{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GGM3PIWQGAWVZTVDYFDIGTTTXC","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":"67acf7e36a19cc64d6c12dac8a1714f055d0566f4418f8ab27ce62399f3aac8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-14T04:56:50Z","title_canon_sha256":"19fd3ba42f29750f81a0cde6f9db288287ef5de6301d7eaa4033e8655f828dbe"},"schema_version":"1.0","source":{"id":"1501.03246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03246","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03246v1","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03246","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"GGM3PIWQGAWV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GGM3PIWQGAWVZTVD","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GGM3PIWQ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:c19b6caa9b0d6c05f7ea79084f5ab98c1a92e45cdbd4fa41cbac50704891553a","target":"graph","created_at":"2026-05-18T02:29:24Z","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":"The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set $P$ of points, and a set $\\mathcal{D}$ of geometric objects in the plane, the goal is to compute a small-sized subset of $P$ that hits all objects in $\\mathcal{D}$. In 1994, Bronniman and Goodrich made an important connection of this problem to the size of fundamental combinatorial structures called $\\epsilon$-nets, showing that small-sized $\\epsilon$-nets imply approximation algorithms with correspondingly small approximation ratios. Very recently, Agarwal and Pan showed that their","authors_text":"Nabil H. Mustafa, Norbert Bus, Saurabh Ray, Shashwat Garg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-14T04:56:50Z","title":"Tighter Estimates for epsilon-nets for Disks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03246","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:c6989231d801be262d97a0bea7d0c7bb560b4eab86b50c7abdc2dc67f41c9f1e","target":"record","created_at":"2026-05-18T02:29:24Z","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":"67acf7e36a19cc64d6c12dac8a1714f055d0566f4418f8ab27ce62399f3aac8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-14T04:56:50Z","title_canon_sha256":"19fd3ba42f29750f81a0cde6f9db288287ef5de6301d7eaa4033e8655f828dbe"},"schema_version":"1.0","source":{"id":"1501.03246","kind":"arxiv","version":1}},"canonical_sha256":"3199b7a2d0302d5ccea3c146834e73b8a0178e17949f2dfa8d65507d6573759f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3199b7a2d0302d5ccea3c146834e73b8a0178e17949f2dfa8d65507d6573759f","first_computed_at":"2026-05-18T02:29:24.402549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:24.402549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jye68hXMbB7rzUCR29el2FNyy4JHLCzTnIvphRxI+cNyN3ykXXOrpWjv3IajjIiA/LF0a74/GPVnycOj1iTlAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:24.402935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6989231d801be262d97a0bea7d0c7bb560b4eab86b50c7abdc2dc67f41c9f1e","sha256:c19b6caa9b0d6c05f7ea79084f5ab98c1a92e45cdbd4fa41cbac50704891553a"],"state_sha256":"793132b7404065cb67bb3842109c41d8221dceafd7f6777cead15fc5f1423975"}