{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LOCSFOUFW2TV5NED26745BKEMY","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":"0d212788a9afc2d81f84d3cc8cd87f7810bd706f09b47ee33fbefc12a2944ea2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-02T16:26:28Z","title_canon_sha256":"9d3955f2650689c3064c2dad7f06e1c22b150cc01b6c942b57a29aef063ee6dc"},"schema_version":"1.0","source":{"id":"1402.0209","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0209","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0209v2","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0209","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"pith_short_12","alias_value":"LOCSFOUFW2TV","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LOCSFOUFW2TV5NED","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LOCSFOUF","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:cf39eace0cd67f65574c7838655e2a9e957d81035b85fc1e3f60a4410d04bab2","target":"graph","created_at":"2026-05-18T02:52:14Z","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":"For any origin-symmetric convex body $K$ in $\\mathbb{R}^n$ in isotropic position, we obtain the bound: \\[ M^*(K) \\leq C \\sqrt{n} \\log(n)^2 L_K ~, \\] where $M^*(K)$ denotes (half) the mean-width of $K$, $L_K$ is the isotropic constant of $K$, and $C>0$ is a universal constant. This improves the previous best-known estimate $M^*(K) \\leq C n^{3/4} L_K$. Up to the power of the $\\log(n)$ term and the $L_K$ one, the improved bound is best possible, and implies that the isotropic position is (up to the $L_K$ term) an almost $2$-regular $M$-position. The bound extends to any arbitrary position, depend","authors_text":"Emanuel Milman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-02T16:26:28Z","title":"On the mean-width of isotropic convex bodies and their associated $L_p$-centroid bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0209","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":"sha256:08dffabc8e0223304b9fd46b275ae1babb3286bc94d8793e64ea53cea81389e2","target":"record","created_at":"2026-05-18T02:52:14Z","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":"0d212788a9afc2d81f84d3cc8cd87f7810bd706f09b47ee33fbefc12a2944ea2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-02T16:26:28Z","title_canon_sha256":"9d3955f2650689c3064c2dad7f06e1c22b150cc01b6c942b57a29aef063ee6dc"},"schema_version":"1.0","source":{"id":"1402.0209","kind":"arxiv","version":2}},"canonical_sha256":"5b8522ba85b6a75eb483d7bfce8544661bb94dabdce7870f28d20da4282e4765","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b8522ba85b6a75eb483d7bfce8544661bb94dabdce7870f28d20da4282e4765","first_computed_at":"2026-05-18T02:52:14.883109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:14.883109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QitUOjq0Qeh1/wsymdABIUYUsg7t53ZUpT8TgIjl2i+6EEHLcC2k4OljiJmvEFfgwahx5V6jGe9hH3kFKGxADA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:14.883696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0209","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08dffabc8e0223304b9fd46b275ae1babb3286bc94d8793e64ea53cea81389e2","sha256:cf39eace0cd67f65574c7838655e2a9e957d81035b85fc1e3f60a4410d04bab2"],"state_sha256":"e17ae295d86968c7f5dcf22b24d4558c8ffa2e92fd09c7642399432aaeed1c0d"}