{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CHM5N5WPNGSK5E2UYA74DY2QLR","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":"6b1ee6e388a8b272d096993c7a5fb4245f97560ebac9deef69242d0e8d38dbf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-30T16:02:12Z","title_canon_sha256":"7bebb118afb9a86d4c0786b72261b2ed23a0ba69974aed78247813e4df7f2bd8"},"schema_version":"1.0","source":{"id":"1804.11287","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11287","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11287v3","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11287","created_at":"2026-05-18T00:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"CHM5N5WPNGSK","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CHM5N5WPNGSK5E2U","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CHM5N5WP","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:6942450e49df42df1b448c3deaef379b05c43fd20782207b0e2b105a46378a26","target":"graph","created_at":"2026-05-18T00:04:37Z","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":"Consider a geometric range space $(X,\\c{A})$ where each data point $x \\in X$ has two or more values (say $r(x)$ and $b(x)$). Also consider a function $\\Phi(A)$ defined on any subset $A \\in (X,\\c{A})$ on the sum of values in that range e.g., $r_A = \\sum_{x \\in A} r(x)$ and $b_A = \\sum_{x \\in A} b(x)$. The $\\Phi$-maximum range is $A^* = \\arg \\max_{A \\in (X,\\c{A})} \\Phi(A)$. Our goal is to find some $\\hat{A}$ such that $|\\Phi(\\hat{A}) - \\Phi(A^*)| \\leq \\varepsilon.$ We develop algorithms for this problem for range spaces with bounded VC-dimension, as well as significant improvements for those def","authors_text":"Jeff M. Phillips, Michael Matheny","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-30T16:02:12Z","title":"Computing Approximate Statistical Discrepancy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11287","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:cb0374138a0441a70e307e4e3936757a2db0feb4c024ac53dc8db6de2bc5dd8d","target":"record","created_at":"2026-05-18T00:04:37Z","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":"6b1ee6e388a8b272d096993c7a5fb4245f97560ebac9deef69242d0e8d38dbf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-04-30T16:02:12Z","title_canon_sha256":"7bebb118afb9a86d4c0786b72261b2ed23a0ba69974aed78247813e4df7f2bd8"},"schema_version":"1.0","source":{"id":"1804.11287","kind":"arxiv","version":3}},"canonical_sha256":"11d9d6f6cf69a4ae9354c03fc1e3505c7594c3df1460c168319682b347435cd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11d9d6f6cf69a4ae9354c03fc1e3505c7594c3df1460c168319682b347435cd8","first_computed_at":"2026-05-18T00:04:37.434144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:37.434144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JC9EyqUvcxeM8PSGJBd29uKqIHsUaudVayBUyMPDbFCo80jmAiu+ql3xmVcb3YR0JDaJdWtki2sEgntUHexXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:37.434626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.11287","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb0374138a0441a70e307e4e3936757a2db0feb4c024ac53dc8db6de2bc5dd8d","sha256:6942450e49df42df1b448c3deaef379b05c43fd20782207b0e2b105a46378a26"],"state_sha256":"ed7495508b1a0fb21f088439d0efa387138484d1b3d0f1983c031510f268b63f"}