{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PWWHASSXZLPKPDZLIQIRWKWUS3","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":"c7ce6b6a4748bb1d5c8fa1b1f3ce911d4eedce989d26b5ff2392dea2f96bf935","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-19T10:56:00Z","title_canon_sha256":"ca8d3c3d9a20aa9a303563d640a6cef1f03cfe771b716486e18efffb304d3f42"},"schema_version":"1.0","source":{"id":"1107.3683","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3683","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3683v1","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3683","created_at":"2026-05-18T04:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"PWWHASSXZLPK","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWWHASSXZLPKPDZL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWWHASSX","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:f89544fd634dcae2c3a712323009d1c4f45f66281d010d8b5609d8f3d7d75b3f","target":"graph","created_at":"2026-05-18T04:17:24Z","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 show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P in R^n by its dual L_{p$-centroid bodies is independent of the geometry of P. In particular we show that if P has volume 1, lim_{p\\rightarrow \\infty} \\frac{p}{\\log{p}} (\\frac{|Z_{p}^{\\circ}(P)|}{|P^{\\circ}|} -1) = n^{2}.\n  We provide an application to the approximation of polytopes by uniformly convex sets.","authors_text":"Elisabeth M. Werner, Grigoris Paouris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-19T10:56:00Z","title":"On the approximation of a polytope by its dual $L_{p}$-centroid bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3683","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":"sha256:38de7ce081db51a71c740d61b13d8915fc7c8aafda25d7b607140039ecf6fbb4","target":"record","created_at":"2026-05-18T04:17:24Z","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":"c7ce6b6a4748bb1d5c8fa1b1f3ce911d4eedce989d26b5ff2392dea2f96bf935","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-07-19T10:56:00Z","title_canon_sha256":"ca8d3c3d9a20aa9a303563d640a6cef1f03cfe771b716486e18efffb304d3f42"},"schema_version":"1.0","source":{"id":"1107.3683","kind":"arxiv","version":1}},"canonical_sha256":"7dac704a57cadea78f2b44111b2ad496ff4b303253abc8442a9b2a66ba5ead79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dac704a57cadea78f2b44111b2ad496ff4b303253abc8442a9b2a66ba5ead79","first_computed_at":"2026-05-18T04:17:24.189369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:24.189369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K4B0eKaGq19v7wEzwD08wjkZ6kHp5LMBsdD0TlVxE0w8LCo+ZlPYh4TjM5QiATapvbbUORQ3vhcM+mdTxe1uDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:24.190114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3683","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38de7ce081db51a71c740d61b13d8915fc7c8aafda25d7b607140039ecf6fbb4","sha256:f89544fd634dcae2c3a712323009d1c4f45f66281d010d8b5609d8f3d7d75b3f"],"state_sha256":"8552b95604c52a1647efc2066acc6d131932e95a4b6f845c4ffb59cf77264535"}