{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7UKVAFLCPX5HT5JOGXRAAANEQA","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":"50854c80e753b3b2e99479f9563e025fd56b2cc95b13976686724b284d19702c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-14T21:14:18Z","title_canon_sha256":"104c18ba826debda12562097f20c8772532dc4416b25efa0cc08989032fcaf1f"},"schema_version":"1.0","source":{"id":"1805.05448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05448","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05448v1","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05448","created_at":"2026-05-18T00:16:00Z"},{"alias_kind":"pith_short_12","alias_value":"7UKVAFLCPX5H","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7UKVAFLCPX5HT5JO","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7UKVAFLC","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:6769fe7a6ba2cfd8599f15c5bc67954c271bb6fe0b95c13509fb7cc7790fc389","target":"graph","created_at":"2026-05-18T00:16:00Z","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 set of $n$ points $P$ in the plane, each colored with one of the $t$ given colors, a color-spanning set $S\\subset P$ is a subset of $t$ points with distinct colors. The minimum diameter color-spanning set (MDCS) is a color-spanning set whose diameter is minimum (among all color-spanning sets of $P$). Somehow symmetrically, the largest closest pair color-spanning set (LCPCS) is a color-spanning set whose closest pair is the largest (among all color-spanning sets of $P$). Both MDCS and LCPCS have been shown to be NP-complete, but whether they are fixed-parameter tractable (FPT) when $t$ ","authors_text":"Binhai Zhu, Feifei Ma, Jian Zhang, Sergey Bereg, Wencheng Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-14T21:14:18Z","title":"On the Fixed-Parameter Tractability of Some Matching Problems Under the Color-Spanning Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05448","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:f29e5b6142a2ab6db162bd995830460583b8240e735a084a043d5965c292c61c","target":"record","created_at":"2026-05-18T00:16:00Z","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":"50854c80e753b3b2e99479f9563e025fd56b2cc95b13976686724b284d19702c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-05-14T21:14:18Z","title_canon_sha256":"104c18ba826debda12562097f20c8772532dc4416b25efa0cc08989032fcaf1f"},"schema_version":"1.0","source":{"id":"1805.05448","kind":"arxiv","version":1}},"canonical_sha256":"fd155015627dfa79f52e35e20001a48006b70f7c9fd3df8c08ff2d3d4725c9f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd155015627dfa79f52e35e20001a48006b70f7c9fd3df8c08ff2d3d4725c9f4","first_computed_at":"2026-05-18T00:16:00.606401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:00.606401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FZsjd1C1QZ/gL6Wj2iOXq3G7ndEIzvx/X9vQONzWTTQHJxI9G3vVd4SUceBVHunJYlE6bK8eo4Fawg72ovKLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:00.606836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.05448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29e5b6142a2ab6db162bd995830460583b8240e735a084a043d5965c292c61c","sha256:6769fe7a6ba2cfd8599f15c5bc67954c271bb6fe0b95c13509fb7cc7790fc389"],"state_sha256":"6b2c74e8846f3ca00616b57784fa5cfd8ccfad2912cabaa00726b1747d7e1a10"}