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Additionally, if $R$ is an $\\mathbb{E}_2$-ring Thom spectrum admitting a map (of homotopy ring spectra) from $X(2)$, e.g. $X(n)$, its topological Hochschild homology has a simple description."},"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":"1708.09486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-30T22:00:57Z","cross_cats_sorted":[],"title_canon_sha256":"e968f34d5bc7437396c3645c8c2aa347af938bdcbf8fc81a508df401694d3627","abstract_canon_sha256":"c39b974ce24edb0b20033cf3f593311f408692bd8a7382c8ac3fc550c1e63912"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:18.651599Z","signature_b64":"pURz2ep1GRucKuZfOFTRJPcFeGqgF29IAHnDb2uFrbdkuX9v+r8/Iksxiak7xtUh8KI2BSkC5sMpRciQHSMuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc11bee7744b663976ed5c8f67e9c51ea92ac078d58adfd9d806cc72ba8692f2","last_reissued_at":"2026-05-18T00:36:18.650883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:18.650883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Hochschild homology of X(n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jonathan Beardsley","submitted_at":"2017-08-30T22:00:57Z","abstract_excerpt":"We show that Ravenel's spectrum $X(2)$ is the versal $E_1$-$S$-algebra of characteristic $\\eta$. 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