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A $\\mathcal{P}$-coloring of a hypergraph $H$ with color set $C$ is a function $\\varphi:V(H) \\to C$ such that $H[\\varphi^{-1}(c)]$ belongs to $\\mathcal{P}$ for all $c \\in C$. Let $L: V(H) \\to 2^C$ be a so called list-assignment of the hypergraph $H$. Then, a $(\\mathcal{P},L)$-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.06338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-17T16:06:43Z","cross_cats_sorted":[],"title_canon_sha256":"4afc3d50cd75478735cad61d4ea56513cd4009c4eaedd58a9239f171b5b6ca34","abstract_canon_sha256":"677cca080be09c1cb0ed26f4e007aaaa4d4d1f655850dc9ab828be593e6b3b39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:20.967765Z","signature_b64":"bDj2YRgBkPTWS/szT87pgCv8wHR+cpCCRzczAdYF3Tv6J+LFMyD6W705WLgmAucYMPqXicWJh2/NxU4+CWqbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"164cb82dc36d2a31f60b0bf74c73b187ebb71bd94f2a7b0f0691dfb1108c74c7","last_reissued_at":"2026-05-18T00:18:20.967139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:20.967139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Hypergraph Coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Thomas Schweser","submitted_at":"2018-04-17T16:06:43Z","abstract_excerpt":"A smooth hypergraph property $\\mathcal{P}$ is a class of hypergraphs that is hereditary and non-trivial, i.e., closed under induced subhypergraphs and it contains a non-empty hypergraph but not all hypergraphs. In this paper we examine $\\mathcal{P}$-colorings of hypergraphs with smooth hypergraph properties $\\mathcal{P}$. A $\\mathcal{P}$-coloring of a hypergraph $H$ with color set $C$ is a function $\\varphi:V(H) \\to C$ such that $H[\\varphi^{-1}(c)]$ belongs to $\\mathcal{P}$ for all $c \\in C$. Let $L: V(H) \\to 2^C$ be a so called list-assignment of the hypergraph $H$. 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