{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:RTF4UGHEHWBNKAUOY4OJMIGSXQ","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":"f8d481e5fff8f7b5405bfe941124ee7725d3624cf42fadd60240a42b1dd086ee","cross_cats_sorted":["cs.DS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-05-04T07:13:14Z","title_canon_sha256":"5ee9cf6586e8efb1c82a86dfe06156401e0379dfe83f9b3f0cb089643749da42"},"schema_version":"1.0","source":{"id":"2005.01299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.01299","created_at":"2026-07-05T01:00:06Z"},{"alias_kind":"arxiv_version","alias_value":"2005.01299v1","created_at":"2026-07-05T01:00:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.01299","created_at":"2026-07-05T01:00:06Z"},{"alias_kind":"pith_short_12","alias_value":"RTF4UGHEHWBN","created_at":"2026-07-05T01:00:06Z"},{"alias_kind":"pith_short_16","alias_value":"RTF4UGHEHWBNKAUO","created_at":"2026-07-05T01:00:06Z"},{"alias_kind":"pith_short_8","alias_value":"RTF4UGHE","created_at":"2026-07-05T01:00:06Z"}],"graph_snapshots":[{"event_id":"sha256:9fb00cdf4b39121763b16b9b5944738c4311727034d8afcef38b998e3eb12cff","target":"graph","created_at":"2026-07-05T01:00:06Z","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/2005.01299/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Low-rank approximations of original samples are playing more and more an important role in many recently proposed mathematical models from data science. A natural and initial requirement is that these representations inherit original structures or properties. With this aim, we propose a new multi-symplectic method based on the Lanzcos bidiagonalization to compute the partial singular triplets of JRS-symmetric matrices. These singular triplets can be used to reconstruct optimal low-rank approximations while preserving the intrinsic multi-symmetry. The augmented Ritz and harmonic Ritz vectors ar","authors_text":"Mei-Xiang Zhao, Xuan Liu, Zhigang Jia","cross_cats":["cs.DS","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-05-04T07:13:14Z","title":"The Multi-Symplectic Lanczos Algorithm and Its Applications to Color Image Processing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.01299","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":"sha256:8a3b89fb1d546c542c1cbec1434dc1ae56eef4672081fcaa11ae5771f029f27b","target":"record","created_at":"2026-07-05T01:00:06Z","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":"f8d481e5fff8f7b5405bfe941124ee7725d3624cf42fadd60240a42b1dd086ee","cross_cats_sorted":["cs.DS","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-05-04T07:13:14Z","title_canon_sha256":"5ee9cf6586e8efb1c82a86dfe06156401e0379dfe83f9b3f0cb089643749da42"},"schema_version":"1.0","source":{"id":"2005.01299","kind":"arxiv","version":1}},"canonical_sha256":"8ccbca18e43d82d5028ec71c9620d2bc2e3b256bea41427a36966a8e0d9df913","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ccbca18e43d82d5028ec71c9620d2bc2e3b256bea41427a36966a8e0d9df913","first_computed_at":"2026-07-05T01:00:06.321693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:00:06.321693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZmodW+jQR++Xsayj5ASDEYFtpguotoDyk2/eSmVCJr1Pi7NuUU5oFZr3+jOj4sezOog622uMGSQeCk/kVUhqCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:00:06.322147Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.01299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a3b89fb1d546c542c1cbec1434dc1ae56eef4672081fcaa11ae5771f029f27b","sha256:9fb00cdf4b39121763b16b9b5944738c4311727034d8afcef38b998e3eb12cff"],"state_sha256":"9b56d65ff96269566633bafbd9d17633c88e9e7a71feac1e38d1420e8f3b4f34"}