhZhM+mwtKicTJOZIeJUnrze6ou97xFRNucAJfB8U6Lw2eT4kgznc69pULZomojLoAgjES1GkvWaNCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:36.500341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02812","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c90234d07a94e876a2978abb209abac96ca7e7571ac171dcf4577750aaa1d4df","sha256:31ed47f7a2cb1241e06fb47dcf1aaa14b67e0f5fb79b0d6dd4e0a60ef1b36fb6"],"state_sha256":"e5a13c19b54bc3cc8202fad71b4afb095dec592f68142bc57812a753ae2f755f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLDchyXp+Qi4yX5wO+PxFVlC/kVy1LAdF/LQsPAU5E12lH8fk1ujpkBR01DwFwLEycrovS7gWUjPO+XaBvw3Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:02:31.365448Z","bundle_sha256":"aedb3c535d21db9f5155415357f389964d22f59f79243277cea631ef66c00b0a"}}