{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WQR7CD75AVAEI2BUA4MPX5ERGA","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":"7c068824b17c0a8a526bae3a5a50f6c3040b9a6c77268236d08137007209a6c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-04T15:41:14Z","title_canon_sha256":"baac68e7eb81f543ea17a1163fe781ffa605b3504c1d63ca4fc07fa42a407540"},"schema_version":"1.0","source":{"id":"1206.0654","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0654","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0654v3","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0654","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"WQR7CD75AVAE","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WQR7CD75AVAEI2BU","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WQR7CD75","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:84cf2bb2238e473a6d843f5d8833f795528dc619b94459253cee8d00179a67ec","target":"graph","created_at":"2026-05-17T23:53:18Z","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 prove a normalized version of the restricted invertibility principle obtained by Spielman-Srivastava. Applying this result, we get a new proof of the proportional Dvoretzky-Rogers factorization theorem recovering the best current estimate. As a consequence, we also recover the best known estimate for the Banach-Mazur distance to the cube: the distance of every n-dimensional normed space from \\ell_{\\infty}^n is at most (2n)^(5/6). Finally, using tools from the work of Batson-Spielman-Srivastava, we give a new proof for a theorem of Kashin-Tzafriri on the norm of restricted matrices.","authors_text":"Pierre Youssef","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-04T15:41:14Z","title":"Restricted Invertibility and the Banach-Mazur distance to the cube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0654","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:f98eaea200cbcab8419c3b376df7ddf3628507ee2fb43ffa1e35e2b78099aadc","target":"record","created_at":"2026-05-17T23:53:18Z","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":"7c068824b17c0a8a526bae3a5a50f6c3040b9a6c77268236d08137007209a6c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-06-04T15:41:14Z","title_canon_sha256":"baac68e7eb81f543ea17a1163fe781ffa605b3504c1d63ca4fc07fa42a407540"},"schema_version":"1.0","source":{"id":"1206.0654","kind":"arxiv","version":3}},"canonical_sha256":"b423f10ffd05404468340718fbf4913006d33f3f0c047ca7fe713b0e5efbea45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b423f10ffd05404468340718fbf4913006d33f3f0c047ca7fe713b0e5efbea45","first_computed_at":"2026-05-17T23:53:18.656735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.656735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+c9N4uXKi8rqI/NclkCKECJK7vDVaKh7fc+Cs5KyptgUZiRSH71gXkEMf+DIvcwYfPAerjKbUjSgEt3dccCCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.657272Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0654","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f98eaea200cbcab8419c3b376df7ddf3628507ee2fb43ffa1e35e2b78099aadc","sha256:84cf2bb2238e473a6d843f5d8833f795528dc619b94459253cee8d00179a67ec"],"state_sha256":"7a2da433f8bbf38e9a50de5e2f9464c7c78c778668f96f15e315e57e79183186"}