{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MCXDRCWL57LA4IOK23ZA46NS76","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":"eee9bb01a2b791c602630f87401a1991c996efb0db40dadaaaf4f31970fac813","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-02-27T17:10:59Z","title_canon_sha256":"6f334275a39a9855a7f58fb9b287b9328fde6cf4ae2b6e1c77f096616c04874f"},"schema_version":"1.0","source":{"id":"1302.6926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6926","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6926v1","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6926","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"MCXDRCWL57LA","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MCXDRCWL57LA4IOK","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MCXDRCWL","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:fa50de5fd511aea974712540db571be923f72ca277b60e2637dace94baee6377","target":"graph","created_at":"2026-05-18T03:32:18Z","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":"Let $(X_i,i\\geq 1)$ be a sequence of i.i.d. random variables with values in $[0,1]$, and $f$ be a function such that $`E(f(X_1)^2)<+\\infty$. We show a functional central limit theorem for the process $t\\mapsto \\sum_{i=1}^n f(X_i)1_{X_i\\leq t}$.","authors_text":"David Renault, Jean-Fran\\c{c}ois Marckert","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-02-27T17:10:59Z","title":"A functional central limit theorem for the partial sums of sorted i.i.d. random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6926","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:d04b212d64905432f16e116dcd77bfc9af831c26b9beccb962da899dac4a25b1","target":"record","created_at":"2026-05-18T03:32:18Z","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":"eee9bb01a2b791c602630f87401a1991c996efb0db40dadaaaf4f31970fac813","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-02-27T17:10:59Z","title_canon_sha256":"6f334275a39a9855a7f58fb9b287b9328fde6cf4ae2b6e1c77f096616c04874f"},"schema_version":"1.0","source":{"id":"1302.6926","kind":"arxiv","version":1}},"canonical_sha256":"60ae388acbefd60e21cad6f20e79b2ffb5a54a573344370c68b39df9cb3191ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60ae388acbefd60e21cad6f20e79b2ffb5a54a573344370c68b39df9cb3191ad","first_computed_at":"2026-05-18T03:32:18.124667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:18.124667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q9Vbse2yg9qzWE9cPkwQvgxxT8ORV3DlqcEFxXZ0wRVSntgge/SEpgdmkUOWX0G5xwpps0lxcieAO+3zkZ+rCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:18.125270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d04b212d64905432f16e116dcd77bfc9af831c26b9beccb962da899dac4a25b1","sha256:fa50de5fd511aea974712540db571be923f72ca277b60e2637dace94baee6377"],"state_sha256":"4bffe2df42b8d3671698b22924c5398dfc05e54e8188f21c12eb744d71ced118"}