{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HMFVKGI5F3N6OAPFZ5IJJPEFAJ","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":"17090f68800aef226af4a9409a4acdef932c376410a13a59c412c82a8ea35d6f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-13T16:09:40Z","title_canon_sha256":"b8b2b00a3c951af2e8d6e288657dd304ed953d5212f6d5d311319e89cf889cd2"},"schema_version":"1.0","source":{"id":"1804.05009","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05009","created_at":"2026-07-05T00:58:30Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05009v4","created_at":"2026-07-05T00:58:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05009","created_at":"2026-07-05T00:58:30Z"},{"alias_kind":"pith_short_12","alias_value":"HMFVKGI5F3N6","created_at":"2026-07-05T00:58:30Z"},{"alias_kind":"pith_short_16","alias_value":"HMFVKGI5F3N6OAPF","created_at":"2026-07-05T00:58:30Z"},{"alias_kind":"pith_short_8","alias_value":"HMFVKGI5","created_at":"2026-07-05T00:58:30Z"}],"graph_snapshots":[{"event_id":"sha256:6ec5c8940abb76e11b97765b902d4bb31dbae8826042311e610fc19bb3f9344f","target":"graph","created_at":"2026-07-05T00:58:30Z","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/1804.05009/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr.~on the reverse question: Every convex body has a linear image whose isodiametric quotient is at least as large as that of a regular simplex. We relate this reverse isodiametric problem to minimal volume enclosing ellipsoids and to the Dvoretzky-Rogers-type problem of finding large volume simplices in any decomposition of the identity matrix.\n  As a result, we solve the reverse isodiametric problem for $o$-symmetric convex bod","authors_text":"Bernardo Gonz\\'alez Merino, Matthias Schymura","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-13T16:09:40Z","title":"On the reverse isodiametric problem and Dvoretzky-Rogers-type volume bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05009","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":"sha256:374dd39774e063c00fd4c1f324fc134db3e8aa76e365f1869e7f99a53249d701","target":"record","created_at":"2026-07-05T00:58:30Z","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":"17090f68800aef226af4a9409a4acdef932c376410a13a59c412c82a8ea35d6f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-13T16:09:40Z","title_canon_sha256":"b8b2b00a3c951af2e8d6e288657dd304ed953d5212f6d5d311319e89cf889cd2"},"schema_version":"1.0","source":{"id":"1804.05009","kind":"arxiv","version":4}},"canonical_sha256":"3b0b55191d2edbe701e5cf5094bc85024845cf25be2e9132fa4aa4a892c91917","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b0b55191d2edbe701e5cf5094bc85024845cf25be2e9132fa4aa4a892c91917","first_computed_at":"2026-07-05T00:58:30.587991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:58:30.587991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Or1F2CGGJNg8KVuz0v70ZCjz4urR995loirdyXw+49WNdVc06D3WXhI8GS4wDjd2bAp52qRKqoBmK6cAuYsOAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:58:30.588428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05009","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:374dd39774e063c00fd4c1f324fc134db3e8aa76e365f1869e7f99a53249d701","sha256:6ec5c8940abb76e11b97765b902d4bb31dbae8826042311e610fc19bb3f9344f"],"state_sha256":"3c0bc1cb2c87bd564d3c347b5302a46f6b1b34c6cb9be2a1bbe32955343c567c"}