{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JZXJL5TDHH5KX5NSQ6EHCF3UQD","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":"5018fa3fbfc782fa503c5ed421d1a4995db9ae5f79b85acaa8c459c52651cb2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-30T09:53:22Z","title_canon_sha256":"6f9e2bb83a5d6696260186afdc122600db836246950585bf6c05d18612caccbe"},"schema_version":"1.0","source":{"id":"1409.0097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0097","created_at":"2026-05-18T02:43:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0097v1","created_at":"2026-05-18T02:43:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0097","created_at":"2026-05-18T02:43:53Z"},{"alias_kind":"pith_short_12","alias_value":"JZXJL5TDHH5K","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JZXJL5TDHH5KX5NS","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JZXJL5TD","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:d7246bc87a1736cf8bcdf8d7f1745b325ad8d52690c3dabb22c6c58ed1e4e2e2","target":"graph","created_at":"2026-05-18T02:43:53Z","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 show that if $\\mathcal{L}$ is a line in the plane containing a badly approximable vector, then almost every point in $\\mathcal{L}$ does not admit an improvement in Dirichlet's theorem. Our proof relies on a measure classification result for certain measures invariant under a non-abelian two dimensional group on the homogeneous space $\\mathrm{SL}_3(\\mathbb{R})/\\mathrm{SL}_3(\\mathbb{Z})$. Using the measure classification theorem, we reprove a result of Shah about planar nondegenerate curves (which are not necessarily analytic), and prove analogous results for the framework of Diophantine appr","authors_text":"Barak Weiss, Ronggang Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-30T09:53:22Z","title":"Invariant measures for solvable groups and diophantine approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0097","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":"sha256:456233997ebc9bc2452abe5b85446ff15faa2122484f4c851574fd7d211ef5f5","target":"record","created_at":"2026-05-18T02:43:53Z","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":"5018fa3fbfc782fa503c5ed421d1a4995db9ae5f79b85acaa8c459c52651cb2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-30T09:53:22Z","title_canon_sha256":"6f9e2bb83a5d6696260186afdc122600db836246950585bf6c05d18612caccbe"},"schema_version":"1.0","source":{"id":"1409.0097","kind":"arxiv","version":1}},"canonical_sha256":"4e6e95f66339faabf5b2878871177480d94dcde3bf74b58b2280b96b82075fca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e6e95f66339faabf5b2878871177480d94dcde3bf74b58b2280b96b82075fca","first_computed_at":"2026-05-18T02:43:53.372006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:53.372006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7mjFwhScpKT4QImAa42zypcWShAc/06e8h4lvKUEGpWG0IiYurfQsBl2WDnbvzaBGkXmEvMOQnchs8rGpUn3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:53.372425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:456233997ebc9bc2452abe5b85446ff15faa2122484f4c851574fd7d211ef5f5","sha256:d7246bc87a1736cf8bcdf8d7f1745b325ad8d52690c3dabb22c6c58ed1e4e2e2"],"state_sha256":"1fa371e3edb62b7f88d92ede2d65b064b3bed5b7b24a614f47cf0fc4130c1d0a"}