{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:W2BFP3J4DWRWF6YYMJSYOWIVB5","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":"1249d7676d95a21fefb09bcb93e473efe55a3d39d60e8077223fa2abbd0c912b","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-01T09:45:45Z","title_canon_sha256":"0577109260d336cba1e0e94d549694becc68d37d7ac247ef46e71bcaa1990640"},"schema_version":"1.0","source":{"id":"2607.00697","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00697","created_at":"2026-07-02T01:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00697v1","created_at":"2026-07-02T01:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00697","created_at":"2026-07-02T01:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"W2BFP3J4DWRW","created_at":"2026-07-02T01:17:51Z"},{"alias_kind":"pith_short_16","alias_value":"W2BFP3J4DWRWF6YY","created_at":"2026-07-02T01:17:51Z"},{"alias_kind":"pith_short_8","alias_value":"W2BFP3J4","created_at":"2026-07-02T01:17:51Z"}],"graph_snapshots":[{"event_id":"sha256:633ef9d02a39144eb9c4c75d9fa9e0c59fad9822e3a76973edb4dbaec6cf5c6f","target":"graph","created_at":"2026-07-02T01:17:51Z","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/2607.00697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that an action by $C^1$ diffeomorphisms of a lattice in a simple $p$-adic group on a compact manifold is finite, provided the dimension is less than the rank. We extend this statement to lattices in totally disconnected $S$-arithmetic groups, where the critical dimension is the maximal rank of the simple factors. This uses the machinery developed by Brown, Fisher, and Hurtado.","authors_text":"Segev Gonen Cohen","cross_cats":["math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-01T09:45:45Z","title":"Actions of lattices in $S$-arithmetic groups on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00697","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":"sha256:4411aea70d9271436931b1d72a6ae8191113aa00840d475afad3173c3cb5edca","target":"record","created_at":"2026-07-02T01:17:51Z","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":"1249d7676d95a21fefb09bcb93e473efe55a3d39d60e8077223fa2abbd0c912b","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-01T09:45:45Z","title_canon_sha256":"0577109260d336cba1e0e94d549694becc68d37d7ac247ef46e71bcaa1990640"},"schema_version":"1.0","source":{"id":"2607.00697","kind":"arxiv","version":1}},"canonical_sha256":"b68257ed3c1da362fb1862658759150f57ac99c48d3d9f1cb1222f98298a06cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b68257ed3c1da362fb1862658759150f57ac99c48d3d9f1cb1222f98298a06cb","first_computed_at":"2026-07-02T01:17:51.953862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:17:51.953862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nbwGFvnwmUPtmQc0bll7CH4KnP/N6fbEFO5Ulpwl/gRm1qNnPT7GwZW38iwvP3FfY8RtQUSHCRP7aQiU9rr1BQ==","signature_status":"signed_v1","signed_at":"2026-07-02T01:17:51.954233Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00697","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4411aea70d9271436931b1d72a6ae8191113aa00840d475afad3173c3cb5edca","sha256:633ef9d02a39144eb9c4c75d9fa9e0c59fad9822e3a76973edb4dbaec6cf5c6f"],"state_sha256":"b1fcc1c992395c01a54a75f9414f010f2d3cbf4fd8a1825234a1565485fa5018"}