{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MB526TWQVKA4YSXL4WHMV3Y2CR","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":"12d81e56e9e11c8c2c30a2a4bb6a1e5ee873f82b46e0757fe62f986741324e6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2009-04-14T13:00:41Z","title_canon_sha256":"c20fef69b0e86383a624209735c108d80b743706a04f13601fe95b971341e41b"},"schema_version":"1.0","source":{"id":"0904.2115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2115","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2115v2","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2115","created_at":"2026-05-18T04:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"MB526TWQVKA4","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MB526TWQVKA4YSXL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MB526TWQ","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:5a54395f108a09c057013da68582ea54ea9f4fd0a03d9113ecaddcac909c9578","target":"graph","created_at":"2026-05-18T04:24:53Z","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":"Given a planar point set and an integer $k$, we wish to color the points with $k$ colors so that any axis-aligned strip containing enough points contains all colors. The goal is to bound the necessary size of such a strip, as a function of $k$. We show that if the strip size is at least $2k{-}1$, such a coloring can always be found. We prove that the size of the strip is also bounded in any fixed number of dimensions. In contrast to the planar case, we show that deciding whether a 3D point set can be 2-colored so that any strip containing at least three points contains both colors is NP-comple","authors_text":"G. Aloupis, J. Cardinal, M. Korman, O. Schwartz, P. Taslakian, S. Collette, S. Imahori, S. Langerman, S. Smorodinsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2009-04-14T13:00:41Z","title":"Colorful Strips"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2115","kind":"arxiv","version":2},"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":"sha256:6b1471545a0b1bf1a8aebb1ee781af836b4dcc46878ff5c762d786e83eb47cfb","target":"record","created_at":"2026-05-18T04:24:53Z","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":"12d81e56e9e11c8c2c30a2a4bb6a1e5ee873f82b46e0757fe62f986741324e6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2009-04-14T13:00:41Z","title_canon_sha256":"c20fef69b0e86383a624209735c108d80b743706a04f13601fe95b971341e41b"},"schema_version":"1.0","source":{"id":"0904.2115","kind":"arxiv","version":2}},"canonical_sha256":"607baf4ed0aa81cc4aebe58ecaef1a146804a6b9db86c5ff882fdf8c6ef98e95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"607baf4ed0aa81cc4aebe58ecaef1a146804a6b9db86c5ff882fdf8c6ef98e95","first_computed_at":"2026-05-18T04:24:53.315340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:53.315340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ZI1SPDyO50yuq5B1ecNMKEXk3F0VDSjacYjPsPIlU7StMPc5HHVxbrmiCf9ilp8S+t1TDU4tgNygfI7ZN+vCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:53.315846Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b1471545a0b1bf1a8aebb1ee781af836b4dcc46878ff5c762d786e83eb47cfb","sha256:5a54395f108a09c057013da68582ea54ea9f4fd0a03d9113ecaddcac909c9578"],"state_sha256":"bc089f65b5ed76db5d41699fd5bdb78bce3a5d93a717befd231805a2337533f8"}