{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TQZWT4QYKHSKDRDJHEK3H64T2S","short_pith_number":"pith:TQZWT4QY","canonical_record":{"source":{"id":"1103.2338","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-11T18:39:45Z","cross_cats_sorted":["cs.NA","physics.comp-ph","physics.data-an"],"title_canon_sha256":"dfaaffc6eef26d12fbf14eeb6cba7ff9b71dc5fe11108c92dcb50038800c6518","abstract_canon_sha256":"b97107312ce78a7188164dcb5b0a9c7796e2521d67ee41e007e20d49c09b3ac9"},"schema_version":"1.0"},"canonical_sha256":"9c3369f21851e4a1c4693915b3fb93d4a371add170761198587bc625a314547d","source":{"kind":"arxiv","id":"1103.2338","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2338","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2338v5","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2338","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"pith_short_12","alias_value":"TQZWT4QYKHSK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TQZWT4QYKHSKDRDJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TQZWT4QY","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TQZWT4QYKHSKDRDJHEK3H64T2S","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2338","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-11T18:39:45Z","cross_cats_sorted":["cs.NA","physics.comp-ph","physics.data-an"],"title_canon_sha256":"dfaaffc6eef26d12fbf14eeb6cba7ff9b71dc5fe11108c92dcb50038800c6518","abstract_canon_sha256":"b97107312ce78a7188164dcb5b0a9c7796e2521d67ee41e007e20d49c09b3ac9"},"schema_version":"1.0"},"canonical_sha256":"9c3369f21851e4a1c4693915b3fb93d4a371add170761198587bc625a314547d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:26.863855Z","signature_b64":"XsO/XMw47f7SrYhJXMz5l2avk+zP3eA9vfNalB8Mtpu3jfLEReDId97CA0ygG0s0i7hwDzhgedbJGGYwT0vqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c3369f21851e4a1c4693915b3fb93d4a371add170761198587bc625a314547d","last_reissued_at":"2026-05-18T04:00:26.863022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:26.863022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2338","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:00:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m1zPZZq+d4n5DF7JYn4tODHZTlDkZgMNceODwX93U7380/z2OprvmjRaBAlSncyIqLFOi90mI8VAI2bgkxXJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:23:31.588083Z"},"content_sha256":"c126748bb692880fad0c070fcb7d6418a5f7e9d2084b91f31443f378223b0446","schema_version":"1.0","event_id":"sha256:c126748bb692880fad0c070fcb7d6418a5f7e9d2084b91f31443f378223b0446"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TQZWT4QYKHSKDRDJHEK3H64T2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Extraordinary SVD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph","physics.data-an"],"primary_cat":"math.NA","authors_text":"Carla D. Martin, Mason A. Porter","submitted_at":"2011-03-11T18:39:45Z","abstract_excerpt":"The singular value decomposition (SVD) is a popular matrix factorization that has been used widely in applications ever since an efficient algorithm for its computation was developed in the 1970s. In recent years, the SVD has become even more prominent due to a surge in applications and increased computational memory and speed.\n  To illustrate the vitality of the SVD in data analysis, we highlight three of its lesser-known yet fascinating applications: the SVD can be used to characterize political positions of Congressmen, measure the growth rate of crystals in igneous rock, and examine entang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2338","kind":"arxiv","version":5},"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":"2026-05-18T04:00:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jgkl4Tww2y0t9qMnErI/fsGc0YKRkWdfOlR59aKPEDUWtm78Us8FJqToXtiHBUXBV717bi6rGNRQl9Eswpj+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:23:31.588490Z"},"content_sha256":"1a35c639500c23cdba9b899c5dc8e0877cce9d3e4f5454d1deb824942b9dfb2f","schema_version":"1.0","event_id":"sha256:1a35c639500c23cdba9b899c5dc8e0877cce9d3e4f5454d1deb824942b9dfb2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQZWT4QYKHSKDRDJHEK3H64T2S/bundle.json","state_url":"https://pith.science/pith/TQZWT4QYKHSKDRDJHEK3H64T2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQZWT4QYKHSKDRDJHEK3H64T2S/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":"2026-06-04T18:23:31Z","links":{"resolver":"https://pith.science/pith/TQZWT4QYKHSKDRDJHEK3H64T2S","bundle":"https://pith.science/pith/TQZWT4QYKHSKDRDJHEK3H64T2S/bundle.json","state":"https://pith.science/pith/TQZWT4QYKHSKDRDJHEK3H64T2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQZWT4QYKHSKDRDJHEK3H64T2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TQZWT4QYKHSKDRDJHEK3H64T2S","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":"b97107312ce78a7188164dcb5b0a9c7796e2521d67ee41e007e20d49c09b3ac9","cross_cats_sorted":["cs.NA","physics.comp-ph","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-11T18:39:45Z","title_canon_sha256":"dfaaffc6eef26d12fbf14eeb6cba7ff9b71dc5fe11108c92dcb50038800c6518"},"schema_version":"1.0","source":{"id":"1103.2338","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2338","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2338v5","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2338","created_at":"2026-05-18T04:00:26Z"},{"alias_kind":"pith_short_12","alias_value":"TQZWT4QYKHSK","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TQZWT4QYKHSKDRDJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TQZWT4QY","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:1a35c639500c23cdba9b899c5dc8e0877cce9d3e4f5454d1deb824942b9dfb2f","target":"graph","created_at":"2026-05-18T04:00:26Z","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":"The singular value decomposition (SVD) is a popular matrix factorization that has been used widely in applications ever since an efficient algorithm for its computation was developed in the 1970s. In recent years, the SVD has become even more prominent due to a surge in applications and increased computational memory and speed.\n  To illustrate the vitality of the SVD in data analysis, we highlight three of its lesser-known yet fascinating applications: the SVD can be used to characterize political positions of Congressmen, measure the growth rate of crystals in igneous rock, and examine entang","authors_text":"Carla D. Martin, Mason A. Porter","cross_cats":["cs.NA","physics.comp-ph","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-11T18:39:45Z","title":"The Extraordinary SVD"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2338","kind":"arxiv","version":5},"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:c126748bb692880fad0c070fcb7d6418a5f7e9d2084b91f31443f378223b0446","target":"record","created_at":"2026-05-18T04:00:26Z","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":"b97107312ce78a7188164dcb5b0a9c7796e2521d67ee41e007e20d49c09b3ac9","cross_cats_sorted":["cs.NA","physics.comp-ph","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-11T18:39:45Z","title_canon_sha256":"dfaaffc6eef26d12fbf14eeb6cba7ff9b71dc5fe11108c92dcb50038800c6518"},"schema_version":"1.0","source":{"id":"1103.2338","kind":"arxiv","version":5}},"canonical_sha256":"9c3369f21851e4a1c4693915b3fb93d4a371add170761198587bc625a314547d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c3369f21851e4a1c4693915b3fb93d4a371add170761198587bc625a314547d","first_computed_at":"2026-05-18T04:00:26.863022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:26.863022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XsO/XMw47f7SrYhJXMz5l2avk+zP3eA9vfNalB8Mtpu3jfLEReDId97CA0ygG0s0i7hwDzhgedbJGGYwT0vqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:26.863855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2338","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c126748bb692880fad0c070fcb7d6418a5f7e9d2084b91f31443f378223b0446","sha256:1a35c639500c23cdba9b899c5dc8e0877cce9d3e4f5454d1deb824942b9dfb2f"],"state_sha256":"c2731769283a63483e71b5e7ee78a5bd948c6913125036648f3e58f6fd208b41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRRRbdUBExFQdko0XJZyls1WjeSdRdUSwZw6gACH9XOmT8rNwT94bmK2ywMUv3BOEvsJCMqYMa5ljgXXCOIDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:23:31.590658Z","bundle_sha256":"bf7c06812e184c5a5d6fd39a4e34717ff4d4d3ad6668fa07b99e171cb1617eee"}}