{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6IFMBBENNG6WKTCIZI67YOT24W","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":"99e9e03f6f23331c7cd4605c5ca4d216aea80cac7e08acfa64a44a876b4c31ce","cross_cats_sorted":["cs.NA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-29T15:38:07Z","title_canon_sha256":"3dc10e48cbf55e1f76227c1605dad54b8662cde1780c6513f7a3f902be80c310"},"schema_version":"1.0","source":{"id":"2408.16631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.16631","created_at":"2026-07-05T09:00:44Z"},{"alias_kind":"arxiv_version","alias_value":"2408.16631v1","created_at":"2026-07-05T09:00:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.16631","created_at":"2026-07-05T09:00:44Z"},{"alias_kind":"pith_short_12","alias_value":"6IFMBBENNG6W","created_at":"2026-07-05T09:00:44Z"},{"alias_kind":"pith_short_16","alias_value":"6IFMBBENNG6WKTCI","created_at":"2026-07-05T09:00:44Z"},{"alias_kind":"pith_short_8","alias_value":"6IFMBBEN","created_at":"2026-07-05T09:00:44Z"}],"graph_snapshots":[{"event_id":"sha256:2a2e8b1aedaceeda7fde810c10f100baf2024733eed2339a2ab7785ae8e66713","target":"graph","created_at":"2026-07-05T09:00:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.16631/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In both real and complex cases, we establish the connection of the problem about $2$-dimensional linear subspaces the most deviating from the coordinate ones with one simply formulated optimization problem for isoperimetric polygons in Euclidean spaces.\n  This study thereby provides a new geometrical point of view on the $2$-dimensional case of the problem formulated by Goreinov, Tyrtyshnikov and Zamarashkin \\cite{GTZ1997}, and at the same time presents a new application of the results by Hausmann and Knutson \\cite{HK1997}.","authors_text":"Yuri Nesterenko","cross_cats":["cs.NA","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-29T15:38:07Z","title":"Submatrices with the best-bounded inverses: Studying $\\mathds{R}^{n \\times 2}$ and $\\mathds{C}^{n \\times 2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.16631","kind":"arxiv","version":1},"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":"sha256:77a1529941fc07036e627faef9e5cc169cac7d117dfb4322287de04bb061c2d3","target":"record","created_at":"2026-07-05T09:00:44Z","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":"99e9e03f6f23331c7cd4605c5ca4d216aea80cac7e08acfa64a44a876b4c31ce","cross_cats_sorted":["cs.NA","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-08-29T15:38:07Z","title_canon_sha256":"3dc10e48cbf55e1f76227c1605dad54b8662cde1780c6513f7a3f902be80c310"},"schema_version":"1.0","source":{"id":"2408.16631","kind":"arxiv","version":1}},"canonical_sha256":"f20ac0848d69bd654c48ca3dfc3a7ae5aaf5a0fc9663ef5aa31b180a9f8fecef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f20ac0848d69bd654c48ca3dfc3a7ae5aaf5a0fc9663ef5aa31b180a9f8fecef","first_computed_at":"2026-07-05T09:00:44.268953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:00:44.268953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tXiHXpIW307S38ALDFF4Jn+nid7iKHA4MuIrtg5twuBd4IZ0MjgqoVI2sk+qQHSDKjwm6c0JsBbpuqt+PAZoCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:00:44.269408Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.16631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77a1529941fc07036e627faef9e5cc169cac7d117dfb4322287de04bb061c2d3","sha256:2a2e8b1aedaceeda7fde810c10f100baf2024733eed2339a2ab7785ae8e66713"],"state_sha256":"1457cc049b50bbb5dfe850fcf163b65b0ed2aee360f7caf80bc82bdfacb8f887"}