{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QZEDEKMSK6SL6VLM7ZSRHW42OS","short_pith_number":"pith:QZEDEKMS","canonical_record":{"source":{"id":"1511.05463","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-17T16:46:23Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"36033419e40dfc6de4683bbcbeb9b09094f810c7e8bfab2b62205d1270dc6833","abstract_canon_sha256":"cb81b51d311ce2eeac40fc18082909f15c354faa60c1f4d82445b402c3fcead0"},"schema_version":"1.0"},"canonical_sha256":"864832299257a4bf556cfe6513db9a7496a5730a1c78efe265dda47968f308b9","source":{"kind":"arxiv","id":"1511.05463","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05463","created_at":"2026-05-18T01:25:17Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05463v2","created_at":"2026-05-18T01:25:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05463","created_at":"2026-05-18T01:25:17Z"},{"alias_kind":"pith_short_12","alias_value":"QZEDEKMSK6SL","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZEDEKMSK6SL6VLM","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZEDEKMS","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QZEDEKMSK6SL6VLM7ZSRHW42OS","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05463","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-17T16:46:23Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"36033419e40dfc6de4683bbcbeb9b09094f810c7e8bfab2b62205d1270dc6833","abstract_canon_sha256":"cb81b51d311ce2eeac40fc18082909f15c354faa60c1f4d82445b402c3fcead0"},"schema_version":"1.0"},"canonical_sha256":"864832299257a4bf556cfe6513db9a7496a5730a1c78efe265dda47968f308b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:17.658142Z","signature_b64":"hxvIv/rQSdWGmIBCxzFwz6GEpPygKqELuzRONb4H4EVF5eOCqy/zx5aZJQyj/rNRKpD6IKTrv6DK6ikXKfuzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"864832299257a4bf556cfe6513db9a7496a5730a1c78efe265dda47968f308b9","last_reissued_at":"2026-05-18T01:25:17.657445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:17.657445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05463","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":"2026-05-18T01:25:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g2yz6QUBet0yWzuIR2jWZvTzB+fuGtZ9u3XIpjCpnkpNRRTkGqqO+g2rGC62qNtIsXoVnE74dExXsx+XIiOpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:26:33.996709Z"},"content_sha256":"379be04e3d8b7bfa80065265880e38396423bfcbaad43c23d23f6aae0d9cad53","schema_version":"1.0","event_id":"sha256:379be04e3d8b7bfa80065265880e38396423bfcbaad43c23d23f6aae0d9cad53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QZEDEKMSK6SL6VLM7ZSRHW42OS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the restricted invertibility problem with an additional orthogonality constraint for random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Stephane Chretien","submitted_at":"2015-11-17T16:46:23Z","abstract_excerpt":"The Restricted Invertibility problem is the problem of selecting the largest subset of columns of a given matrix $X$, while keeping the smallest singular value of the extracted submatrix above a certain threshold. In this paper, we address this problem in the simpler case where $X$ is a random matrix but with the additional constraint that the selected columns be almost orthogonal to a given vector $v$. Our main result is a lower bound on the number of columns we can extract from a normalized i.i.d. Gaussian matrix for the worst $v$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05463","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":"2026-05-18T01:25:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z5jTNOP5N0Lixcnykul5mcttbvZwDIjXodJSBNmYodWNskj9MZLb1C8tsFuM0TCVcKlXfJZykUnJO7SkCA2yCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:26:33.997057Z"},"content_sha256":"4a182a4744cb9e1faf2b51ebd7c183372832deb26c17b1287221ee17073ccd46","schema_version":"1.0","event_id":"sha256:4a182a4744cb9e1faf2b51ebd7c183372832deb26c17b1287221ee17073ccd46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZEDEKMSK6SL6VLM7ZSRHW42OS/bundle.json","state_url":"https://pith.science/pith/QZEDEKMSK6SL6VLM7ZSRHW42OS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZEDEKMSK6SL6VLM7ZSRHW42OS/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":"2026-05-29T17:26:33Z","links":{"resolver":"https://pith.science/pith/QZEDEKMSK6SL6VLM7ZSRHW42OS","bundle":"https://pith.science/pith/QZEDEKMSK6SL6VLM7ZSRHW42OS/bundle.json","state":"https://pith.science/pith/QZEDEKMSK6SL6VLM7ZSRHW42OS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZEDEKMSK6SL6VLM7ZSRHW42OS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QZEDEKMSK6SL6VLM7ZSRHW42OS","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":"cb81b51d311ce2eeac40fc18082909f15c354faa60c1f4d82445b402c3fcead0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-17T16:46:23Z","title_canon_sha256":"36033419e40dfc6de4683bbcbeb9b09094f810c7e8bfab2b62205d1270dc6833"},"schema_version":"1.0","source":{"id":"1511.05463","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05463","created_at":"2026-05-18T01:25:17Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05463v2","created_at":"2026-05-18T01:25:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05463","created_at":"2026-05-18T01:25:17Z"},{"alias_kind":"pith_short_12","alias_value":"QZEDEKMSK6SL","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZEDEKMSK6SL6VLM","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZEDEKMS","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:4a182a4744cb9e1faf2b51ebd7c183372832deb26c17b1287221ee17073ccd46","target":"graph","created_at":"2026-05-18T01:25:17Z","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 Restricted Invertibility problem is the problem of selecting the largest subset of columns of a given matrix $X$, while keeping the smallest singular value of the extracted submatrix above a certain threshold. In this paper, we address this problem in the simpler case where $X$ is a random matrix but with the additional constraint that the selected columns be almost orthogonal to a given vector $v$. Our main result is a lower bound on the number of columns we can extract from a normalized i.i.d. Gaussian matrix for the worst $v$.","authors_text":"Stephane Chretien","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-17T16:46:23Z","title":"On the restricted invertibility problem with an additional orthogonality constraint for random matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05463","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":"sha256:379be04e3d8b7bfa80065265880e38396423bfcbaad43c23d23f6aae0d9cad53","target":"record","created_at":"2026-05-18T01:25:17Z","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":"cb81b51d311ce2eeac40fc18082909f15c354faa60c1f4d82445b402c3fcead0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-17T16:46:23Z","title_canon_sha256":"36033419e40dfc6de4683bbcbeb9b09094f810c7e8bfab2b62205d1270dc6833"},"schema_version":"1.0","source":{"id":"1511.05463","kind":"arxiv","version":2}},"canonical_sha256":"864832299257a4bf556cfe6513db9a7496a5730a1c78efe265dda47968f308b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"864832299257a4bf556cfe6513db9a7496a5730a1c78efe265dda47968f308b9","first_computed_at":"2026-05-18T01:25:17.657445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:17.657445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hxvIv/rQSdWGmIBCxzFwz6GEpPygKqELuzRONb4H4EVF5eOCqy/zx5aZJQyj/rNRKpD6IKTrv6DK6ikXKfuzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:17.658142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05463","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:379be04e3d8b7bfa80065265880e38396423bfcbaad43c23d23f6aae0d9cad53","sha256:4a182a4744cb9e1faf2b51ebd7c183372832deb26c17b1287221ee17073ccd46"],"state_sha256":"0e6d2b924da679dd3dd7dc60662457c27d1e89cd885ca8aadf0f2c75bdf10938"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"neINdEsnQPZ4/D9WUe97nfJ4W+ROjcxCDaEN4WYUHM623MmtyQzvimJBwsCuEXmK0mNatf0gHvNWTCRafpKRAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:26:33.999191Z","bundle_sha256":"931f2abcafac6dfe7ae5a0522874fafbd072760f6d119a9d424f8bd8eb153d2d"}}