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To prove this we set up a spectral sequence computing the homotopy groups of the moduli space of A-infinity structures on a spectrum, and use the theory of S-algebra k-invariants for connective S-algebras due to Dugger and Shipley to show that all the uniqueness obstructions are hit by differentials."},"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":"0810.5032","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-10-28T14:20:36Z","cross_cats_sorted":[],"title_canon_sha256":"f74da998291f616e60089ebb1965c38b5175648b99b96abcc894b8f9ae5f798e","abstract_canon_sha256":"11705128671bfd84461c2cab48e61ba5edec8b8236ecb6321be30bde4741dd97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.807225Z","signature_b64":"z7dWjODgotOadLkBWKpOJLIxmr2+OC3rMbWkKvKWyNThg+qlQHGZyXXctFJxbcbrHTTAgroLuDwqRr1IkNfdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2579dc9b1fa222809030c38b85a4c3cb31a728a6b913c6e7efb4e7f9f6aabc1","last_reissued_at":"2026-05-18T03:02:44.806556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.806556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of Morava K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Vigleik Angeltveit","submitted_at":"2008-10-28T14:20:36Z","abstract_excerpt":"We show that there is an essentially unique S-algebra structure on the Morava K-theory spectrum K(n), while K(n) has uncountably many MU or \\hE{n}-algebra structures. 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