{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:QDXK63J643RXSJ6JMAZJOM24NV","short_pith_number":"pith:QDXK63J6","canonical_record":{"source":{"id":"0707.1838","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2007-07-12T17:26:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b96e77cd7bbc1e2440d03b13c541c9262da8f2b50f7681998b4e5aa4a38231a2","abstract_canon_sha256":"1ffa32a16aa0d8ac522b85534ce73b87e8c98c9eacca961ef4b46d7334ab9505"},"schema_version":"1.0"},"canonical_sha256":"80eeaf6d3ee6e37927c9603297335c6d50f8af354077838a031d39aaeb0acab0","source":{"kind":"arxiv","id":"0707.1838","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.1838","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"0707.1838v3","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.1838","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"QDXK63J643RX","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_16","alias_value":"QDXK63J643RXSJ6J","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_8","alias_value":"QDXK63J6","created_at":"2026-06-03T22:06:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:QDXK63J643RXSJ6JMAZJOM24NV","target":"record","payload":{"canonical_record":{"source":{"id":"0707.1838","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2007-07-12T17:26:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b96e77cd7bbc1e2440d03b13c541c9262da8f2b50f7681998b4e5aa4a38231a2","abstract_canon_sha256":"1ffa32a16aa0d8ac522b85534ce73b87e8c98c9eacca961ef4b46d7334ab9505"},"schema_version":"1.0"},"canonical_sha256":"80eeaf6d3ee6e37927c9603297335c6d50f8af354077838a031d39aaeb0acab0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:01.542961Z","signature_b64":"xzoLtE8EbgUGHoOsmr28oZD++2iQ+uMTxQidQ4eFWkWFNL7/q0fBseVYZBpgoB34d2SZhXbPp8QmZkW0zh71CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80eeaf6d3ee6e37927c9603297335c6d50f8af354077838a031d39aaeb0acab0","last_reissued_at":"2026-06-03T22:06:01.542366Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:01.542366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.1838","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T22:06:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YhS+A26UrKzfrzcUI96JtXmbxH4eA0nuA/70uWWV+N4N/ykue/MUR18BOf//xTSC8y1BI8p0mNnkb5S+QrVxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T09:57:27.767999Z"},"content_sha256":"5619602c5dd9cc80e9da4f6b5fa92cc10babdbe5bb15da22468c491d4f12d14e","schema_version":"1.0","event_id":"sha256:5619602c5dd9cc80e9da4f6b5fa92cc10babdbe5bb15da22468c491d4f12d14e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:QDXK63J643RXSJ6JMAZJOM24NV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing the complete CS decomposition","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Brian D. Sutton","submitted_at":"2007-07-12T17:26:40Z","abstract_excerpt":"An algorithm is developed to compute the complete CS decomposition (CSD) of a partitioned unitary matrix. Although the existence of the CSD has been recognized since 1977, prior algorithms compute only a reduced version (the 2-by-1 CSD) that is equivalent to two simultaneous singular value decompositions. The algorithm presented here computes the complete 2-by-2 CSD, which requires the simultaneous diagonalization of all four blocks of a unitary matrix partitioned into a 2-by-2 block structure. The algorithm appears to be the only fully specified algorithm available. The computation occurs in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.1838","kind":"arxiv","version":3},"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/0707.1838/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":"2026-06-03T22:06:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9F1sMn+jMcRuF62WrsTeDWLZyvBRcb7/iAwLjMCkHoO+UbM9PCcdvr+DpZ3ZPr3Bl7Gc9WYAbQHA6RHsJMiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T09:57:27.768381Z"},"content_sha256":"31a1814d29271cadde981aac57a34382fcdbc7600334da59645e0aaeb7c2c65b","schema_version":"1.0","event_id":"sha256:31a1814d29271cadde981aac57a34382fcdbc7600334da59645e0aaeb7c2c65b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDXK63J643RXSJ6JMAZJOM24NV/bundle.json","state_url":"https://pith.science/pith/QDXK63J643RXSJ6JMAZJOM24