{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EUJF7PU7I4ELT2R22AO2DHTZD7","short_pith_number":"pith:EUJF7PU7","schema_version":"1.0","canonical_sha256":"25125fbe9f4708b9ea3ad01da19e791ffa948b1e53e1d9d53fc425157737ba82","source":{"kind":"arxiv","id":"1512.02973","version":1},"attestation_state":"computed","paper":{"title":"On Uniform f-vectors of Cutsets 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, Shahriar Shahriari","submitted_at":"2015-12-09T18:11:38Z","abstract_excerpt":"Let $[n] = \\{1, 2, \\ldots, n\\}$ and let $2^{[n]}$ be the collection of all subsets of $[n]$ ordered by inclusion. ${\\cal C} \\subseteq 2^{[n]}$ is a {\\em cutset} if it meets every maximal chain in $2^{[n]}$, and the {\\em width} of ${\\cal C} \\subseteq 2^{[n]}$ is the minimum number of chains in a chain decomposition of ${\\cal C}$. Fix $0 \\leq m \\leq l \\leq n$. What is the smallest value of $k$ such that there exists a cutset that consists only of subsets of sizes between $m$ and $l$, and such that it contains exactly $k$ subsets of size $i$ for each $m \\leq i \\leq l$? The answer, which we denote"},"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":"1512.02973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-09T18:11:38Z","cross_cats_sorted":[],"title_canon_sha256":"d68c71c263f36dece851ea82597582a6c805d8bf6da67cdef7117767ae024565","abstract_canon_sha256":"3a8f16db127c66ae3a836de00f564ec18974342d7509cfc05187ca8a7b5e3665"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:39.139001Z","signature_b64":"tQF/5XF5GeojWSKjd0ZuOYbnKL9Dvugd8x+9jBMmFuSfEjZIHVXXY/x4vGaeISbO4iYl7Y0Z3ZFlDKVYO9t8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25125fbe9f4708b9ea3ad01da19e791ffa948b1e53e1d9d53fc425157737ba82","last_reissued_at":"2026-05-18T01:24:39.138526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:39.138526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Uniform f-vectors of Cutsets 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, Shahriar Shahriari","submitted_at":"2015-12-09T18:11:38Z","abstract_excerpt":"Let $[n] = \\{1, 2, \\ldots, n\\}$ and let $2^{[n]}$ be the collection of all subsets of $[n]$ ordered by inclusion. ${\\cal C} \\subseteq 2^{[n]}$ is a {\\em cutset} if it meets every maximal chain in $2^{[n]}$, and the {\\em width} of ${\\cal C} \\subseteq 2^{[n]}$ is the minimum number of chains in a chain decomposition of ${\\cal C}$. Fix $0 \\leq m \\leq l \\leq n$. What is the smallest value of $k$ such that there exists a cutset that consists only of subsets of sizes between $m$ and $l$, and such that it contains exactly $k$ subsets of size $i$ for each $m \\leq i \\leq l$? The answer, which we denote"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02973","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":"1512.02973","created_at":"2026-05-18T01:24:39.138602+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02973v1","created_at":"2026-05-18T01:24:39.138602+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02973","created_at":"2026-05-18T01:24:39.138602+00:00"},{"alias_kind":"pith_short_12","alias_value":"EUJF7PU7I4EL","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EUJF7PU7I4ELT2R2","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EUJF7PU7","created_at":"2026-05-18T12:29:19.899920+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/EUJF7PU7I4ELT2R22AO2DHTZD7","json":"https://pith.science/pith/EUJF7PU7I4ELT2R22AO2DHTZD7.json","graph_json":"https://pith.science/api/pith-number/EUJF7PU7I4ELT2R22AO2DHTZD7/graph.json","events_json":"https://pith.science/api/pith-number/EUJF7PU7I4ELT2R22AO2DHTZD7/events.json","paper":"https://pith.science/paper/EUJF7PU7"},"agent_actions":{"view_html":"https://pith.science/pith/EUJF7PU7I4ELT2R22AO2DHTZD7","download_json":"https://pith.science/pith/EUJF7PU7I4ELT2R22AO2DHTZD7.json","view_paper":"https://pith.science/paper/EUJF7PU7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02973&json=true","fetch_graph":"https://pith.science/api/pith-number/EUJF7PU7I4ELT2R22AO2DHTZD7/graph.json","fetch_events":"https://pith.science/api/pith-number/EUJF7PU7I4ELT2R22AO2DHTZD7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EUJF7PU7I4ELT2R22AO2DHTZD7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EUJF7PU7I4ELT2R22AO2DHTZD7/action/storage_attestation","attest_author":"https://pith.science/pith/EUJF7PU7I4ELT2R22AO2DHTZD7/action/author_attestation","sign_citation":"https://pith.science/pith/EUJF7PU7I4ELT2R22AO2DHTZD7/action/citation_signature","submit_replication":"https://pith.science/pith/EUJF7PU7I4ELT2R22AO2DHTZD7/action/replication_record"}},"created_at":"2026-05-18T01:24:39.138602+00:00","updated_at":"2026-05-18T01:24:39.138602+00:00"}