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Let $\\rho_{an}(E;V)$ be the analytic torsion of $E$ with coefficients in $V$ and let $\\Pf_B$ be the Pfaffian $\\dim(B)$-form. Let $H^q_{dR}(F;V)$ be the flat vector bundle over $B$ whose fiber over $b \\in B$ is $H^q_{dR}(F_b;V)$ with the Riemannian metric whi"},"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":"dg-ga/9707010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1997-07-10T12:38:09Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"5cda1fc182f6ca53cc24080232b06b4123b3c9a500183b921e065c463a2e3639","abstract_canon_sha256":"b91c84cf1a81c5f257493f17dbd09202d956f4bb0d7eae97cccf71339480cf48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:45.086443Z","signature_b64":"FohphPeMu5q5bQezl41TFwWWPE1Wro5/HTPu5ABuDaTiuKZl4ZkaZQbZmTLLrR8glKc9lYBfMXd+UNlZ6tonCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"515ee2c6cdd2f2943b23c4f8e8a0a98441558afa4cc00acf0d8875a6a3494083","last_reissued_at":"2026-05-17T23:59:45.085934Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:45.085934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torsion and fibrations","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Thomas Schick, Thomas Thielmann, Wolfgang Lueck","submitted_at":"1997-07-10T12:38:09Z","abstract_excerpt":"We study the behaviour of analytic torsion under smooth fibrations. 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