{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:77Z6D342NWZ6I673O2CNH7VELJ","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":"9070ae04ec26cccaa331025e8d32a31dec764facbef8d377b569cc45eae8376f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-28T20:39:54Z","title_canon_sha256":"a69ea0b7a0618a5026d1ace9bbe80f5530170bc70eae904b9cde1ce74a597c7d"},"schema_version":"1.0","source":{"id":"1801.09283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09283","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09283v1","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09283","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"77Z6D342NWZ6","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"77Z6D342NWZ6I673","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"77Z6D342","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:fd8be397fdd026dba27873c3722f7d7aca22eff75793e78dcc34f7e9882228fb","target":"graph","created_at":"2026-05-18T00:24:57Z","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 $X$ be a higher rank symmetric space or a Bruhat-Tits building of dimension at least $2$ such that the isometry group of $X$ has property $(T)$. We prove that for every torsion free lattice $\\Gamma\\subset {\\rm Isom} X$ any homology class in $H_1(\\Gamma\\backslash X,\\mathbb F_2)$ has a representative cycle of total length $o_X({\\rm Vol}(\\Gamma\\backslash X))$. As an application we show that $\\dim_{\\mathbb F_2} H_1(\\Gamma\\backslash X,\\mathbb F_2)=o_X({\\rm Vol}(\\Gamma\\backslash X)).$","authors_text":"Mikolaj Fraczyk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-28T20:39:54Z","title":"Growth of mod$-2$ homology in higher rank locally symmetric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09283","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":"sha256:4e707e8f7a575517cb1f4dddc2166e9d9b34910768b3ccdf82ee4936d1ee4404","target":"record","created_at":"2026-05-18T00:24:57Z","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":"9070ae04ec26cccaa331025e8d32a31dec764facbef8d377b569cc45eae8376f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-28T20:39:54Z","title_canon_sha256":"a69ea0b7a0618a5026d1ace9bbe80f5530170bc70eae904b9cde1ce74a597c7d"},"schema_version":"1.0","source":{"id":"1801.09283","kind":"arxiv","version":1}},"canonical_sha256":"fff3e1ef9a6db3e47bfb7684d3fea45a555d59c5d9f6f9f93be0ed10a7dff0a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fff3e1ef9a6db3e47bfb7684d3fea45a555d59c5d9f6f9f93be0ed10a7dff0a8","first_computed_at":"2026-05-18T00:24:57.958352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:57.958352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cNmYTB6631rAPROcD8vRILh+deOHZNWaZ1+cN55zuNbY+tVfgvuQejaM/ejbxPQ/tPlPhxHNVqpQh+Tif09+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:57.959141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e707e8f7a575517cb1f4dddc2166e9d9b34910768b3ccdf82ee4936d1ee4404","sha256:fd8be397fdd026dba27873c3722f7d7aca22eff75793e78dcc34f7e9882228fb"],"state_sha256":"23ff99de887b9fb503c3430eb1203f3f54b00c9e30b46199d781f7d922e14f57"}