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The mod $p$ reduction $\\lambda_i(E) \\in H^*(B; \\F_p)$ has zero indeterminacy and satisfies $p\\lambda_i(E) = \\kappa_{i(p-1)-1}(E) \\in H^*(B;\\Z/p^2)$."},"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":"math/0402226","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-02-13T14:02:42Z","cross_cats_sorted":[],"title_canon_sha256":"d568daad15bada18b550809a87d83b188f4cad3006650a7cc96f9dd77648b1e8","abstract_canon_sha256":"82267d37174e052c2a4331eb3e5886a9e9a39446889d6b852c4b28aefe5e1bcc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:32.511087Z","signature_b64":"OxPbulwNWaGGqrMBtOuDbxOG3mviyLOp5A87VIXcGNK4ZZ1AVtuQjtb2Pp0lfDtqi3cEx4mIn2GINbF8V8j0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90d17adf232590a121d3da60968c499c63a6345756393daf2bd486b42a817d23","last_reissued_at":"2026-05-18T02:41:32.510715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:32.510715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Secondary Characteristic Classes of Surface Bundles","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Soren Galatius","submitted_at":"2004-02-13T14:02:42Z","abstract_excerpt":"The Miller-Morita-Mumford classes associate to an oriented surface bundle $E\\to B$ a class $\\kappa_i(E) \\in H^{2i}(B;\\Z)$. 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