{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SPDT7AOPSKDG4OTECO4JIV7UJR","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":"e02fffbd8435b954d025adeb66632d15d57d44a3b365be0c88462d68b18d20fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-15T11:50:43Z","title_canon_sha256":"9aa4f054c39eed1cdad099095baa620cda9989353181bf8ed82def0156016c85"},"schema_version":"1.0","source":{"id":"1708.04464","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04464","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04464v2","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04464","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"SPDT7AOPSKDG","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SPDT7AOPSKDG4OTE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SPDT7AOP","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:82e6b0146f7b1e73aabaee014c1e1cd421c901c5657a2e7e9ded2c1a6dc17567","target":"graph","created_at":"2026-05-17T23:53:12Z","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 study the dynamics of $SL_3(\\mathbb{R})$ and its subgroups on the homogeneous space $X$ consisting of homothety classes of rank-2 discrete subgroups of $\\mathbb{R}^3$. We focus on the case where the acting group is Zariski dense in either $SL_3(\\mathbb{R})$ or $SO(2,1)(\\mathbb{R})$. Using techniques of Benoist and Quint we prove that for a compactly supported probability measure $\\mu$ on $SL_3(\\mathbb{R})$ whose support generates a group which is Zariski dense in $SL_3(\\mathbb{R})$, there exists a unique $\\mu$-stationary probability measure on $X$. When the Zariski closure is $SO(2,1)(\\math","authors_text":"Oliver Sargent, Uri Shapira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-15T11:50:43Z","title":"Dynamics on the space of 2-lattices in 3-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04464","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":"sha256:6fc8817c2a29c7fb29ca34083c56061804f087d9a322441897eec0afde586035","target":"record","created_at":"2026-05-17T23:53:12Z","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":"e02fffbd8435b954d025adeb66632d15d57d44a3b365be0c88462d68b18d20fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-15T11:50:43Z","title_canon_sha256":"9aa4f054c39eed1cdad099095baa620cda9989353181bf8ed82def0156016c85"},"schema_version":"1.0","source":{"id":"1708.04464","kind":"arxiv","version":2}},"canonical_sha256":"93c73f81cf92866e3a6413b89457f44c5821e602bf6aa0f98dd0a5375b403a7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93c73f81cf92866e3a6413b89457f44c5821e602bf6aa0f98dd0a5375b403a7a","first_computed_at":"2026-05-17T23:53:12.017159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:12.017159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DJx+DnJVkatqgxl9kIFXObtFI5Lo2+AG5UhunIni0FwzjZ/Qsf+DxmKDzxKH1nJE92a52yUphsJGw31mQx6vDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:12.017847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04464","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fc8817c2a29c7fb29ca34083c56061804f087d9a322441897eec0afde586035","sha256:82e6b0146f7b1e73aabaee014c1e1cd421c901c5657a2e7e9ded2c1a6dc17567"],"state_sha256":"7c51f3e457d133abc23dd3bb4e9ce4262ec4b079508e1e580c079b352868940a"}