{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JP6RY44PMLLTEAKJVT7LOFNINS","short_pith_number":"pith:JP6RY44P","schema_version":"1.0","canonical_sha256":"4bfd1c738f62d7320149acfeb715a86c98d08125385bf701175d433667107e0c","source":{"kind":"arxiv","id":"1805.06944","version":5},"attestation_state":"computed","paper":{"title":"Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Simkin, Roman Glebov, Zur Luria","submitted_at":"2018-05-17T19:33:59Z","abstract_excerpt":"Consider the random process in which the edges of a graph $G$ are added one by one in a random order. A classical result states that if $G$ is the complete graph $K_{2n}$ or the complete bipartite graph $K_{n,n}$, then typically a perfect matching appears at the moment at which the last isolated vertex disappears. We extend this result to arbitrary $k$-regular bipartite graphs $G$ on $2n$ vertices for all $k = \\omega \\left( \\frac{n}{\\log^{1/3} n} \\right)$.\n  Surprisingly, this is not the case for smaller values of $k$. Using a construction due to Goel, Kapralov and Khanna, we show that there e"},"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":"1805.06944","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-17T19:33:59Z","cross_cats_sorted":[],"title_canon_sha256":"987e3d27be26d162d5f87604c751c89b0ed78cc952e82a7e995840eef59a9be1","abstract_canon_sha256":"315f462aac01a48aefe57467484e7d2f911ab49d7ae2e17e9e48c426ce71b688"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:48:04.586554Z","signature_b64":"avWYb3UGBz7IOJohw5UQD09IFwLIU5QRSEcLFaNvN8n8wKxHsM6/DU2G+etl1JP4+nK9qhAgnBw1j4TOUHfvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bfd1c738f62d7320149acfeb715a86c98d08125385bf701175d433667107e0c","last_reissued_at":"2026-07-05T01:48:04.586129Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:48:04.586129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Simkin, Roman Glebov, Zur Luria","submitted_at":"2018-05-17T19:33:59Z","abstract_excerpt":"Consider the random process in which the edges of a graph $G$ are added one by one in a random order. A classical result states that if $G$ is the complete graph $K_{2n}$ or the complete bipartite graph $K_{n,n}$, then typically a perfect matching appears at the moment at which the last isolated vertex disappears. We extend this result to arbitrary $k$-regular bipartite graphs $G$ on $2n$ vertices for all $k = \\omega \\left( \\frac{n}{\\log^{1/3} n} \\right)$.\n  Surprisingly, this is not the case for smaller values of $k$. Using a construction due to Goel, Kapralov and Khanna, we show that there e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06944","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1805.06944/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1805.06944","created_at":"2026-07-05T01:48:04.586186+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.06944v5","created_at":"2026-07-05T01:48:04.586186+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06944","created_at":"2026-07-05T01:48:04.586186+00:00"},{"alias_kind":"pith_short_12","alias_value":"JP6RY44PMLLT","created_at":"2026-07-05T01:48:04.586186+00:00"},{"alias_kind":"pith_short_16","alias_value":"JP6RY44PMLLTEAKJ","created_at":"2026-07-05T01:48:04.586186+00:00"},{"alias_kind":"pith_short_8","alias_value":"JP6RY44P","created_at":"2026-07-05T01:48:04.586186+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/JP6RY44PMLLTEAKJVT7LOFNINS","json":"https://pith.science/pith/JP6RY44PMLLTEAKJVT7LOFNINS.json","graph_json":"https://pith.science/api/pith-number/JP6RY44PMLLTEAKJVT7LOFNINS/graph.json","events_json":"https://pith.science/api/pith-number/JP6RY44PMLLTEAKJVT7LOFNINS/events.json","paper":"https://pith.science/paper/JP6RY44P"},"agent_actions":{"view_html":"https://pith.science/pith/JP6RY44PMLLTEAKJVT7LOFNINS","download_json":"https://pith.science/pith/JP6RY44PMLLTEAKJVT7LOFNINS.json","view_paper":"https://pith.science/paper/JP6RY44P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.06944&json=true","fetch_graph":"https://pith.science/api/pith-number/JP6RY44PMLLTEAKJVT7LOFNINS/graph.json","fetch_events":"https://pith.science/api/pith-number/JP6RY44PMLLTEAKJVT7LOFNINS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JP6RY44PMLLTEAKJVT7LOFNINS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JP6RY44PMLLTEAKJVT7LOFNINS/action/storage_attestation","attest_author":"https://pith.science/pith/JP6RY44PMLLTEAKJVT7LOFNINS/action/author_attestation","sign_citation":"https://pith.science/pith/JP6RY44PMLLTEAKJVT7LOFNINS/action/citation_signature","submit_replication":"https://pith.science/pith/JP6RY44PMLLTEAKJVT7LOFNINS/action/replication_record"}},"created_at":"2026-07-05T01:48:04.586186+00:00","updated_at":"2026-07-05T01:48:04.586186+00:00"}