{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:P5JXG23UWIG5Q6FL54NEJ2OIDS","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":"ab93f97fa7552456fc54ca548b06c370c029cab913c7605e482f5015032dc829","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-04-06T17:32:50Z","title_canon_sha256":"2acc4fac6b7d37f6d132232a829f3de1a70d8d22047bc69f8b69e54359a9b68f"},"schema_version":"1.0","source":{"id":"0704.0909","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.0909","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"0704.0909v2","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.0909","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"P5JXG23UWIG5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"P5JXG23UWIG5Q6FL","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"P5JXG23U","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:96daa2d2b4533a991434ddd7c97cf649d3d6d762e23f18137a814d1bbc7134f4","target":"graph","created_at":"2026-05-18T04:14:38Z","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 define the secondary invariants L^2- eta and -rho forms for families of generalized Dirac operators on normal coverings of fibre bundles. On the covering family we assume transversally smooth spectral projections, and Novikov--Shubin invariants bigger than 3(dim B+1) to treat the large time asymptotic for general operators. In the particular case of a bundle of spin manifolds, we study the L^2- rho class in relation to the space of positive scalar curvature vertical metrics.","authors_text":"Sara Azzali","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-04-06T17:32:50Z","title":"L^2 rho form for normal coverings of fibre bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.0909","kind":"arxiv","version":2},"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:ed007007281e73ccc6e573b1873230109a4a41ab254e16fa83434488c0ada8b3","target":"record","created_at":"2026-05-18T04:14:38Z","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":"ab93f97fa7552456fc54ca548b06c370c029cab913c7605e482f5015032dc829","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2007-04-06T17:32:50Z","title_canon_sha256":"2acc4fac6b7d37f6d132232a829f3de1a70d8d22047bc69f8b69e54359a9b68f"},"schema_version":"1.0","source":{"id":"0704.0909","kind":"arxiv","version":2}},"canonical_sha256":"7f53736b74b20dd878abef1a44e9c81c8892712ec492dff43a3b19c09efcc5ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f53736b74b20dd878abef1a44e9c81c8892712ec492dff43a3b19c09efcc5ff","first_computed_at":"2026-05-18T04:14:38.401267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:38.401267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xdhH3/bfbW9iVCzF3X48F0gQAMiKklafUKG3ReHQmW7ywEQA7nOfbhxgWSp/Ohb4z7uakGmP1FrVLbXOcjboDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:38.401809Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.0909","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed007007281e73ccc6e573b1873230109a4a41ab254e16fa83434488c0ada8b3","sha256:96daa2d2b4533a991434ddd7c97cf649d3d6d762e23f18137a814d1bbc7134f4"],"state_sha256":"03469b0a21c2840a4a8c90306a6526b1cd40faa05ea0984fe04ebf4a90dd4753"}