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It is part of the folklore of semigroup theory that almost all finite semigroups are nilpotent of degree 3.\n  We give formulae for the number of nilpotent semigroups of degree 3 with $n\\in\\N$ elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups with $n$ elements up to equality and up to isomorphism."},"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":"1201.3529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-17T15:31:16Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"4babe13a2f0d0ba3219d8af5b9440f0719c2bfcb2fc1fe1dad98c6751097f24a","abstract_canon_sha256":"6258a94e3969a8ba480556f091a14286b98f95ed0d2dc7defbc3035dddd6568f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:23.292479Z","signature_b64":"LzQBZscMjvLOt5OeSi8EVtEUv4acFME+prQwZAS5ECL4xu5jTqSTA9EhYwCuU+j1PTR3Up8I49xOvJkACAU1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a20675267a2d54db9c4719872d48f4d89a0ab6a85008ed3fb2e07f3f28c8f1e6","last_reissued_at":"2026-05-18T03:48:23.291646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:23.291646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of nilpotent semigroups of degree 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Andreas Distler, James D. 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