{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HURDJ2GE3MX5NRQUKB52NHOYFZ","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":"d4fe247049a04883c55f88bf949ac65c0d2e6fb6e9790544ccd0fcb44f47d175","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-23T17:50:13Z","title_canon_sha256":"99bb929ebd8d731f2dc2a1dbac020b00e6b0596ddf9eb93bfc57db5212fb7f86"},"schema_version":"1.0","source":{"id":"1407.6312","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6312","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6312v2","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6312","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"HURDJ2GE3MX5","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HURDJ2GE3MX5NRQU","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HURDJ2GE","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:168c568a2052e6bc606c16ab0e135e7045f387f558ff1cbd8f28a5e682542c33","target":"graph","created_at":"2026-05-18T00:29:21Z","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 study the asymptotic behavior of the diameter or maximum interpoint distance of a cloud of i.i.d. $d$-dimensional random vectors when the number of points in the cloud tends to infinity. This is a non standard extreme value problem since the diameter is a max-$U$-statistic, hence a maximum of dependent random variables. Therefore, the limiting distributions may not be extreme value distributions. We obtain exhaustive results for the Euclidean diameter of a cloud of elliptical vectors whose Euclidean norm is in the domain of attraction for the maximum of the Gumbel distribution. We also obta","authors_text":"Ana Karina Fermin, Philippe Soulier, Yann Demichel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-23T17:50:13Z","title":"The diameter of a random elliptical cloud"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6312","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":"sha256:90194ef999e742f7108648bfcc2f5f40574dbfacd630dded5c5a2796fddcf73c","target":"record","created_at":"2026-05-18T00:29:21Z","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":"d4fe247049a04883c55f88bf949ac65c0d2e6fb6e9790544ccd0fcb44f47d175","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-23T17:50:13Z","title_canon_sha256":"99bb929ebd8d731f2dc2a1dbac020b00e6b0596ddf9eb93bfc57db5212fb7f86"},"schema_version":"1.0","source":{"id":"1407.6312","kind":"arxiv","version":2}},"canonical_sha256":"3d2234e8c4db2fd6c614507ba69dd82e5c222b57553842696c5d8f25ffaa478a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d2234e8c4db2fd6c614507ba69dd82e5c222b57553842696c5d8f25ffaa478a","first_computed_at":"2026-05-18T00:29:21.501733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:21.501733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f8Mobpl0wtz6ZhCb6BiKpDcoJ4rni/axu1Q+6AVACcxI629HUae16a0JTSy8wcJYeEhMTlM2jxJsbX2sCPeGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:21.502119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6312","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90194ef999e742f7108648bfcc2f5f40574dbfacd630dded5c5a2796fddcf73c","sha256:168c568a2052e6bc606c16ab0e135e7045f387f558ff1cbd8f28a5e682542c33"],"state_sha256":"e7920ac6ceda8151339185c86eacc7caecfe0be2401dbe15c7e2b1718d318734"}