{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:BYDRAJ3XEFO2WCCCTXDLNHZ3DY","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":"ea16cb2fca403ea3aed4ea3e977569398ee1ac898a87bb0b7b939b113c9914ae","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.PR","submitted_at":"2005-05-27T23:07:27Z","title_canon_sha256":"c23a04f7aa97ae8f167318ccb8408d929b95df2a566bc722ffeea8c8a1c3829e"},"schema_version":"1.0","source":{"id":"math/0505618","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505618","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505618v3","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505618","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"BYDRAJ3XEFO2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"BYDRAJ3XEFO2WCCC","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"BYDRAJ3X","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:c4a210edf88965b1537d66d5bc42cbe5622aeff3c0ac606bb5464dae39763927","target":"graph","created_at":"2026-05-18T01:05:23Z","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":"Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method wh","authors_text":"Elizabeth S. Meckes, Mark W. Meckes","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2005-05-27T23:07:27Z","title":"The central limit problem for random vectors with symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505618","kind":"arxiv","version":3},"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:fd77c0b1543896ff41cea917cfcc79799a297dca3aebc7bdf9e04a95227f8a04","target":"record","created_at":"2026-05-18T01:05:23Z","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":"ea16cb2fca403ea3aed4ea3e977569398ee1ac898a87bb0b7b939b113c9914ae","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.PR","submitted_at":"2005-05-27T23:07:27Z","title_canon_sha256":"c23a04f7aa97ae8f167318ccb8408d929b95df2a566bc722ffeea8c8a1c3829e"},"schema_version":"1.0","source":{"id":"math/0505618","kind":"arxiv","version":3}},"canonical_sha256":"0e07102777215dab08429dc6b69f3b1e09c13d8219cea1dab3805b4048b77bc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e07102777215dab08429dc6b69f3b1e09c13d8219cea1dab3805b4048b77bc6","first_computed_at":"2026-05-18T01:05:23.424788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:23.424788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iqx2Nz7gClGxmgT0c1J0piNxLK07PSkgjjBJ9RVeHVQdVTKEisjQ9sW8dyhY7Fg35E9FI70Y1P26QlIGGYBDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:23.425246Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0505618","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd77c0b1543896ff41cea917cfcc79799a297dca3aebc7bdf9e04a95227f8a04","sha256:c4a210edf88965b1537d66d5bc42cbe5622aeff3c0ac606bb5464dae39763927"],"state_sha256":"598fd3be69ea3b5d294261e15167cd641db1cbce8246a6581df8c998062dfe13"}