{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U3OCVW2S4NX3H3M2RP2ANVL3ZJ","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":"aef9cf1f66367854b3e7c4b75e87377b1a8ebae8a9f5b0be22cd7e38d6fb3ce4","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-05T23:43:40Z","title_canon_sha256":"d2b4e4bf6fb453d3ad6820c8d67a209a864d7afffe7b25bf57ef006926d1701d"},"schema_version":"1.0","source":{"id":"1512.01713","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01713","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01713v3","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01713","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"U3OCVW2S4NX3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U3OCVW2S4NX3H3M2","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U3OCVW2S","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:09286fdfe2ede8a435327fe758770c6a739521e03de9e5d6a169a21a36df927a","target":"graph","created_at":"2026-05-18T00:48:20Z","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 range-searching for colored objects, where one has to count (approximately) the number of colors present in a query range. The problems studied mostly involve orthogonal range-searching in two and three dimensions, and the dual setting of rectangle stabbing by points. We present optimal and near-optimal solutions for these problems. Most of the results are obtained via reductions to the approximate uncolored version, and improved data-structures for them. An additional contribution of this work is the introduction of nested shallow cuttings.","authors_text":"Saladi Rahul","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-05T23:43:40Z","title":"Approximate Range Counting Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01713","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":"sha256:90a8fcfc12ff318158582b5a7e44eedf51c06b93499ffb16847129b356e2777c","target":"record","created_at":"2026-05-18T00:48:20Z","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":"aef9cf1f66367854b3e7c4b75e87377b1a8ebae8a9f5b0be22cd7e38d6fb3ce4","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-05T23:43:40Z","title_canon_sha256":"d2b4e4bf6fb453d3ad6820c8d67a209a864d7afffe7b25bf57ef006926d1701d"},"schema_version":"1.0","source":{"id":"1512.01713","kind":"arxiv","version":3}},"canonical_sha256":"a6dc2adb52e36fb3ed9a8bf406d57bca7d8b90874569fca890056d5cf512c5b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6dc2adb52e36fb3ed9a8bf406d57bca7d8b90874569fca890056d5cf512c5b6","first_computed_at":"2026-05-18T00:48:20.417649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:20.417649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hYE6aGFD7GUWzWpIDi79rpF50544lSy2rvml5LjkmEn3CQH3PvvvUKjUlIKKI0O4jVsl1VTGiVVi+2633QulBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:20.418477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01713","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90a8fcfc12ff318158582b5a7e44eedf51c06b93499ffb16847129b356e2777c","sha256:09286fdfe2ede8a435327fe758770c6a739521e03de9e5d6a169a21a36df927a"],"state_sha256":"4c68e68e7f4ad9321eab7708981ef9b424a067053c77209f9ed017a00336c917"}