{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DIS4G7GD5JT3AZ3ZCOJWYFM77N","short_pith_number":"pith:DIS4G7GD","canonical_record":{"source":{"id":"1401.6434","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-24T19:46:22Z","cross_cats_sorted":[],"title_canon_sha256":"764048f78a8aa194cb633e0d724c84503678e66ec29c92b5a09ad9f2f3003929","abstract_canon_sha256":"d9ae6d3562413aa18adefec8934eb7b0231d7b72daa842f7f24a7dd8bcd66b61"},"schema_version":"1.0"},"canonical_sha256":"1a25c37cc3ea67b0677913936c159ffb6f184b455ba6ea98a2dbe0519762c12f","source":{"kind":"arxiv","id":"1401.6434","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6434","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6434v3","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6434","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"DIS4G7GD5JT3","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DIS4G7GD5JT3AZ3Z","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DIS4G7GD","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DIS4G7GD5JT3AZ3ZCOJWYFM77N","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6434","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-24T19:46:22Z","cross_cats_sorted":[],"title_canon_sha256":"764048f78a8aa194cb633e0d724c84503678e66ec29c92b5a09ad9f2f3003929","abstract_canon_sha256":"d9ae6d3562413aa18adefec8934eb7b0231d7b72daa842f7f24a7dd8bcd66b61"},"schema_version":"1.0"},"canonical_sha256":"1a25c37cc3ea67b0677913936c159ffb6f184b455ba6ea98a2dbe0519762c12f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:05.784144Z","signature_b64":"j1rRCxHA+QqS/vqllpvGakv7Ramw+GSCEqekn1Q74MB9xfsyW5/IXRFXFZf8meE6JPfHwFirzohB+QLljP86CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a25c37cc3ea67b0677913936c159ffb6f184b455ba6ea98a2dbe0519762c12f","last_reissued_at":"2026-05-18T01:27:05.783445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:05.783445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6434","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":"2026-05-18T01:27:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NoHlNDHXrzGAmi2LWHlJvvrjwYR7BMrSbRbivCCB+X5sl1Hpyvwna2OWisO3lt7OQBgNfzg7me+yaHM3ixANCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:51:27.811658Z"},"content_sha256":"83930ed8190691ed378e22e831a0e0c790ba86f12422ef8983ea3191fdf0b225","schema_version":"1.0","event_id":"sha256:83930ed8190691ed378e22e831a0e0c790ba86f12422ef8983ea3191fdf0b225"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DIS4G7GD5JT3AZ3ZCOJWYFM77N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extracting a basis with fixed block inside a matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pierre Youssef","submitted_at":"2014-01-24T19:46:22Z","abstract_excerpt":"Given $U$ an $n\\times m$ matrix of rank $n$ and $V$ block of columns inside $U$, we consider the problem of extracting a block of columns of rank $n$ which minimize the Hilbert-Schmidt norm of the inverse while preserving the block $V$. This generalizes a previous result of Gluskin-Olevskii, and improves the estimates when given a \"good\" block $V$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6434","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":""},"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":"2026-05-18T01:27:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MxLsYI1BvHrUjwhKFgslSPjQHeSrL7IRe4Bb+Y2Vr53jicm4nwegLNqzndfpg4auFjQGSNNx9LABU+lUhktDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:51:27.812013Z"},"content_sha256":"8d3db1557d1bee747ef497a9e015c1d805649c639eaab1953a65e2e32884783f","schema_version":"1.0","event_id":"sha256:8d3db1557d1bee747ef497a9e015c1d805649c639eaab1953a65e2e32884783f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DIS4G7GD5JT3AZ3ZCOJWYFM77N/bundle.json","state_url":"https://pith.science/pith/DIS4G7GD5JT3AZ3ZCOJWYFM77N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DIS4G7GD5JT3AZ3ZCOJWYFM77N/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":"2026-05-30T07:51:27Z","links":{"resolver":"https://pith.science/pith/DIS4G7GD5JT3AZ3ZCOJWYFM77N","bundle":"https://pith.science/pith/DIS4G7GD5JT3AZ3ZCOJWYFM77N/bundle.json","state":"https://pith.science/pith/DIS4G7GD5JT3AZ3ZCOJWYFM77N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DIS4G7GD5JT3AZ3ZCOJWYFM77N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DIS4G7GD5JT3AZ3ZCOJWYFM77N","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":"d9ae6d3562413aa18adefec8934eb7b0231d7b72daa842f7f24a7dd8bcd66b61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-24T19:46:22Z","title_canon_sha256":"764048f78a8aa194cb633e0d724c84503678e66ec29c92b5a09ad9f2f3003929"},"schema_version":"1.0","source":{"id":"1401.6434","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6434","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6434v3","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6434","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"DIS4G7GD5JT3","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DIS4G7GD5JT3AZ3Z","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DIS4G7GD","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8d3db1557d1bee747ef497a9e015c1d805649c639eaab1953a65e2e32884783f","target":"graph","created_at":"2026-05-18T01:27:05Z","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":"Given $U$ an $n\\times m$ matrix of rank $n$ and $V$ block of columns inside $U$, we consider the problem of extracting a block of columns of rank $n$ which minimize the Hilbert-Schmidt norm of the inverse while preserving the block $V$. This generalizes a previous result of Gluskin-Olevskii, and improves the estimates when given a \"good\" block $V$.","authors_text":"Pierre Youssef","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-24T19:46:22Z","title":"Extracting a basis with fixed block inside a matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6434","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":"sha256:83930ed8190691ed378e22e831a0e0c790ba86f12422ef8983ea3191fdf0b225","target":"record","created_at":"2026-05-18T01:27:05Z","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":"d9ae6d3562413aa18adefec8934eb7b0231d7b72daa842f7f24a7dd8bcd66b61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-24T19:46:22Z","title_canon_sha256":"764048f78a8aa194cb633e0d724c84503678e66ec29c92b5a09ad9f2f3003929"},"schema_version":"1.0","source":{"id":"1401.6434","kind":"arxiv","version":3}},"canonical_sha256":"1a25c37cc3ea67b0677913936c159ffb6f184b455ba6ea98a2dbe0519762c12f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a25c37cc3ea67b0677913936c159ffb6f184b455ba6ea98a2dbe0519762c12f","first_computed_at":"2026-05-18T01:27:05.783445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:05.783445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j1rRCxHA+QqS/vqllpvGakv7Ramw+GSCEqekn1Q74MB9xfsyW5/IXRFXFZf8meE6JPfHwFirzohB+QLljP86CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:05.784144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6434","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83930ed8190691ed378e22e831a0e0c790ba86f12422ef8983ea3191fdf0b225","sha256:8d3db1557d1bee747ef497a9e015c1d805649c639eaab1953a65e2e32884783f"],"state_sha256":"c08f1e59c75aac034b0320e03e1e1dc428829021d826603df7c917453325b739"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1mBUpjSB/VOEfZy1L4ssYqhzmetElxgQ5ikpimvwTAgVzifLkCbVtu+S4Bz9AFmqo4PMrgypuk+CBdFIsPtAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:51:27.814080Z","bundle_sha256":"f3c15f6e7faf37c4aba43a544e4f810194856bec3f084dd8fb1c13e68d2a1658"}}