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It is known, due to the pioneering work of Meshulam and Wallach, that \\[\\lceil n/3\\rceil\\geq h_1(\\Delta^{[n]})\\geq n/3, \\textrm{ for all } n,\\] and that the equality $h_1(\\Delta^{[n]})=n/3$ is achieved when $n$ is divisibl"},"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":"1610.07136","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-10-23T09:10:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7bd05888cfc72ca64532ca017f286d302ec7c3654946f46480a5bed527d652d6","abstract_canon_sha256":"3d7a303f6766fec03a309357f3a935bbcd859710683795ec99057d95540ac74a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.513224Z","signature_b64":"zuZsaD1K9+6x96fA7FG5lyQP/9KgJDijV6ReVhZtcq3Sg1n+xOGzEesOA2gZZNLApQDWsX77kXWHqFYQ/Db6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ffa63944328e1d30828419d6588aaef398691288e5f800cfcaa7d96cdb3a868","last_reissued_at":"2026-05-18T00:35:55.512733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.512733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The first Cheeger constant of a simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"D.N. 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