{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SE5JK42NNXXOXVL52VF75ADO7P","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":"64f46498a9bb9f0ca647de1e3b42827dbeda824d1e9e046dd9d560f637cf723c","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-09-07T11:59:07Z","title_canon_sha256":"e56364ef25b3f1f42790d25612a5bff1e904454d85e9aedf451682521b7f8419"},"schema_version":"1.0","source":{"id":"2309.03662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.03662","created_at":"2026-07-05T06:48:40Z"},{"alias_kind":"arxiv_version","alias_value":"2309.03662v1","created_at":"2026-07-05T06:48:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.03662","created_at":"2026-07-05T06:48:40Z"},{"alias_kind":"pith_short_12","alias_value":"SE5JK42NNXXO","created_at":"2026-07-05T06:48:40Z"},{"alias_kind":"pith_short_16","alias_value":"SE5JK42NNXXOXVL5","created_at":"2026-07-05T06:48:40Z"},{"alias_kind":"pith_short_8","alias_value":"SE5JK42N","created_at":"2026-07-05T06:48:40Z"}],"graph_snapshots":[{"event_id":"sha256:982571845a91b89fdb9db9b9983bbe1026572db2b062d2011b49228fb0c53b51","target":"graph","created_at":"2026-07-05T06:48:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.03662/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\{\\Lambda_n=\\{\\lambda_{1,n},\\ldots,\\lambda_{d_n,n}\\}\\}_n$ be a sequence of finite multisets of real numbers such that $d_n\\to\\infty$ as $n\\to\\infty$, and let $f:\\Omega\\subset\\mathbb R^d\\to\\mathbb R$ be a Lebesgue measurable function defined on a domain $\\Omega$ with $0<\\mu_d(\\Omega)<\\infty$, where $\\mu_d$ is the Lebesgue measure in $\\mathbb R^d$. We say that $\\{\\Lambda_n\\}_n$ has an asymptotic distribution described by $f$, and we write $\\{\\Lambda_n\\}_n\\sim f$, if \\[ \\lim_{n\\to\\infty}\\frac1{d_n}\\sum_{i=1}^{d_n}F(\\lambda_{i,n})=\\frac1{\\mu_d(\\Omega)}\\int_\\Omega F(f({\\boldsymbol x})){\\rm d}{","authors_text":"Carlo Garoni, David Meadon, Giovanni Barbarino, Paris Vassalos, Stefano Serra-Capizzano, Sven-Erik Ekstr\\\"om","cross_cats":["cs.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-09-07T11:59:07Z","title":"From asymptotic distribution and vague convergence to uniform convergence, with numerical applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.03662","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":"sha256:3ab726b06b054b2ce823921db8763dff10dc20e627b4f2d6e7d0b62556ed2fb8","target":"record","created_at":"2026-07-05T06:48:40Z","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":"64f46498a9bb9f0ca647de1e3b42827dbeda824d1e9e046dd9d560f637cf723c","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-09-07T11:59:07Z","title_canon_sha256":"e56364ef25b3f1f42790d25612a5bff1e904454d85e9aedf451682521b7f8419"},"schema_version":"1.0","source":{"id":"2309.03662","kind":"arxiv","version":1}},"canonical_sha256":"913a95734d6deeebd57dd54bfe806efbe12a34b576923ed409ab0dcd901dd5d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"913a95734d6deeebd57dd54bfe806efbe12a34b576923ed409ab0dcd901dd5d1","first_computed_at":"2026-07-05T06:48:40.244072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:48:40.244072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JLQS7O+8D2T2vxZaCa1V/i7gjl2neXGQvS30A+fs0PcHEKhYY85saoD1PITNzYzS8iFEwWLmdkKgbWiI8g19Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:48:40.244550Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.03662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ab726b06b054b2ce823921db8763dff10dc20e627b4f2d6e7d0b62556ed2fb8","sha256:982571845a91b89fdb9db9b9983bbe1026572db2b062d2011b49228fb0c53b51"],"state_sha256":"9fcb9eca125bbbf9f699f570cb18362e3c64b8f4569ff8911c63ece2008b1a63"}