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Ilinca and Kahn determined the logarithmic asymptotics and reiterated the question of what their order of magnitude is. We show that the number of maximal independent sets in $B(2d-1,d)$ is \\[ \\left(1+o(1)\\right)(2d-1)\\exp\\left(\\frac{(d-1)^2}{2^{2d-1}}\\binom{2d-2}{d-1}\\right)\\cdot 2^{\\binom{2d-2}{d-1}}, \\] and describe their typical structur"},"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":"2505.00132","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-30T19:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"77f12b791447390498e437b62787daa532a59c1c52041c034e5bc1870b0608e5","abstract_canon_sha256":"382cad8226c4dad3325e3c9581cddfa9fd64d24e6fae572791dcafb6e82cc131"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:56:42.189157Z","signature_b64":"w8yO1I3aUqlti9LxjDK8BZguSco6mI03b3CVpZXzshHemm4rwyO0QK8YF/7BmyfaTkx95hyB4KqSEsZwmSm1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f241a23ec3925417c2700bbfe8e7db73e2c9dff17463047701f4aa74cf581203","last_reissued_at":"2026-07-05T10:56:42.188700Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:56:42.188700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal independent sets in the middle two layers of the Boolean lattice","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ce Chen, J\\'ozsef Balogh, Ramon I. 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