{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OFBOBFOYNUAY2YPNKKPCLIBOW7","short_pith_number":"pith:OFBOBFOY","canonical_record":{"source":{"id":"1502.07838","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-02-27T09:29:07Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8b78617bddf60d95bf0a454813f7a8907be6b33ba6d54ac2f61d76974a2c8de8","abstract_canon_sha256":"d81c76e5adfe38f57f9ab6592e746d80434ccf77547596b2d58af184bcc00674"},"schema_version":"1.0"},"canonical_sha256":"7142e095d86d018d61ed529e25a02eb7ef3809d91f90a3a469f26445f0018cca","source":{"kind":"arxiv","id":"1502.07838","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07838","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07838v4","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07838","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"OFBOBFOYNUAY","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OFBOBFOYNUAY2YPN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OFBOBFOY","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OFBOBFOYNUAY2YPNKKPCLIBOW7","target":"record","payload":{"canonical_record":{"source":{"id":"1502.07838","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-02-27T09:29:07Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8b78617bddf60d95bf0a454813f7a8907be6b33ba6d54ac2f61d76974a2c8de8","abstract_canon_sha256":"d81c76e5adfe38f57f9ab6592e746d80434ccf77547596b2d58af184bcc00674"},"schema_version":"1.0"},"canonical_sha256":"7142e095d86d018d61ed529e25a02eb7ef3809d91f90a3a469f26445f0018cca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:39.853981Z","signature_b64":"wuiG17XPZdLX7gXVksZ3OK4lYCp6Y7caJsHpmLbaERz+kZ2FCSuSSbxw8mHVbD2T8Iir0Gcj4YoJVgglZAppDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7142e095d86d018d61ed529e25a02eb7ef3809d91f90a3a469f26445f0018cca","last_reissued_at":"2026-05-18T00:29:39.853279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:39.853279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.07838","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6sl6Yg5M6gaFiZHIR3uIrw7GMH4SaMNoMvYjnURNIVnw8oLTpnjz74Ho4KeJqgCU/28YTVI/gerK23bYcb0RBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:34:37.180793Z"},"content_sha256":"6da79230bc768db19ba7068c7a58cc0ed0019f2923aed53015ab83b5258fb2c0","schema_version":"1.0","event_id":"sha256:6da79230bc768db19ba7068c7a58cc0ed0019f2923aed53015ab83b5258fb2c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OFBOBFOYNUAY2YPNKKPCLIBOW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rectangular maximum-volume submatrices and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"A. Mikhalev, I. V. Oseledets","submitted_at":"2015-02-27T09:29:07Z","abstract_excerpt":"We introduce a definition of the volume for a general rectangular matrix, which for square matrices is equivalent to the absolute value of the determinant. We generalize results for square maximum-volume submatrices to the case of rectangular maximal-volume submatrices, show connection of the rectangular volume with optimal experimental design and provide estimates for the growth of the coefficients and approximation error in spectral and Chebyshev norms. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07838","kind":"arxiv","version":4},"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":"2026-05-18T00:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N/jPmaDQjdNejSEKjXSOh8rQl4qyvLIie2VYEUceDF030elHOHxP3/xrc8oMjOlu7nsXsXs/vdpPxL7bNyqTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:34:37.181134Z"},"content_sha256":"6d6e43206ab9c2a323ca51d91ce45183ab8f45cce0918c51f09de62e225ba58e","schema_version":"1.0","event_id":"sha256:6d6e43206ab9c2a323ca51d91ce45183ab8f45cce0918c51f09de62e225ba58e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFBOBFOYNUAY2YPNKKPCLIBOW7/bundle.json","state_url":"https://pith.science/pith/OFBOBFOYNUAY2YPNKKPCLIBOW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFBOBFOYNUAY2YPNKKPCLIBOW7/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":"2026-06-27T18:34:37Z","links":{"resolver":"https://pith.science/pith/OFBOBFOYNUAY2YPNKKPCLIBOW7","bundle":"https://pith.science/pith/OFBOBFOYNUAY2YPNKKPCLIBOW7/bundle.json","state":"https://pith.science/pith/OFBOBFOYNUAY2YPNKKPCLIBOW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFBOBFOYNUAY2YPNKKPCLIBOW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OFBOBFOYNUAY2YPNKKPCLIBOW7","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":"d81c76e5adfe38f57f9ab6592e746d80434ccf77547596b2d58af184bcc00674","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-02-27T09:29:07Z","title_canon_sha256":"8b78617bddf60d95bf0a454813f7a8907be6b33ba6d54ac2f61d76974a2c8de8"},"schema_version":"1.0","source":{"id":"1502.07838","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07838","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07838v4","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07838","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"OFBOBFOYNUAY","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OFBOBFOYNUAY2YPN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OFBOBFOY","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:6d6e43206ab9c2a323ca51d91ce45183ab8f45cce0918c51f09de62e225ba58e","target":"graph","created_at":"2026-05-18T00:29:39Z","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":"We introduce a definition of the volume for a general rectangular matrix, which for square matrices is equivalent to the absolute value of the determinant. We generalize results for square maximum-volume submatrices to the case of rectangular maximal-volume submatrices, show connection of the rectangular volume with optimal experimental design and provide estimates for the growth of the coefficients and approximation error in spectral and Chebyshev norms. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preco","authors_text":"A. Mikhalev, I. V. Oseledets","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-02-27T09:29:07Z","title":"Rectangular maximum-volume submatrices and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07838","kind":"arxiv","version":4},"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":"sha256:6da79230bc768db19ba7068c7a58cc0ed0019f2923aed53015ab83b5258fb2c0","target":"record","created_at":"2026-05-18T00:29:39Z","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":"d81c76e5adfe38f57f9ab6592e746d80434ccf77547596b2d58af184bcc00674","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-02-27T09:29:07Z","title_canon_sha256":"8b78617bddf60d95bf0a454813f7a8907be6b33ba6d54ac2f61d76974a2c8de8"},"schema_version":"1.0","source":{"id":"1502.07838","kind":"arxiv","version":4}},"canonical_sha256":"7142e095d86d018d61ed529e25a02eb7ef3809d91f90a3a469f26445f0018cca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7142e095d86d018d61ed529e25a02eb7ef3809d91f90a3a469f26445f0018cca","first_computed_at":"2026-05-18T00:29:39.853279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:39.853279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wuiG17XPZdLX7gXVksZ3OK4lYCp6Y7caJsHpmLbaERz+kZ2FCSuSSbxw8mHVbD2T8Iir0Gcj4YoJVgglZAppDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:39.853981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07838","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6da79230bc768db19ba7068c7a58cc0ed0019f2923aed53015ab83b5258fb2c0","sha256:6d6e43206ab9c2a323ca51d91ce45183ab8f45cce0918c51f09de62e225ba58e"],"state_sha256":"7a19878673e3c3ffc890751d93a1855d525ad7ffa505e944e358d346af43c2a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8RHRByMZGJOZJWkI8b3GhoWf8Oe0IedfohhLtmyLtHzYhtjn4FUFmhVGIxTAte0XQSWIzx/itVbQT0dkMSMoBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T18:34:37.183091Z","bundle_sha256":"c89c80a899239afea34fd531279ce586e0771b234a601e60d32a14d85f59b444"}}