{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BRVUQL6XC3TTABE7TPPHETPMLM","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":"06126d4e764c4274be2932c61987555a2d63f31afd3202644ed7bd4a3ac4301b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-12T21:04:03Z","title_canon_sha256":"fddd03c121410a5a207da86748d385ef09fa8003b73ee74925c955076b457eda"},"schema_version":"1.0","source":{"id":"1707.03910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03910","created_at":"2026-05-17T23:58:08Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03910v2","created_at":"2026-05-17T23:58:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03910","created_at":"2026-05-17T23:58:08Z"},{"alias_kind":"pith_short_12","alias_value":"BRVUQL6XC3TT","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BRVUQL6XC3TTABE7","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BRVUQL6X","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:60f5bd1ec641f836f33f60904ce1baff1039669dcc1d401b75ff1904019438f5","target":"graph","created_at":"2026-05-17T23:58:08Z","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 classify the trees on $n$ vertices with the maximum and the minimum number of certain generalized colorings, including conflict-free, odd, non-monochromatic, star, and star rainbow vertex colorings. We also extend a result of Cutler and Radcliffe on the maximum and minimum number of existence homomorphisms from a tree to a completely looped graph on $q$ vertices.","authors_text":"Christopher Stocker, John Engbers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-12T21:04:03Z","title":"Maximizing and minimizing the number of generalized colorings of trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03910","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":"sha256:3038acf2b734ed4cbc8622251af90d7a0aa534da439aa3872ac33d5ff9334ae8","target":"record","created_at":"2026-05-17T23:58:08Z","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":"06126d4e764c4274be2932c61987555a2d63f31afd3202644ed7bd4a3ac4301b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-12T21:04:03Z","title_canon_sha256":"fddd03c121410a5a207da86748d385ef09fa8003b73ee74925c955076b457eda"},"schema_version":"1.0","source":{"id":"1707.03910","kind":"arxiv","version":2}},"canonical_sha256":"0c6b482fd716e730049f9bde724dec5b0638d13eca08d520be40abc2ab5d4a25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c6b482fd716e730049f9bde724dec5b0638d13eca08d520be40abc2ab5d4a25","first_computed_at":"2026-05-17T23:58:08.798923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:08.798923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yf8MgIZ+V++srfovOBhtVchnZ2z6/maRCPW7yBQJpNucVwQy5xL5d/1RXTFtX2GgKoz1BkkuVA6UEnU+QB90BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:08.799441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3038acf2b734ed4cbc8622251af90d7a0aa534da439aa3872ac33d5ff9334ae8","sha256:60f5bd1ec641f836f33f60904ce1baff1039669dcc1d401b75ff1904019438f5"],"state_sha256":"f341624f5a715e01354a2959fba2edec1abe744e61f655663a51f75c077837c7"}