NV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDXK63J643RXSJ6JMAZJOM24NV/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":"2026-06-30T09:57:27Z","links":{"resolver":"https://pith.science/pith/QDXK63J643RXSJ6JMAZJOM24NV","bundle":"https://pith.science/pith/QDXK63J643RXSJ6JMAZJOM24NV/bundle.json","state":"https://pith.science/pith/QDXK63J643RXSJ6JMAZJOM24NV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDXK63J643RXSJ6JMAZJOM24NV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:QDXK63J643RXSJ6JMAZJOM24NV","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":"1ffa32a16aa0d8ac522b85534ce73b87e8c98c9eacca961ef4b46d7334ab9505","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2007-07-12T17:26:40Z","title_canon_sha256":"b96e77cd7bbc1e2440d03b13c541c9262da8f2b50f7681998b4e5aa4a38231a2"},"schema_version":"1.0","source":{"id":"0707.1838","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.1838","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"arxiv_version","alias_value":"0707.1838v3","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.1838","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_12","alias_value":"QDXK63J643RX","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_16","alias_value":"QDXK63J643RXSJ6J","created_at":"2026-06-03T22:06:01Z"},{"alias_kind":"pith_short_8","alias_value":"QDXK63J6","created_at":"2026-06-03T22:06:01Z"}],"graph_snapshots":[{"event_id":"sha256:31a1814d29271cadde981aac57a34382fcdbc7600334da59645e0aaeb7c2c65b","target":"graph","created_at":"2026-06-03T22:06:01Z","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/0707.1838/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An algorithm is developed to compute the complete CS decomposition (CSD) of a partitioned unitary matrix. Although the existence of the CSD has been recognized since 1977, prior algorithms compute only a reduced version (the 2-by-1 CSD) that is equivalent to two simultaneous singular value decompositions. The algorithm presented here computes the complete 2-by-2 CSD, which requires the simultaneous diagonalization of all four blocks of a unitary matrix partitioned into a 2-by-2 block structure. The algorithm appears to be the only fully specified algorithm available. The computation occurs in ","authors_text":"Brian D. Sutton","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2007-07-12T17:26:40Z","title":"Computing the complete CS decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.1838","kind":"arxiv","version":3},"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":"sha256:5619602c5dd9cc80e9da4f6b5fa92cc10babdbe5bb15da22468c491d4f12d14e","target":"record","created_at":"2026-06-03T22:06:01Z","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":"1ffa32a16aa0d8ac522b85534ce73b87e8c98c9eacca961ef4b46d7334ab9505","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2007-07-12T17:26:40Z","title_canon_sha256":"b96e77cd7bbc1e2440d03b13c541c9262da8f2b50f7681998b4e5aa4a38231a2"},"schema_version":"1.0","source":{"id":"0707.1838","kind":"arxiv","version":3}},"canonical_sha256":"80eeaf6d3ee6e37927c9603297335c6d50f8af354077838a031d39aaeb0acab0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80eeaf6d3ee6e37927c9603297335c6d50f8af354077838a031d39aaeb0acab0","first_computed_at":"2026-06-03T22:06:01.542366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:01.542366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xzoLtE8EbgUGHoOsmr28oZD++2iQ+uMTxQidQ4eFWkWFNL7/q0fBseVYZBpgoB34d2SZhXbPp8QmZkW0zh71CA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:01.542961Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.1838","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5619602c5dd9cc80e9da4f6b5fa92cc10babdbe5bb15da22468c491d4f12d14e","sha256:31a1814d29271cadde981aac57a34382fcdbc7600334da59645e0aaeb7c2c65b"],"state_sha256":"10c578bb4014e7b6039be98a694fe705f699c9e67efab1ed015b59944f3d16fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SLTfra2zNXOB86cDIurpQCbzaLjqPyfeUPF0VGCAGiAvIBeWEkfnlyBdVKHv0BhGyfpITK4Jhnyh+566R7dQAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T09:57:27.770399Z","bundle_sha256":"fb2019ffa1fd34961c49e2a2bc2a08df93c4a237fef5fb6d495be58a5d1caa32"}}