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We assume that $M(\\boldsymbol{k})$ is divisible by $r$ for infinitely many values of $n$, and restrict our attention to these values. Let $X=X(n)$ be a simple $r$-uniform hypergraph on the vertex set $V=\\{v_1,v_2, \\ldots, v_n\\}$ with $t$ edges and maximum degree $x_{\\max}$. We denote by $\\mathcal{H}_r(\\boldsymbol{k})$ the set of all simple $r$-uniform hypergraphs on the vertex set $V$ with degree sequence $\\boldsym"},"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":"1805.04991","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-14T02:47:51Z","cross_cats_sorted":[],"title_canon_sha256":"7f23bc5f13fd9f249c71a696c589f7ab8c8f47dd7b632e4dfc400f575c3dcaed","abstract_canon_sha256":"18c2fb9775f0ed86c264956ed9ff8d7425f642609fdd90565de73b6477d7efbd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:15.012671Z","signature_b64":"SM+0Mn6my5J/BSz+AYRKKpj6e8iTSsX1LW5Fl8jaKbQkrgST1ZhIeGXg8Q4cZV+avGLEnt8gAV2tMLkwTc/PBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af33bbf2d3776a414d8bfc94e02d046da6c4f92a450679cf1020b74d34a97dec","last_reissued_at":"2026-05-18T00:01:15.012261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:15.012261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumerating sparse uniform hypergraphs with given degree sequence and forbidden edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine Greenhill, Haya S. 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We denote by $\\mathcal{H}_r(\\boldsymbol{k})$ the set of all simple $r$-uniform hypergraphs on the vertex set $V$ with degree sequence $\\boldsym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04991","kind":"arxiv","version":4},"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":"1805.04991","created_at":"2026-05-18T00:01:15.012325+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.04991v4","created_at":"2026-05-18T00:01:15.012325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04991","created_at":"2026-05-18T00:01:15.012325+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4Z3X4WTO5VE","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4Z3X4WTO5VECTML","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4Z3X4WT","created_at":"2026-05-18T12:32:56.356000+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/V4Z3X4WTO5VECTML7SKOALIENW","json":"https://pith.science/pith/V4Z3X4WTO5VECTML7SKOALIENW.json","graph_json":"https://pith.science/api/pith-number/V4Z3X4WTO5VECTML7SKOALIENW/graph.json","events_json":"https://pith.science/api/pith-number/V4Z3X4WTO5VECTML7SKOALIENW/events.json","paper":"https://pith.science/paper/V4Z3X4WT"},"agent_actions":{"view_html":"https://pith.science/pith/V4Z3X4WTO5VECTML7SKOALIENW","download_json":"https://pith.science/pith/V4Z3X4WTO5VECTML7SKOALIENW.json","view_paper":"https://pith.science/paper/V4Z3X4WT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.04991&json=true","fetch_graph":"https://pith.science/api/pith-number/V4Z3X4WTO5VECTML7SKOALIENW/graph.json","fetch_events":"https://pith.science/api/pith-number/V4Z3X4WTO5VECTML7SKOALIENW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4Z3X4WTO5VECTML7SKOALIENW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4Z3X4WTO5VECTML7SKOALIENW/action/storage_attestation","attest_author":"https://pith.science/pith/V4Z3X4WTO5VECTML7SKOALIENW/action/author_attestation","sign_citation":"https://pith.science/pith/V4Z3X4WTO5VECTML7SKOALIENW/action/citation_signature","submit_replication":"https://pith.science/pith/V4Z3X4WTO5VECTML7SKOALIENW/action/replication_record"}},"created_at":"2026-05-18T00:01:15.012325+00:00","updated_at":"2026-05-18T00:01:15.012325+00:00"}