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As an example of interest to chromatic homotopy theorists, we also show that Ravenel's $X(n)$ filtration of $MU$ is a tower of intermediate Thom spectra determined by a natural filtration of $BU$ by sub-bialagebras."},"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":"1601.04123","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-01-16T04:51:11Z","cross_cats_sorted":[],"title_canon_sha256":"a702214f6da8cb3837ad7528ae427626e9173d141f91f35e54d89504bae345c2","abstract_canon_sha256":"83fedc8cbfa1417987fd37d3c1cb089ab30d0ebb20f4d724f038c7f12fe94b99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:58.195836Z","signature_b64":"ox0lgDgJDrdHrcuJise1d2bMwLdMgqzxvIm96Ij81xwGNop7snzfT6FUofUa6E4MdsNFuAwzSCmHydJtlfbXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"243dcf7211fd75e71891d135fc63d87e40570558439cd3702a5bc1dbc68df9b4","last_reissued_at":"2026-05-18T00:44:58.195392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:58.195392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative Thom Spectra Via Operadic Kan Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jonathan Beardsley","submitted_at":"2016-01-16T04:51:11Z","abstract_excerpt":"We show that a large number of Thom spectra, i.e. colimits of morphisms $BG\\to BGL_1(\\mathbb{S})$, can be obtained as iterated Thom spectra, i.e. colimits of morphisms $BG\\to BGL_1(Mf)$ for some Thom spectrum $Mf$. 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