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We conjecture that for $n >> m$ the minimum width $h_n(m,l)$ of a cutset in ${\\cal B}_n(m,l)$ is $\\Sigma_{j \\geq 0} \\Delta_n(m-jc) = \\Delta_n(m)+\\Delta_n(m-c)+\\Delta_n(m-2c)+ \\dots$, where $c=l-m+1$ is t"},"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":"1512.02978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-09T18:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"ae18f82a7c85eb8a3e940ec6773ce819553f176d6713e21876aad97016d4a3f4","abstract_canon_sha256":"d6e13d6b9ccebf836c4c9d42763ab6df281c1b914062c2674002cfa81c917f1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:39.120120Z","signature_b64":"LsMNUnSyNWcT6/lr+FTSNAyyZa8SwCE6rTAblF18Igm69VAWgpIPjjQ6+V4X4dMqm2TXb74otG8bNgH7ge2dBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"369f7845693efd252d4e5b87cbf2ad82ba70fcaa02017261fdb2d1207e7825bb","last_reissued_at":"2026-05-18T01:24:39.119683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:39.119683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Minimum Width of a Cutset in the Truncated Boolean Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B\\'ela Bajnok","submitted_at":"2015-12-09T18:22:37Z","abstract_excerpt":"For integers $0 \\leq m \\leq l \\leq n-m$, the truncated Boolean lattice ${\\cal B}_n(m,l)$ is the poset of all subsets of $[n] = \\{1, 2, \\ldots, n\\}$ which have size at least $m$ and at most $l$. ${\\cal C} \\subseteq {\\cal B}_n(m,l)$ is a {\\em cutset} if it meets every chain of length $l-m$ in ${\\cal B}_n(m,l)$, and the {\\em width} of ${\\cal C}$ is the size of the largest antichain in ${\\cal C}$. We conjecture that for $n >> m$ the minimum width $h_n(m,l)$ of a cutset in ${\\cal B}_n(m,l)$ is $\\Sigma_{j \\geq 0} \\Delta_n(m-jc) = \\Delta_n(m)+\\Delta_n(m-c)+\\Delta_n(m-2c)+ \\dots$, where $c=l-m+1$ is t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02978","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":"1512.02978","created_at":"2026-05-18T01:24:39.119768+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02978v1","created_at":"2026-05-18T01:24:39.119768+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02978","created_at":"2026-05-18T01:24:39.119768+00:00"},{"alias_kind":"pith_short_12","alias_value":"G2PXQRLJH36S","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"G2PXQRLJH36SKLKO","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"G2PXQRLJ","created_at":"2026-05-18T12:29:22.688609+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/G2PXQRLJH36SKLKOLOD4X4VNQK","json":"https://pith.science/pith/G2PXQRLJH36SKLKOLOD4X4VNQK.json","graph_json":"https://pith.science/api/pith-number/G2PXQRLJH36SKLKOLOD4X4VNQK/graph.json","events_json":"https://pith.science/api/pith-number/G2PXQRLJH36SKLKOLOD4X4VNQK/events.json","paper":"https://pith.science/paper/G2PXQRLJ"},"agent_actions":{"view_html":"https://pith.science/pith/G2PXQRLJH36SKLKOLOD4X4VNQK","download_json":"https://pith.science/pith/G2PXQRLJH36SKLKOLOD4X4VNQK.json","view_paper":"https://pith.science/paper/G2PXQRLJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02978&json=true","fetch_graph":"https://pith.science/api/pith-number/G2PXQRLJH36SKLKOLOD4X4VNQK/graph.json","fetch_events":"https://pith.science/api/pith-number/G2PXQRLJH36SKLKOLOD4X4VNQK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G2PXQRLJH36SKLKOLOD4X4VNQK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G2PXQRLJH36SKLKOLOD4X4VNQK/action/storage_attestation","attest_author":"https://pith.science/pith/G2PXQRLJH36SKLKOLOD4X4VNQK/action/author_attestation","sign_citation":"https://pith.science/pith/G2PXQRLJH36SKLKOLOD4X4VNQK/action/citation_signature","submit_replication":"https://pith.science/pith/G2PXQRLJH36SKLKOLOD4X4VNQK/action/replication_record"}},"created_at":"2026-05-18T01:24:39.119768+00:00","updated_at":"2026-05-18T01:24:39.119768+00:00"}