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We consider the random greedy algorithm for forming a matching in $ \\mathcal{H}$. We choose a matching at random by iteratively choosing edges uniformly at random to be in the matching and deleting all edges that share at least one vertex with a chosen edge before moving on to the next choice. This process terminates"},"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":"1210.3581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-12T17:19:29Z","cross_cats_sorted":[],"title_canon_sha256":"84517a5086d91a4a830457c3e1481ea3de8278375e3ce4d087e59732a870e7bb","abstract_canon_sha256":"ce6376b7dc0ddd919928dfbba23735c7a30b8ffba8d5c9cb77cd85ff07fc2e2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:10:24.760641Z","signature_b64":"eisrqI4oy+Hh751q8iRngS3Y7jcKAWq/d0NR3mHBjX6SaRepzCSE4OTxeRkxGA/iFL5J1IVAc2KY/ouwN+tWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"898155151a3c387d7f1bf0728d4ff45097c3022dcaae5c2a7bb5a099fb8481e2","last_reissued_at":"2026-07-05T00:10:24.760161Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:10:24.760161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A natural barrier in random greedy hypergraph matching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Patrick Bennett, Tom Bohman","submitted_at":"2012-10-12T17:19:29Z","abstract_excerpt":"Let $r \\ge 2$ be a fixed constant and let $ {\\mathcal H}$ be an $r$-uniform, $D$-regular hypergraph on $N$ vertices. 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