{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FXOYZCL5W5PZWXONX5SQGULBRO","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":"57b58b2292aa75dc03c6c4f52387499d383f221e0961598a7daebca84ed5ee63","cross_cats_sorted":["math.DG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-16T19:41:51Z","title_canon_sha256":"64240f78cfd42b6d84319a553c7eddd4a7d15193956deb0d253f3d13f2e087bd"},"schema_version":"1.0","source":{"id":"1503.04785","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04785","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04785v2","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04785","created_at":"2026-05-18T02:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"FXOYZCL5W5PZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FXOYZCL5W5PZWXON","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FXOYZCL5","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:f8d5613fc64cf6e9fbff28ad06ebbd027b515f69aef45eeacc4dbd5dd18f5105","target":"graph","created_at":"2026-05-18T02:16:50Z","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":"In this paper we prove that for a fixed neat principal congruence subgroup of a Bianchi group the order of the torsion part of its second cohomology group with coefficients in an integral lattice associated to the m-th symmetric power of the standard representation of SL_2(C) grows exponentially in m^2. We give upper and lower bounds for the growth rate. Our result extends a result of Mueller and Marshall, who proved the corresponding statement for closed arithmetic 3-manifolds, to the finite-volume case. We also prove a limit multiplicity formula for twisted combinatorial Reidemeister torsion","authors_text":"Jean Raimbault, Jonathan Pfaff","cross_cats":["math.DG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-16T19:41:51Z","title":"On the torsion in symmetric powers on congruence subgroups of Bianchi groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04785","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:e650ee9f2cbf2751d564ce57c6aa75a1964af5630abc4b3b7caa734d77b29e2b","target":"record","created_at":"2026-05-18T02:16:50Z","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":"57b58b2292aa75dc03c6c4f52387499d383f221e0961598a7daebca84ed5ee63","cross_cats_sorted":["math.DG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-16T19:41:51Z","title_canon_sha256":"64240f78cfd42b6d84319a553c7eddd4a7d15193956deb0d253f3d13f2e087bd"},"schema_version":"1.0","source":{"id":"1503.04785","kind":"arxiv","version":2}},"canonical_sha256":"2ddd8c897db75f9b5dcdbf650351618b81fee79f7bd1c3ec8b26f1d49cc8c38c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ddd8c897db75f9b5dcdbf650351618b81fee79f7bd1c3ec8b26f1d49cc8c38c","first_computed_at":"2026-05-18T02:16:50.752593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:50.752593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZTioIJ83wLrwNx9DTuhJSLHnsohViIOogVRXA0T5maK8bSDZX1nrfe4A0xZS5Lb2NTZqm39DT5bQxRoRnMNwBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:50.753193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04785","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e650ee9f2cbf2751d564ce57c6aa75a1964af5630abc4b3b7caa734d77b29e2b","sha256:f8d5613fc64cf6e9fbff28ad06ebbd027b515f69aef45eeacc4dbd5dd18f5105"],"state_sha256":"0e66590b9fd179f547666265e2c851d402723ce654cee417c8f597ce8d4db5c8"}