{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:G3WMBNZXP54MNAZBD3DQOBW6Y2","short_pith_number":"pith:G3WMBNZX","schema_version":"1.0","canonical_sha256":"36ecc0b7377f78c683211ec70706dec69e3398cb9f8d01b52da3774f57fac6b9","source":{"kind":"arxiv","id":"0706.0497","version":3},"attestation_state":"computed","paper":{"title":"Local Limit Theorems and Number of Connected Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Amin Coja-Oghlan, Michael Behrisch, Mihyun Kang","submitted_at":"2007-06-04T18:49:03Z","abstract_excerpt":"Let $H_d(n,p)$ signify a random $d$-uniform hypergraph with $n$ vertices in which each of the ${n}\\choose{d}$ possible edges is present with probability $p=p(n)$ independently, and let $H_d(n,m)$ denote a uniformly distributed with $n$ vertices and $m$ edges. We derive local limit theorems for the joint distribution of the number of vertices and the number of edges in the largest component of $H_d(n,p)$ and $H_d(n,m)$ for the regime ${{n-1}\\choose{d-1}} p,dm/n >(d-1)^{-1}+\\epsilon$. As an application, we obtain an asymptotic formula for the probability that $H_d(n,p)$ or $H_d(n,m)$ is connecte"},"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":"0706.0497","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-06-04T18:49:03Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"f6af65549fdd04920e4a32fe441bd3b11cf91075cf00774c9feaf50dfba706dd","abstract_canon_sha256":"41e9a4a7cad79477a16db1251527f1264f14617d888a8a66b4f46dd5c906fd50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:02.218264Z","signature_b64":"2gzq8ZEDz3lspH3mTIs1yDhWjVtRR5E3N3F3t3i9Ie6+NUglBsfUuzWdRI94k3REIaTSvUhGeQcfM7gGk30nAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36ecc0b7377f78c683211ec70706dec69e3398cb9f8d01b52da3774f57fac6b9","last_reissued_at":"2026-05-18T02:49:02.217850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:02.217850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Limit Theorems and Number of Connected Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Amin Coja-Oghlan, Michael Behrisch, Mihyun Kang","submitted_at":"2007-06-04T18:49:03Z","abstract_excerpt":"Let $H_d(n,p)$ signify a random $d$-uniform hypergraph with $n$ vertices in which each of the ${n}\\choose{d}$ possible edges is present with probability $p=p(n)$ independently, and let $H_d(n,m)$ denote a uniformly distributed with $n$ vertices and $m$ edges. We derive local limit theorems for the joint distribution of the number of vertices and the number of edges in the largest component of $H_d(n,p)$ and $H_d(n,m)$ for the regime ${{n-1}\\choose{d-1}} p,dm/n >(d-1)^{-1}+\\epsilon$. As an application, we obtain an asymptotic formula for the probability that $H_d(n,p)$ or $H_d(n,m)$ is connecte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0497","kind":"arxiv","version":3},"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":"0706.0497","created_at":"2026-05-18T02:49:02.217910+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.0497v3","created_at":"2026-05-18T02:49:02.217910+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0497","created_at":"2026-05-18T02:49:02.217910+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3WMBNZXP54M","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3WMBNZXP54MNAZB","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3WMBNZX","created_at":"2026-05-18T12:25:55.427421+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/G3WMBNZXP54MNAZBD3DQOBW6Y2","json":"https://pith.science/pith/G3WMBNZXP54MNAZBD3DQOBW6Y2.json","graph_json":"https://pith.science/api/pith-number/G3WMBNZXP54MNAZBD3DQOBW6Y2/graph.json","events_json":"https://pith.science/api/pith-number/G3WMBNZXP54MNAZBD3DQOBW6Y2/events.json","paper":"https://pith.science/paper/G3WMBNZX"},"agent_actions":{"view_html":"https://pith.science/pith/G3WMBNZXP54MNAZBD3DQOBW6Y2","download_json":"https://pith.science/pith/G3WMBNZXP54MNAZBD3DQOBW6Y2.json","view_paper":"https://pith.science/paper/G3WMBNZX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.0497&json=true","fetch_graph":"https://pith.science/api/pith-number/G3WMBNZXP54MNAZBD3DQOBW6Y2/graph.json","fetch_events":"https://pith.science/api/pith-number/G3WMBNZXP54MNAZBD3DQOBW6Y2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3WMBNZXP54MNAZBD3DQOBW6Y2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3WMBNZXP54MNAZBD3DQOBW6Y2/action/storage_attestation","attest_author":"https://pith.science/pith/G3WMBNZXP54MNAZBD3DQOBW6Y2/action/author_attestation","sign_citation":"https://pith.science/pith/G3WMBNZXP54MNAZBD3DQOBW6Y2/action/citation_signature","submit_replication":"https://pith.science/pith/G3WMBNZXP54MNAZBD3DQOBW6Y2/action/replication_record"}},"created_at":"2026-05-18T02:49:02.217910+00:00","updated_at":"2026-05-18T02:49:02.217910+00:00"}