{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UNFKHNBQFVH6JMMXQKQKC3LNDV","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":"d04fc2b494beffc10b6928a04935c8fbc9987d612e6d1ccdb642e05a12fc9d7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-14T09:28:45Z","title_canon_sha256":"c0ccd80b5768f8c3f646cfe4da146bddf338df29ef5d890c8886c4fb4e1aeb0c"},"schema_version":"1.0","source":{"id":"1512.04226","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04226","created_at":"2026-05-17T23:44:33Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04226v3","created_at":"2026-05-17T23:44:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04226","created_at":"2026-05-17T23:44:33Z"},{"alias_kind":"pith_short_12","alias_value":"UNFKHNBQFVH6","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UNFKHNBQFVH6JMMX","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UNFKHNBQ","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:83402cfd57153dda950318d1592dfd196c312f5adb6b68c1c7541eae855d26a4","target":"graph","created_at":"2026-05-17T23:44:33Z","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 randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such algorithms typically involve a step of finding the optimal solution for a random sample of the constraints. They exploit the condition that, in finite dimension $\\delta$, this sample optimum violates a provably small expected fraction of the non-sampled constraints, with the fraction decreasing in the sample size~$r$. We extend such algorithms by considering","authors_text":"Bernd G\\\"artner, Johannes Lengler, Kenneth L. Clarkson, May Szedlak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-14T09:28:45Z","title":"Random Sampling with Removal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04226","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:d08b65ab702e6d2e4277a896d4d4d161cc8d1d3271040d9746540b1324caac52","target":"record","created_at":"2026-05-17T23:44:33Z","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":"d04fc2b494beffc10b6928a04935c8fbc9987d612e6d1ccdb642e05a12fc9d7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-14T09:28:45Z","title_canon_sha256":"c0ccd80b5768f8c3f646cfe4da146bddf338df29ef5d890c8886c4fb4e1aeb0c"},"schema_version":"1.0","source":{"id":"1512.04226","kind":"arxiv","version":3}},"canonical_sha256":"a34aa3b4302d4fe4b19782a0a16d6d1d679e7d7f33a118a47a6ea77ef06efc6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a34aa3b4302d4fe4b19782a0a16d6d1d679e7d7f33a118a47a6ea77ef06efc6b","first_computed_at":"2026-05-17T23:44:33.216455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:33.216455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WH+J1MhRD8SWdxMgvNlvDitAdpyEi3BbKqbk9F1bPHusmv2cevMkYp0XHVqlqugmcY/pri5LuDuLt3ZIP3/MBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:33.216970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04226","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d08b65ab702e6d2e4277a896d4d4d161cc8d1d3271040d9746540b1324caac52","sha256:83402cfd57153dda950318d1592dfd196c312f5adb6b68c1c7541eae855d26a4"],"state_sha256":"ef7d4af37342fa2d2e9e20a9185ae0a248c67a377d291c3073362ebcc255f1f3"}