{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SPDT7AOPSKDG4OTECO4JIV7UJR","short_pith_number":"pith:SPDT7AOP","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"},"canonical_sha256":"93c73f81cf92866e3a6413b89457f44c5821e602bf6aa0f98dd0a5375b403a7a","source":{"kind":"arxiv","id":"1708.04464","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SPDT7AOPSKDG4OTECO4JIV7UJR","target":"record","payload":{"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"},"canonical_sha256":"93c73f81cf92866e3a6413b89457f44c5821e602bf6aa0f98dd0a5375b403a7a","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"},"source_kind":"arxiv","source_id":"1708.04464","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5KP9CL617ZzDwKfNZeQNQAMQs5ZDiSyQzv9tFDNDSTmxvs88on2usL8CVgik3AeCdzfJYvOsoJTGogMsoMzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:10:46.776256Z"},"content_sha256":"6fc8817c2a29c7fb29ca34083c56061804f087d9a322441897eec0afde586035","schema_version":"1.0","event_id":"sha256:6fc8817c2a29c7fb29ca34083c56061804f087d9a322441897eec0afde586035"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SPDT7AOPSKDG4OTECO4JIV7UJR","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gXp+7C6ThHLZ61kj7XF6XQyA6kiOyuf7mpDaoVBafjKxlSSRu1BGCgMeE5RmkXQXnhuHsu158aG8dzmMzGP9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:10:46.776636Z"},"content_sha256":"82e6b0146f7b1e73aabaee014c1e1cd421c901c5657a2e7e9ded2c1a6dc17567","schema_version":"1.0","event_id":"sha256:82e6b0146f7b1e73aabaee014c1e1cd421c901c5657a2e7e9ded2c1a6dc17567"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/bundle.json","state_url":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T18:10:46Z","links":{"resolver":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR","bundle":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/bundle.json","state":"https://pith.science/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPDT7AOPSKDG4OTECO4JIV7UJR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/sydI2+vIrzprjrQZFnG69b2Zy/oH80JCeNuSdduXHT8cxDGhg2Bvt5Wtx6LMVbRygXAzENr5IJWaMBHbxu6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:10:46.778452Z","bundle_sha256":"06e8ae7ee28d8b7302ec8520ad82510e1f6d918ab2e2aad48b94586601cf6ad3"}}