{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZJYFHS4HZPJFWOSIKUIMTWXTGV","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":"d52f1c95bcbd0679cb650783a649a9db6638b9c0ff858c8f47a21e54722f67ca","cross_cats_sorted":["math.DG","math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-17T15:19:38Z","title_canon_sha256":"27fb99b204d2afd6c7d74c39e6c7840de6c2bfa6ac22968c77cecf73858f499c"},"schema_version":"1.0","source":{"id":"1608.04995","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04995","created_at":"2026-07-05T01:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04995v4","created_at":"2026-07-05T01:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04995","created_at":"2026-07-05T01:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZJYFHS4HZPJF","created_at":"2026-07-05T01:17:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZJYFHS4HZPJFWOSI","created_at":"2026-07-05T01:17:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZJYFHS4H","created_at":"2026-07-05T01:17:54Z"}],"graph_snapshots":[{"event_id":"sha256:3570779c76dc4094581e902a8888e7d710dd67876fee16bfcd542363a7622082","target":"graph","created_at":"2026-07-05T01:17:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1608.04995/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove several cases of Zimmer's conjecture for actions of higher-rank cocompact lattices on low dimensional manifolds. For example, if $\\Gamma$ is a cocompact lattice in $\\mathrm{Sl}(n, \\mathbb R)$, $M$ is a compact manifold, and $\\omega$ a volume form on $M$ we show that any homomorphism $\\rho\\colon \\Gamma \\rightarrow \\mathrm{Diff}(M)$ has finite image if the dimension of $M$ is less than $n-1$ and that any homomorphism $\\rho\\colon \\Gamma \\rightarrow \\mathrm{Diff}(M,\\omega)$ has finite image if the dimension of $M$ is less than $n$. The key step in the proof is to show any such action has ","authors_text":"Aaron Brown, David Fisher, Sebastian Hurtado","cross_cats":["math.DG","math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-17T15:19:38Z","title":"Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04995","kind":"arxiv","version":4},"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":"sha256:30caab413e7a89a879ee4026de9a08123c768bdbfb145b8707b83d1ea4def5f3","target":"record","created_at":"2026-07-05T01:17:54Z","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":"d52f1c95bcbd0679cb650783a649a9db6638b9c0ff858c8f47a21e54722f67ca","cross_cats_sorted":["math.DG","math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-17T15:19:38Z","title_canon_sha256":"27fb99b204d2afd6c7d74c39e6c7840de6c2bfa6ac22968c77cecf73858f499c"},"schema_version":"1.0","source":{"id":"1608.04995","kind":"arxiv","version":4}},"canonical_sha256":"ca7053cb87cbd25b3a485510c9daf3355d2ca3fd698555023f24acdedf099168","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca7053cb87cbd25b3a485510c9daf3355d2ca3fd698555023f24acdedf099168","first_computed_at":"2026-07-05T01:17:54.490134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:54.490134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"llMpQTaCjqvYsdFxu8j5/EMY0/JdF3pOrGD6Lf4BXW+rxeAOw6owyEU9YAwe8YpGd+wsCjikqxp/R3RKP5xNBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:54.490537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04995","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30caab413e7a89a879ee4026de9a08123c768bdbfb145b8707b83d1ea4def5f3","sha256:3570779c76dc4094581e902a8888e7d710dd67876fee16bfcd542363a7622082"],"state_sha256":"d0d373224332206683f98adbc61c3d598f19707423cbd9bb870dc82b4df0abea"}