{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ORTTJ5IC3XGWZR2Z4OX6KCNPE2","short_pith_number":"pith:ORTTJ5IC","canonical_record":{"source":{"id":"1110.3743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-17T17:54:22Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f3c7e072303af0edf6d8100b40f30c40af58255c127e40429132f791af94d0da","abstract_canon_sha256":"7b3c26063373ae49602ed07ad241dd158117112117f4c7c96f9c3cc74da06583"},"schema_version":"1.0"},"canonical_sha256":"746734f502ddcd6cc759e3afe509af26b3092c57c244b97068f47123e2fbe800","source":{"kind":"arxiv","id":"1110.3743","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3743","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3743v1","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3743","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"ORTTJ5IC3XGW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"ORTTJ5IC3XGWZR2Z","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"ORTTJ5IC","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ORTTJ5IC3XGWZR2Z4OX6KCNPE2","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3743","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-17T17:54:22Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f3c7e072303af0edf6d8100b40f30c40af58255c127e40429132f791af94d0da","abstract_canon_sha256":"7b3c26063373ae49602ed07ad241dd158117112117f4c7c96f9c3cc74da06583"},"schema_version":"1.0"},"canonical_sha256":"746734f502ddcd6cc759e3afe509af26b3092c57c244b97068f47123e2fbe800","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:48.611584Z","signature_b64":"XyyXK9PWjNunoG3ieWJgfmwOq4eq+5Opax3+pBG1bL0azQEIKc1OqROFO+GgY9knDAkun6wleS12vUVRWOlyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"746734f502ddcd6cc759e3afe509af26b3092c57c244b97068f47123e2fbe800","last_reissued_at":"2026-05-18T04:10:48.611156Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:48.611156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3743","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33Apesan/maeH/V5UOGYrIqlgDV3cj9krDVEiBd90k3G32CvBdKcvEaWU6rS9tknu5ivt5vo5rp39xwl5OYuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:20:55.036898Z"},"content_sha256":"069803b35b9c7f126b8b849bb45397358c56f68ed043f30b8d126b4fdb11dc1e","schema_version":"1.0","event_id":"sha256:069803b35b9c7f126b8b849bb45397358c56f68ed043f30b8d126b4fdb11dc1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ORTTJ5IC3XGWZR2Z4OX6KCNPE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The action of mapping classes on nilpotent covers of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Thomas Koberda","submitted_at":"2011-10-17T17:54:22Z","abstract_excerpt":"Let $\\Sigma$ be a surface whose interior admits a hyperbolic structure of finite volume. In this paper, we show that any infinite order mapping class acts with infinite order on the homology of some universal $k$--step nilpotent cover of $\\Sigma$. We show that a Torelli mapping class either acts with infinite order on the homology of a finite abelian cover, or the suspension of the mapping class is a 3--manifold whose fundamental group has positive homology gradient. In the latter case, it follows that the suspended 3--manifold has a large fundamental group. It follows that every element of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3743","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dk7kYTtTniNtslmoAjLX7otFLOBuYugPQ12DsRQta1d5phVfqG9icktNGuXQZq8Di/LCp6+h79yRCbaPsWElCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:20:55.037579Z"},"content_sha256":"5986cbcdc0e5d61cce348601f7d658c67d0f82ea828ccb6e38d20fb5d357af6a","schema_version":"1.0","event_id":"sha256:5986cbcdc0e5d61cce348601f7d658c67d0f82ea828ccb6e38d20fb5d357af6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ORTTJ5IC3XGWZR2Z4OX6KCNPE2/bundle.json","state_url":"https://pith.science/pith/ORTTJ5IC3XGWZR2Z4OX6KCNPE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ORTTJ5IC3XGWZR2Z4OX6KCNPE2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T18:20:55Z","links":{"resolver":"https://pith.science/pith/ORTTJ5IC3XGWZR2Z4OX6KCNPE2","bundle":"https://pith.science/pith/ORTTJ5IC3XGWZR2Z4OX6KCNPE2/bundle.json","state":"https://pith.science/pith/ORTTJ5IC3XGWZR2Z4OX6KCNPE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ORTTJ5IC3XGWZR2Z4OX6KCNPE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ORTTJ5IC3XGWZR2Z4OX6KCNPE2","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":"7b3c26063373ae49602ed07ad241dd158117112117f4c7c96f9c3cc74da06583","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-17T17:54:22Z","title_canon_sha256":"f3c7e072303af0edf6d8100b40f30c40af58255c127e40429132f791af94d0da"},"schema_version":"1.0","source":{"id":"1110.3743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3743","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3743v1","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3743","created_at":"2026-05-18T04:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"ORTTJ5IC3XGW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"ORTTJ5IC3XGWZR2Z","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"ORTTJ5IC","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:5986cbcdc0e5d61cce348601f7d658c67d0f82ea828ccb6e38d20fb5d357af6a","target":"graph","created_at":"2026-05-18T04:10:48Z","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":"Let $\\Sigma$ be a surface whose interior admits a hyperbolic structure of finite volume. In this paper, we show that any infinite order mapping class acts with infinite order on the homology of some universal $k$--step nilpotent cover of $\\Sigma$. We show that a Torelli mapping class either acts with infinite order on the homology of a finite abelian cover, or the suspension of the mapping class is a 3--manifold whose fundamental group has positive homology gradient. In the latter case, it follows that the suspended 3--manifold has a large fundamental group. It follows that every element of th","authors_text":"Thomas Koberda","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-17T17:54:22Z","title":"The action of mapping classes on nilpotent covers of surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3743","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":"sha256:069803b35b9c7f126b8b849bb45397358c56f68ed043f30b8d126b4fdb11dc1e","target":"record","created_at":"2026-05-18T04:10:48Z","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":"7b3c26063373ae49602ed07ad241dd158117112117f4c7c96f9c3cc74da06583","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-17T17:54:22Z","title_canon_sha256":"f3c7e072303af0edf6d8100b40f30c40af58255c127e40429132f791af94d0da"},"schema_version":"1.0","source":{"id":"1110.3743","kind":"arxiv","version":1}},"canonical_sha256":"746734f502ddcd6cc759e3afe509af26b3092c57c244b97068f47123e2fbe800","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"746734f502ddcd6cc759e3afe509af26b3092c57c244b97068f47123e2fbe800","first_computed_at":"2026-05-18T04:10:48.611156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:48.611156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XyyXK9PWjNunoG3ieWJgfmwOq4eq+5Opax3+pBG1bL0azQEIKc1OqROFO+GgY9knDAkun6wleS12vUVRWOlyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:48.611584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:069803b35b9c7f126b8b849bb45397358c56f68ed043f30b8d126b4fdb11dc1e","sha256:5986cbcdc0e5d61cce348601f7d658c67d0f82ea828ccb6e38d20fb5d357af6a"],"state_sha256":"7701b2e7aadef200e8ed5eca8eb568d0b9412a170b103b7ba993d0d5e5b7d864"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hesgArGNjuwyfT9Ciq+qguMOYRshQGyEGr426ixnGhggm1Win9ZQdI56pN4sIwQ4oNjgzfgbZZ90FVGK1RgHAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:20:55.041513Z","bundle_sha256":"84b43ff6449c09042052f0f9c3f25916cab1123cc3aeac53537e3bde5fcccaf2"}}