{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:B3JE6A2JHKCIHSG3HQAV537TNC","short_pith_number":"pith:B3JE6A2J","canonical_record":{"source":{"id":"1804.09838","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-26T00:18:58Z","cross_cats_sorted":[],"title_canon_sha256":"f917860d7c8c140a2f09f9015a720a56a30111b3cc814feb2d500850987b6e4d","abstract_canon_sha256":"b7d19f1307d5a0d976d6012cccb73a7d337f9c892947b0d94c11da33ce734dbd"},"schema_version":"1.0"},"canonical_sha256":"0ed24f03493a8483c8db3c015eeff3688ec4632025bcb40dae0428d3ea9e75fb","source":{"kind":"arxiv","id":"1804.09838","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09838","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09838v2","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09838","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"B3JE6A2JHKCI","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B3JE6A2JHKCIHSG3","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B3JE6A2J","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:B3JE6A2JHKCIHSG3HQAV537TNC","target":"record","payload":{"canonical_record":{"source":{"id":"1804.09838","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-26T00:18:58Z","cross_cats_sorted":[],"title_canon_sha256":"f917860d7c8c140a2f09f9015a720a56a30111b3cc814feb2d500850987b6e4d","abstract_canon_sha256":"b7d19f1307d5a0d976d6012cccb73a7d337f9c892947b0d94c11da33ce734dbd"},"schema_version":"1.0"},"canonical_sha256":"0ed24f03493a8483c8db3c015eeff3688ec4632025bcb40dae0428d3ea9e75fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:40.025340Z","signature_b64":"KXt90EZRttN62sJWKUBzHbYx6N/8iNSYlcJnIg+v0bnYqyYQ4mVUFdQl8djOsWoKKZGdMsAUMmHUrJ2YHA7IDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ed24f03493a8483c8db3c015eeff3688ec4632025bcb40dae0428d3ea9e75fb","last_reissued_at":"2026-05-18T00:14:40.024692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:40.024692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.09838","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":"2026-05-18T00:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0HtGDRVfbON7bVSM5C0c1zsaQ6WbixCOz9NYv1eZwUeHroEd2WO5kbICPv8LQrJx2bnZE601VPFvdu5h9utCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:54:25.365180Z"},"content_sha256":"0d4b4224b876397c2a029023734ed8cd257e60db027b36f398b424849e2175e2","schema_version":"1.0","event_id":"sha256:0d4b4224b876397c2a029023734ed8cd257e60db027b36f398b424849e2175e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:B3JE6A2JHKCIHSG3HQAV537TNC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular value decomposition of complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andrew J. Sommese, Danielle A. Brake, Frank-Olaf Schreyer, Jonathan D. Hauenstein, Michael E. Stillman","submitted_at":"2018-04-26T00:18:58Z","abstract_excerpt":"Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two methods to compute them and present several applications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09838","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":"2026-05-18T00:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1xO66/56QZ2rm1gXbrGj/3+0x/sMGeld8ZXCs3Q0N53jpyctxSb5LRN/87+Irh6rICiGOYhrQaPznG5h9oPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:54:25.365817Z"},"content_sha256":"d39cf83af2d34b0529eabbe8178759a778e53de34f8cacda834259461de621ca","schema_version":"1.0","event_id":"sha256:d39cf83af2d34b0529eabbe8178759a778e53de34f8cacda834259461de621ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3JE6A2JHKCIHSG3HQAV537TNC/bundle.json","state_url":"https://pith.science/pith/B3JE6A2JHKCIHSG3HQAV537TNC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3JE6A2JHKCIHSG3HQAV537TNC/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":"2026-05-27T19:54:25Z","links":{"resolver":"https://pith.science/pith/B3JE6A2JHKCIHSG3HQAV537TNC","bundle":"https://pith.science/pith/B3JE6A2JHKCIHSG3HQAV537TNC/bundle.json","state":"https://pith.science/pith/B3JE6A2JHKCIHSG3HQAV537TNC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3JE6A2JHKCIHSG3HQAV537TNC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B3JE6A2JHKCIHSG3HQAV537TNC","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":"b7d19f1307d5a0d976d6012cccb73a7d337f9c892947b0d94c11da33ce734dbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-26T00:18:58Z","title_canon_sha256":"f917860d7c8c140a2f09f9015a720a56a30111b3cc814feb2d500850987b6e4d"},"schema_version":"1.0","source":{"id":"1804.09838","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09838","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09838v2","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09838","created_at":"2026-05-18T00:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"B3JE6A2JHKCI","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B3JE6A2JHKCIHSG3","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B3JE6A2J","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:d39cf83af2d34b0529eabbe8178759a778e53de34f8cacda834259461de621ca","target":"graph","created_at":"2026-05-18T00:14:40Z","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 decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two methods to compute them and present several applications.","authors_text":"Andrew J. Sommese, Danielle A. Brake, Frank-Olaf Schreyer, Jonathan D. Hauenstein, Michael E. Stillman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-26T00:18:58Z","title":"Singular value decomposition of complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09838","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":"sha256:0d4b4224b876397c2a029023734ed8cd257e60db027b36f398b424849e2175e2","target":"record","created_at":"2026-05-18T00:14:40Z","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":"b7d19f1307d5a0d976d6012cccb73a7d337f9c892947b0d94c11da33ce734dbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-26T00:18:58Z","title_canon_sha256":"f917860d7c8c140a2f09f9015a720a56a30111b3cc814feb2d500850987b6e4d"},"schema_version":"1.0","source":{"id":"1804.09838","kind":"arxiv","version":2}},"canonical_sha256":"0ed24f03493a8483c8db3c015eeff3688ec4632025bcb40dae0428d3ea9e75fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ed24f03493a8483c8db3c015eeff3688ec4632025bcb40dae0428d3ea9e75fb","first_computed_at":"2026-05-18T00:14:40.024692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:40.024692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KXt90EZRttN62sJWKUBzHbYx6N/8iNSYlcJnIg+v0bnYqyYQ4mVUFdQl8djOsWoKKZGdMsAUMmHUrJ2YHA7IDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:40.025340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09838","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d4b4224b876397c2a029023734ed8cd257e60db027b36f398b424849e2175e2","sha256:d39cf83af2d34b0529eabbe8178759a778e53de34f8cacda834259461de621ca"],"state_sha256":"a210150a66f98dd50309efb7138b59ada1b978908e8c3865964a1117314d60c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uUIIsCeuEpAg6q7/tVpuK/myB9VxXOqpFbQulDj/xo0+4v+XpV3AxrphduIaueXvv0Cl2rM10Sy71tiBu6FNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:54:25.369611Z","bundle_sha256":"ecbe91c6173be305503803ab79184871ff4b5ea50b193569d6dd134429683541"}}