{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5ZC652VUU5NUMVZKBOC7P7K6OX","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":"a63a247b78738628cee70d643588c2e5f8242caef40df55c1977bf9a4a6d9645","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-03-27T16:43:28Z","title_canon_sha256":"e9536b570fe54dd49c430d9cb63524a8e2a0b04ec9cfb91a1fa34ed9c6eaafca"},"schema_version":"1.0","source":{"id":"1803.10175","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10175","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10175v2","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10175","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"5ZC652VUU5NU","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5ZC652VUU5NUMVZK","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5ZC652VU","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:db39c951b0481070941b3f24a5ea2e1e85f1dc3e73d2e7bb489a463a9169f320","target":"graph","created_at":"2026-05-18T00:17:59Z","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 show that certain representations over fields with positive characteristic of groups having CAT(0) fixed point property ${\\rm F}\\mathcal{B}_{\\widetilde{A}_n}$ have finite image. In particular, we obtain rigidity results for representations of the following groups: the special linear group over $\\mathbb{Z}$, $SL_k(\\mathbb{Z})$, the special automorphism group of a free group, ${\\rm SAut}(F_k)$, the mapping class group of a closed orientable surface, ${\\rm Mod}(\\Sigma_g)$, and many other groups.\n  In the case of characteristic zero we show that low dimensional complex representations of groups","authors_text":"Olga Varghese","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-03-27T16:43:28Z","title":"Representations of groups with CAT(0) fixed point property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10175","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":"sha256:5e6077a8292029797615c4d8886ff5ed795669708d1afbf6c0a1c839a5e7ec74","target":"record","created_at":"2026-05-18T00:17:59Z","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":"a63a247b78738628cee70d643588c2e5f8242caef40df55c1977bf9a4a6d9645","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-03-27T16:43:28Z","title_canon_sha256":"e9536b570fe54dd49c430d9cb63524a8e2a0b04ec9cfb91a1fa34ed9c6eaafca"},"schema_version":"1.0","source":{"id":"1803.10175","kind":"arxiv","version":2}},"canonical_sha256":"ee45eeeab4a75b46572a0b85f7fd5e75e10875e3f32ccad78eacb1cea74fcc77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee45eeeab4a75b46572a0b85f7fd5e75e10875e3f32ccad78eacb1cea74fcc77","first_computed_at":"2026-05-18T00:17:59.450435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:59.450435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UiYq9zqSDWueNuh9vorVVE5HHdEl9hAwQqwdvR6gBnloG66oeHvm/JmAfckd/FmtFSaZqqsvCmLYlILaqD6FBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:59.451085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10175","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e6077a8292029797615c4d8886ff5ed795669708d1afbf6c0a1c839a5e7ec74","sha256:db39c951b0481070941b3f24a5ea2e1e85f1dc3e73d2e7bb489a463a9169f320"],"state_sha256":"f02b45071942a8a9cea4e9984d0b1658dbbdadb7a90dfc3b3a951353d0d3e3f8"}