{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2PCJV764BZ5VN73S3DXMMFBTFG","short_pith_number":"pith:2PCJV764","schema_version":"1.0","canonical_sha256":"d3c49affdc0e7b56ff72d8eec6143329b3d0d1dcf9bb302e15aa60f5c94703e7","source":{"kind":"arxiv","id":"1404.5887","version":2},"attestation_state":"computed","paper":{"title":"Counting connected hypergraphs via the probabilistic method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"B\\'ela Bollob\\'as, Oliver Riordan","submitted_at":"2014-04-23T16:52:07Z","abstract_excerpt":"In 1990 Bender, Canfield and McKay gave an asymptotic formula for the number of connected graphs on $[n]$ with $m$ edges, whenever $n$ and the nullity $m-n+1$ tend to infinity. Asymptotic formulae for the number of connected $r$-uniform hypergraphs on $[n]$ with $m$ edges and so nullity $t=(r-1)m-n+1$ were proved by Karo\\'nski and \\L uczak for the case $t=o(\\log n/\\log\\log n)$, and Behrisch, Coja-Oghlan and Kang for $t=\\Theta(n)$. Here we prove such a formula for any $r\\ge 3$ fixed, and any $t=t(n)$ satisfying $t=o(n)$ and $t\\to\\infty$ as $n\\to\\infty$. This leaves open only the (much simpler) "},"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":"1404.5887","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-23T16:52:07Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"a9b94d0de9922633b031cc5a7adb74404c9045915c02183de40d967bbd3237b7","abstract_canon_sha256":"0f6534afb192db5358ecf6fbbc8f852a3f4f75ad3fb76514cb5a30ca6bf2a22a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:58.524867Z","signature_b64":"f41MIc4inBtgAqcM8UF8w/zAmWRT+VEmScnSXD/UHFCzG6Rm53an6Z6NUZuY3gC3xPGHXfkKlrHm0kiDdLCcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3c49affdc0e7b56ff72d8eec6143329b3d0d1dcf9bb302e15aa60f5c94703e7","last_reissued_at":"2026-05-18T01:22:58.524237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:58.524237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting connected hypergraphs via the probabilistic method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"B\\'ela Bollob\\'as, Oliver Riordan","submitted_at":"2014-04-23T16:52:07Z","abstract_excerpt":"In 1990 Bender, Canfield and McKay gave an asymptotic formula for the number of connected graphs on $[n]$ with $m$ edges, whenever $n$ and the nullity $m-n+1$ tend to infinity. Asymptotic formulae for the number of connected $r$-uniform hypergraphs on $[n]$ with $m$ edges and so nullity $t=(r-1)m-n+1$ were proved by Karo\\'nski and \\L uczak for the case $t=o(\\log n/\\log\\log n)$, and Behrisch, Coja-Oghlan and Kang for $t=\\Theta(n)$. Here we prove such a formula for any $r\\ge 3$ fixed, and any $t=t(n)$ satisfying $t=o(n)$ and $t\\to\\infty$ as $n\\to\\infty$. This leaves open only the (much simpler) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5887","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":"1404.5887","created_at":"2026-05-18T01:22:58.524333+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5887v2","created_at":"2026-05-18T01:22:58.524333+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5887","created_at":"2026-05-18T01:22:58.524333+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PCJV764BZ5V","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PCJV764BZ5VN73S","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PCJV764","created_at":"2026-05-18T12:28:11.866339+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/2PCJV764BZ5VN73S3DXMMFBTFG","json":"https://pith.science/pith/2PCJV764BZ5VN73S3DXMMFBTFG.json","graph_json":"https://pith.science/api/pith-number/2PCJV764BZ5VN73S3DXMMFBTFG/graph.json","events_json":"https://pith.science/api/pith-number/2PCJV764BZ5VN73S3DXMMFBTFG/events.json","paper":"https://pith.science/paper/2PCJV764"},"agent_actions":{"view_html":"https://pith.science/pith/2PCJV764BZ5VN73S3DXMMFBTFG","download_json":"https://pith.science/pith/2PCJV764BZ5VN73S3DXMMFBTFG.json","view_paper":"https://pith.science/paper/2PCJV764","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5887&json=true","fetch_graph":"https://pith.science/api/pith-number/2PCJV764BZ5VN73S3DXMMFBTFG/graph.json","fetch_events":"https://pith.science/api/pith-number/2PCJV764BZ5VN73S3DXMMFBTFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PCJV764BZ5VN73S3DXMMFBTFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PCJV764BZ5VN73S3DXMMFBTFG/action/storage_attestation","attest_author":"https://pith.science/pith/2PCJV764BZ5VN73S3DXMMFBTFG/action/author_attestation","sign_citation":"https://pith.science/pith/2PCJV764BZ5VN73S3DXMMFBTFG/action/citation_signature","submit_replication":"https://pith.science/pith/2PCJV764BZ5VN73S3DXMMFBTFG/action/replication_record"}},"created_at":"2026-05-18T01:22:58.524333+00:00","updated_at":"2026-05-18T01:22:58.524333+00:00"}