{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B6HPHU4XDS6NQVPTQZA2SAF6TF","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":"76c079fa0fa233c92cc48c9505b6e3c0ea12c6c8795450e7a4fd63ecb1a16eda","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-02T13:12:32Z","title_canon_sha256":"17ee553cf6a7a1161ff824a43905561f437cf5a5bbf434f0583342f0e0381647"},"schema_version":"1.0","source":{"id":"1205.0416","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0416","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0416v2","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0416","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"B6HPHU4XDS6N","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B6HPHU4XDS6NQVPT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B6HPHU4X","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:66913bcd791ee61fd41c2a821faddbd383b40bbbe53c7f2d84a53ffef6cdefb9","target":"graph","created_at":"2026-05-18T02:38:46Z","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 consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by rational points with any prescribed denominator and an almost prime numerator.","authors_text":"Alexander Gorodnik, Shirali Kadyrov","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-02T13:12:32Z","title":"Diophantine approximation with restricted numerators and denominators on semisimple groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0416","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:a9e19bd8693495ace065cde8945252376bdcb3948d471f1e24092a66a295489d","target":"record","created_at":"2026-05-18T02:38:46Z","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":"76c079fa0fa233c92cc48c9505b6e3c0ea12c6c8795450e7a4fd63ecb1a16eda","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-02T13:12:32Z","title_canon_sha256":"17ee553cf6a7a1161ff824a43905561f437cf5a5bbf434f0583342f0e0381647"},"schema_version":"1.0","source":{"id":"1205.0416","kind":"arxiv","version":2}},"canonical_sha256":"0f8ef3d3971cbcd855f38641a900be99488967b4770ed10364a66ef3d00b017c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f8ef3d3971cbcd855f38641a900be99488967b4770ed10364a66ef3d00b017c","first_computed_at":"2026-05-18T02:38:46.409676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:46.409676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I5Ec0cfJjDKqaPG/Ya+PP7htsYP2AtWQuZPbVkDEWDmHe6VexM0AEi8N+/9jiyA9+Pv+65xPaGhzSv9tD51GCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:46.410096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0416","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9e19bd8693495ace065cde8945252376bdcb3948d471f1e24092a66a295489d","sha256:66913bcd791ee61fd41c2a821faddbd383b40bbbe53c7f2d84a53ffef6cdefb9"],"state_sha256":"cad95327de1ac2ae6dc61f8e6b37e219c58417525a21a555044994cc2eb78740"}