{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JZXJL5TDHH5KX5NSQ6EHCF3UQD","short_pith_number":"pith:JZXJL5TD","schema_version":"1.0","canonical_sha256":"4e6e95f66339faabf5b2878871177480d94dcde3bf74b58b2280b96b82075fca","source":{"kind":"arxiv","id":"1409.0097","version":1},"attestation_state":"computed","paper":{"title":"Invariant measures for solvable groups and diophantine approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Barak Weiss, Ronggang Shi","submitted_at":"2014-08-30T09:53:22Z","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"},"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":"1409.0097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-30T09:53:22Z","cross_cats_sorted":[],"title_canon_sha256":"6f9e2bb83a5d6696260186afdc122600db836246950585bf6c05d18612caccbe","abstract_canon_sha256":"5018fa3fbfc782fa503c5ed421d1a4995db9ae5f79b85acaa8c459c52651cb2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:53.372425Z","signature_b64":"7mjFwhScpKT4QImAa42zypcWShAc/06e8h4lvKUEGpWG0IiYurfQsBl2WDnbvzaBGkXmEvMOQnchs8rGpUn3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e6e95f66339faabf5b2878871177480d94dcde3bf74b58b2280b96b82075fca","last_reissued_at":"2026-05-18T02:43:53.372006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:53.372006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant measures for solvable groups and diophantine approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Barak Weiss, Ronggang Shi","submitted_at":"2014-08-30T09:53:22Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0097","kind":"arxiv","version":1},"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":"1409.0097","created_at":"2026-05-18T02:43:53.372077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.0097v1","created_at":"2026-05-18T02:43:53.372077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0097","created_at":"2026-05-18T02:43:53.372077+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZXJL5TDHH5K","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZXJL5TDHH5KX5NS","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZXJL5TD","created_at":"2026-05-18T12:28:35.611951+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/JZXJL5TDHH5KX5NSQ6EHCF3UQD","json":"https://pith.science/pith/JZXJL5TDHH5KX5NSQ6EHCF3UQD.json","graph_json":"https://pith.science/api/pith-number/JZXJL5TDHH5KX5NSQ6EHCF3UQD/graph.json","events_json":"https://pith.science/api/pith-number/JZXJL5TDHH5KX5NSQ6EHCF3UQD/events.json","paper":"https://pith.science/paper/JZXJL5TD"},"agent_actions":{"view_html":"https://pith.science/pith/JZXJL5TDHH5KX5NSQ6EHCF3UQD","download_json":"https://pith.science/pith/JZXJL5TDHH5KX5NSQ6EHCF3UQD.json","view_paper":"https://pith.science/paper/JZXJL5TD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.0097&json=true","fetch_graph":"https://pith.science/api/pith-number/JZXJL5TDHH5KX5NSQ6EHCF3UQD/graph.json","fetch_events":"https://pith.science/api/pith-number/JZXJL5TDHH5KX5NSQ6EHCF3UQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZXJL5TDHH5KX5NSQ6EHCF3UQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZXJL5TDHH5KX5NSQ6EHCF3UQD/action/storage_attestation","attest_author":"https://pith.science/pith/JZXJL5TDHH5KX5NSQ6EHCF3UQD/action/author_attestation","sign_citation":"https://pith.science/pith/JZXJL5TDHH5KX5NSQ6EHCF3UQD/action/citation_signature","submit_replication":"https://pith.science/pith/JZXJL5TDHH5KX5NSQ6EHCF3UQD/action/replication_record"}},"created_at":"2026-05-18T02:43:53.372077+00:00","updated_at":"2026-05-18T02:43:53.372077+00:00"}