{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:5TUKQR7D57TR2W744XVESFIYOQ","short_pith_number":"pith:5TUKQR7D","schema_version":"1.0","canonical_sha256":"ece8a847e3efe71d5bfce5ea49151874068065985961511e914aa58a1e87addd","source":{"kind":"arxiv","id":"1804.04894","version":2},"attestation_state":"computed","paper":{"title":"Partitions of hypergraphs under variable degeneracy constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Stiebitz, Thomas Schweser","submitted_at":"2018-04-13T11:39:00Z","abstract_excerpt":"The paper deals with partitions of hypergraphs into induced subhypergraphs satisfying constraints on their degeneracy. Our hypergraphs may have multiple edges, but no loops. Given a hypergraph $H$ and a sequence $f=(f_1,f_2, \\ldots, f_p)$ of $p\\geq 1$ vertex functions $f_i:V(H) \\to \\mathbb{N}_0$ such that $f_1(v)+f_2(v)+ \\cdots + f_p(v)\\geq d_H(v)$ for all $v\\in V(H)$, we want to find a sequence $(H_1,H_2, \\ldots, H_p)$ of vertex disjoint induced subhypergraphs containing all vertices of $H$ such that each hypergraph $H_i$ is strictly $f_i$-degenerate, that is, for every non-empty subhypergrap"},"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":"1804.04894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-13T11:39:00Z","cross_cats_sorted":[],"title_canon_sha256":"e87890163b889417a3382c3d7f33eee6bffe5178f55322e2f706273a03b5039f","abstract_canon_sha256":"c8fd0f51f8d032f304516d66cab45925440b31cbbe85343bb66d2b86ba624f50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:08.887045Z","signature_b64":"pYl3wFEy8F1fximX36rEvUHTTFJsSb+4ZVac0fS+69u3xPbuTxiil1JKmV/HufsrV1aYxHu35Ay5h0f2PPHdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ece8a847e3efe71d5bfce5ea49151874068065985961511e914aa58a1e87addd","last_reissued_at":"2026-05-18T00:18:08.886409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:08.886409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partitions of hypergraphs under variable degeneracy constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Stiebitz, Thomas Schweser","submitted_at":"2018-04-13T11:39:00Z","abstract_excerpt":"The paper deals with partitions of hypergraphs into induced subhypergraphs satisfying constraints on their degeneracy. Our hypergraphs may have multiple edges, but no loops. Given a hypergraph $H$ and a sequence $f=(f_1,f_2, \\ldots, f_p)$ of $p\\geq 1$ vertex functions $f_i:V(H) \\to \\mathbb{N}_0$ such that $f_1(v)+f_2(v)+ \\cdots + f_p(v)\\geq d_H(v)$ for all $v\\in V(H)$, we want to find a sequence $(H_1,H_2, \\ldots, H_p)$ of vertex disjoint induced subhypergraphs containing all vertices of $H$ such that each hypergraph $H_i$ is strictly $f_i$-degenerate, that is, for every non-empty subhypergrap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04894","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.04894","created_at":"2026-05-18T00:18:08.886499+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.04894v2","created_at":"2026-05-18T00:18:08.886499+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04894","created_at":"2026-05-18T00:18:08.886499+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TUKQR7D57TR","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TUKQR7D57TR2W74","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TUKQR7D","created_at":"2026-05-18T12:32:08.215937+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ","json":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ.json","graph_json":"https://pith.science/api/pith-number/5TUKQR7D57TR2W744XVESFIYOQ/graph.json","events_json":"https://pith.science/api/pith-number/5TUKQR7D57TR2W744XVESFIYOQ/events.json","paper":"https://pith.science/paper/5TUKQR7D"},"agent_actions":{"view_html":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ","download_json":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ.json","view_paper":"https://pith.science/paper/5TUKQR7D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.04894&json=true","fetch_graph":"https://pith.science/api/pith-number/5TUKQR7D57TR2W744XVESFIYOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/5TUKQR7D57TR2W744XVESFIYOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ/action/storage_attestation","attest_author":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ/action/author_attestation","sign_citation":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ/action/citation_signature","submit_replication":"https://pith.science/pith/5TUKQR7D57TR2W744XVESFIYOQ/action/replication_record"}},"created_at":"2026-05-18T00:18:08.886499+00:00","updated_at":"2026-05-18T00:18:08.886499+00:00"}