{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SPDT7AOPSKDG4OTECO4JIV7UJR","short_pith_number":"pith:SPDT7AOP","schema_version":"1.0","canonical_sha256":"93c73f81cf92866e3a6413b89457f44c5821e602bf6aa0f98dd0a5375b403a7a","source":{"kind":"arxiv","id":"1708.04464","version":2},"attestation_state":"computed","paper":{"title":"Dynamics on the space of 2-lattices in 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Oliver Sargent, Uri Shapira","submitted_at":"2017-08-15T11:50:43Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.04464","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-15T11:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"9aa4f054c39eed1cdad099095baa620cda9989353181bf8ed82def0156016c85","abstract_canon_sha256":"e02fffbd8435b954d025adeb66632d15d57d44a3b365be0c88462d68b18d20fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:12.017847Z","signature_b64":"DJx+DnJVkatqgxl9kIFXObtFI5Lo2+AG5UhunIni0FwzjZ/Qsf+DxmKDzxKH1nJE92a52yUphsJGw31mQx6vDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93c73f81cf92866e3a6413b89457f44c5821e602bf6aa0f98dd0a5375b403a7a","last_reissued_at":"2026-05-17T23:53:12.017159Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:12.017159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics on the space of 2-lattices in 3-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Oliver Sargent, Uri Shapira","submitted_at":"2017-08-15T11:50:43Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04464","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.04464","created_at":"2026-05-17T23:53:12.017265+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.04464v2","created_at":"2026-05-17T23:53:12.017265+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04464","created_at":"2026-05-17T23:53:12.017265+00:00"},{"alias_kind":"pith_short_12","alias_value":"SPDT7AOPSKDG","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SPDT7AOPSKDG4OTE","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SPDT7AOP","created_at":"2026-05-18T12:31:43.269735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR","json":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR.json","graph_json":"https://pith.science/api/pith-number/SPDT7AOPSKDG4OTECO4JIV7UJR/graph.json","events_json":"https://pith.science/api/pith-number/SPDT7AOPSKDG4OTECO4JIV7UJR/events.json","paper":"https://pith.science/paper/SPDT7AOP"},"agent_actions":{"view_html":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR","download_json":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR.json","view_paper":"https://pith.science/paper/SPDT7AOP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.04464&json=true","fetch_graph":"https://pith.science/api/pith-number/SPDT7AOPSKDG4OTECO4JIV7UJR/graph.json","fetch_events":"https://pith.science/api/pith-number/SPDT7AOPSKDG4OTECO4JIV7UJR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/action/storage_attestation","attest_author":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/action/author_attestation","sign_citation":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/action/citation_signature","submit_replication":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/action/replication_record"}},"created_at":"2026-05-17T23:53:12.017265+00:00","updated_at":"2026-05-17T23:53:12.017265+00:00"}