{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:KFPOFRWN2LZJIOZDYT4ORIFJQR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b91c84cf1a81c5f257493f17dbd09202d956f4bb0d7eae97cccf71339480cf48","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1997-07-10T12:38:09Z","title_canon_sha256":"5cda1fc182f6ca53cc24080232b06b4123b3c9a500183b921e065c463a2e3639"},"schema_version":"1.0","source":{"id":"dg-ga/9707010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9707010","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9707010v1","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9707010","created_at":"2026-05-17T23:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"KFPOFRWN2LZJ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"KFPOFRWN2LZJIOZD","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"KFPOFRWN","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:db09fb5b50a4399d37a4007f1d1c2f1990b248974a955e69d30190a3a6893d79","target":"graph","created_at":"2026-05-17T23:59:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the behaviour of analytic torsion under smooth fibrations. Namely, let F \\to E \\to^{f} B be a smooth fiber bundle of connected closed oriented smooth manifolds and let $V$ be a flat vector bundle over $E$. Assume that $E$ and $B$ come with Riemannian metrics and $V$ comes with a unimodular (not necessarily flat) Riemannian metric. 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","authors_text":"Thomas Schick, Thomas Thielmann, Wolfgang Lueck","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"dg-ga","submitted_at":"1997-07-10T12:38:09Z","title":"Torsion and fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9707010","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:006a2c734575d6c6915933fc3bfbeb04b45d52be7313aea133501fbf2dad9b71","target":"record","created_at":"2026-05-17T23:59:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b91c84cf1a81c5f257493f17dbd09202d956f4bb0d7eae97cccf71339480cf48","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1997-07-10T12:38:09Z","title_canon_sha256":"5cda1fc182f6ca53cc24080232b06b4123b3c9a500183b921e065c463a2e3639"},"schema_version":"1.0","source":{"id":"dg-ga/9707010","kind":"arxiv","version":1}},"canonical_sha256":"515ee2c6cdd2f2943b23c4f8e8a0a98441558afa4cc00acf0d8875a6a3494083","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"515ee2c6cdd2f2943b23c4f8e8a0a98441558afa4cc00acf0d8875a6a3494083","first_computed_at":"2026-05-17T23:59:45.085934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:45.085934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FohphPeMu5q5bQezl41TFwWWPE1Wro5/HTPu5ABuDaTiuKZl4ZkaZQbZmTLLrR8glKc9lYBfMXd+UNlZ6tonCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:45.086443Z","signed_message":"canonical_sha256_bytes"},"source_id":"dg-ga/9707010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:006a2c734575d6c6915933fc3bfbeb04b45d52be7313aea133501fbf2dad9b71","sha256:db09fb5b50a4399d37a4007f1d1c2f1990b248974a955e69d30190a3a6893d79"],"state_sha256":"05c50dbd03d095c3a63a4e445f272db5f7a6dcf0d8fc0bf9a2fda3c4d6735ed5"}