{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LYGBYJG5E3KALB6CUIS4AACSOU","short_pith_number":"pith:LYGBYJG5","schema_version":"1.0","canonical_sha256":"5e0c1c24dd26d40587c2a225c000527521e31441e589acbc9cb7d0634fa5c919","source":{"kind":"arxiv","id":"1409.1489","version":2},"attestation_state":"computed","paper":{"title":"On the strength of connectedness of a random hypergraph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Daniel Poole","submitted_at":"2014-09-04T16:55:16Z","abstract_excerpt":"Bollob\\'{a}s and Thomason (1985) proved that for each $k=k(n) \\in [1, n-1]$, with high probability, the random graph process, where edges are added to vertex set $V=[n]$ uniformly at random one after another, is such that the stopping time of having minimal degree $k$ is equal to the stopping time of becoming $k$-(vertex-)connected. We extend this result to the $d$-uniform random hypergraph process, where $k$ and $d$ are fixed. Consequently, for $m=\\frac{n}{d}(\\ln n +(k-1)\\ln \\ln n +c)$ and $p=(d-1)! \\frac{\\ln n + (k-1) \\ln \\ln n +c}{n^{d-1}}$, the probability that the random hypergraph models"},"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":"1409.1489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-04T16:55:16Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"24eb5d27d7bfb389fa237795c5cf3048c71e207c3f1fa4b7f2ed9c7c236aad44","abstract_canon_sha256":"4315db4d1b1f8af2d39a7f4909ced04e375e988564f8092f0b8e3cabbbd9a9a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.826677Z","signature_b64":"5datVFc+X0qHP5u+1D/snY1mLbmZzEtGnHM2IG/TQQQNQoAZbFpnzEw3TUglddfNat99KV5EZ9vFHWjLJTClBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e0c1c24dd26d40587c2a225c000527521e31441e589acbc9cb7d0634fa5c919","last_reissued_at":"2026-05-18T02:25:19.826327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.826327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the strength of connectedness of a random hypergraph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Daniel Poole","submitted_at":"2014-09-04T16:55:16Z","abstract_excerpt":"Bollob\\'{a}s and Thomason (1985) proved that for each $k=k(n) \\in [1, n-1]$, with high probability, the random graph process, where edges are added to vertex set $V=[n]$ uniformly at random one after another, is such that the stopping time of having minimal degree $k$ is equal to the stopping time of becoming $k$-(vertex-)connected. We extend this result to the $d$-uniform random hypergraph process, where $k$ and $d$ are fixed. Consequently, for $m=\\frac{n}{d}(\\ln n +(k-1)\\ln \\ln n +c)$ and $p=(d-1)! \\frac{\\ln n + (k-1) \\ln \\ln n +c}{n^{d-1}}$, the probability that the random hypergraph models"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1489","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":"1409.1489","created_at":"2026-05-18T02:25:19.826385+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1489v2","created_at":"2026-05-18T02:25:19.826385+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1489","created_at":"2026-05-18T02:25:19.826385+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYGBYJG5E3KA","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYGBYJG5E3KALB6C","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYGBYJG5","created_at":"2026-05-18T12:28:38.356838+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/LYGBYJG5E3KALB6CUIS4AACSOU","json":"https://pith.science/pith/LYGBYJG5E3KALB6CUIS4AACSOU.json","graph_json":"https://pith.science/api/pith-number/LYGBYJG5E3KALB6CUIS4AACSOU/graph.json","events_json":"https://pith.science/api/pith-number/LYGBYJG5E3KALB6CUIS4AACSOU/events.json","paper":"https://pith.science/paper/LYGBYJG5"},"agent_actions":{"view_html":"https://pith.science/pith/LYGBYJG5E3KALB6CUIS4AACSOU","download_json":"https://pith.science/pith/LYGBYJG5E3KALB6CUIS4AACSOU.json","view_paper":"https://pith.science/paper/LYGBYJG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1489&json=true","fetch_graph":"https://pith.science/api/pith-number/LYGBYJG5E3KALB6CUIS4AACSOU/graph.json","fetch_events":"https://pith.science/api/pith-number/LYGBYJG5E3KALB6CUIS4AACSOU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYGBYJG5E3KALB6CUIS4AACSOU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYGBYJG5E3KALB6CUIS4AACSOU/action/storage_attestation","attest_author":"https://pith.science/pith/LYGBYJG5E3KALB6CUIS4AACSOU/action/author_attestation","sign_citation":"https://pith.science/pith/LYGBYJG5E3KALB6CUIS4AACSOU/action/citation_signature","submit_replication":"https://pith.science/pith/LYGBYJG5E3KALB6CUIS4AACSOU/action/replication_record"}},"created_at":"2026-05-18T02:25:19.826385+00:00","updated_at":"2026-05-18T02:25:19.826385+00:00"}