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We show that, up to diffeomorphism, $M^{6}$ has a unique differentiable structure and $M^{8}$ has at most two distinct differentiable structures. We also show that, up to concordance, there exist at least two distinct differentiable structures on a finite sheeted cover $N^{2n}$ of $\\mathbb{C}\\textbf{P}^n$ for $n=4, 7$ or $8$ and six distinct di"},"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":"1510.03032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-10-11T10:02:52Z","cross_cats_sorted":[],"title_canon_sha256":"58366375ecbe392411947dac7da3b4837df66eea9756a937c853859f0958a69c","abstract_canon_sha256":"1519400856c3c1bb09acffb7e48637df9cf6b57cc87c4934ef0cb3dff1afeb61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:48.808799Z","signature_b64":"/y/c1AOIDQ0KUJcGIxz+I2E6+Xu8HNk7A7aAqcwDbmDLYWMY2l3oZrccJsDblovShL8eCWj3nv8Q78TGanSyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"947cb481a10d8d48a31085dd2512c0b9fcb0161efd36858530847a301a94f276","last_reissued_at":"2026-05-18T00:37:48.808196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:48.808196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The classification of smooth structures on a homotopy complex projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ramesh Kasilingam","submitted_at":"2015-10-11T10:02:52Z","abstract_excerpt":"We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective $n$-space $\\mathbb{C}\\textbf{P}^n$, where $n=3$ and $4$. 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