{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BWDXGD5VRWKQV7JUFWHSDDHGD2","short_pith_number":"pith:BWDXGD5V","schema_version":"1.0","canonical_sha256":"0d87730fb58d950afd342d8f218ce61e9d9780eadcf856c51c68c70bb31f656e","source":{"kind":"arxiv","id":"1803.02809","version":1},"attestation_state":"computed","paper":{"title":"The size of the giant component in random hypergraphs: a short proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Christoph Koch, Mihyun Kang, Oliver Cooley","submitted_at":"2018-03-07T18:36:42Z","abstract_excerpt":"We consider connected components in $k$-uniform hypergraphs for the following notion of connectedness: given integers $k\\ge 2$ and $1\\le j \\le k-1$, two $j$-sets (of vertices) lie in the same $j$-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least $j$ vertices.\n  We prove that certain collections of $j$-sets constructed during a breadth-first search process on $j$-components in a random $k$-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic s"},"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":"1803.02809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-07T18:36:42Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b7ba80cbf27c180c67caa664f6ddb2c698c2898348b531706c3578ea1c032053","abstract_canon_sha256":"81fb00399adf8896f99c2e537857d738e225ef25b43e1b0661cf75c444a3256d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:49.177639Z","signature_b64":"tLQqlTxU0XxZ5dURGPVBERMZLdt13KNUA1RBf/oy9grh7RT7tT6fb6+7vNh/pNG7h/ASHjNSwkbM3sRuH+G6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d87730fb58d950afd342d8f218ce61e9d9780eadcf856c51c68c70bb31f656e","last_reissued_at":"2026-05-18T00:21:49.177063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:49.177063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The size of the giant component in random hypergraphs: a short proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Christoph Koch, Mihyun Kang, Oliver Cooley","submitted_at":"2018-03-07T18:36:42Z","abstract_excerpt":"We consider connected components in $k$-uniform hypergraphs for the following notion of connectedness: given integers $k\\ge 2$ and $1\\le j \\le k-1$, two $j$-sets (of vertices) lie in the same $j$-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least $j$ vertices.\n  We prove that certain collections of $j$-sets constructed during a breadth-first search process on $j$-components in a random $k$-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02809","kind":"arxiv","version":1},"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":"1803.02809","created_at":"2026-05-18T00:21:49.177151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.02809v1","created_at":"2026-05-18T00:21:49.177151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02809","created_at":"2026-05-18T00:21:49.177151+00:00"},{"alias_kind":"pith_short_12","alias_value":"BWDXGD5VRWKQ","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BWDXGD5VRWKQV7JU","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BWDXGD5V","created_at":"2026-05-18T12:32:16.446611+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/BWDXGD5VRWKQV7JUFWHSDDHGD2","json":"https://pith.science/pith/BWDXGD5VRWKQV7JUFWHSDDHGD2.json","graph_json":"https://pith.science/api/pith-number/BWDXGD5VRWKQV7JUFWHSDDHGD2/graph.json","events_json":"https://pith.science/api/pith-number/BWDXGD5VRWKQV7JUFWHSDDHGD2/events.json","paper":"https://pith.science/paper/BWDXGD5V"},"agent_actions":{"view_html":"https://pith.science/pith/BWDXGD5VRWKQV7JUFWHSDDHGD2","download_json":"https://pith.science/pith/BWDXGD5VRWKQV7JUFWHSDDHGD2.json","view_paper":"https://pith.science/paper/BWDXGD5V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.02809&json=true","fetch_graph":"https://pith.science/api/pith-number/BWDXGD5VRWKQV7JUFWHSDDHGD2/graph.json","fetch_events":"https://pith.science/api/pith-number/BWDXGD5VRWKQV7JUFWHSDDHGD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BWDXGD5VRWKQV7JUFWHSDDHGD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BWDXGD5VRWKQV7JUFWHSDDHGD2/action/storage_attestation","attest_author":"https://pith.science/pith/BWDXGD5VRWKQV7JUFWHSDDHGD2/action/author_attestation","sign_citation":"https://pith.science/pith/BWDXGD5VRWKQV7JUFWHSDDHGD2/action/citation_signature","submit_replication":"https://pith.science/pith/BWDXGD5VRWKQV7JUFWHSDDHGD2/action/replication_record"}},"created_at":"2026-05-18T00:21:49.177151+00:00","updated_at":"2026-05-18T00:21:49.177151+00:00"}