{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VVGNGTMUXE45YTR74AOAMCKJLJ","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":"a971d385a735b6981323f02a99ef107812bc41c1f7e02e545720bc63b71d9092","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-06T08:23:25Z","title_canon_sha256":"0e061ab19f37dc7124f2d5d25337477a3c1c9713a08fef5dfeccfb720dd0268b"},"schema_version":"1.0","source":{"id":"1009.0987","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0987","created_at":"2026-05-18T04:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0987v2","created_at":"2026-05-18T04:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0987","created_at":"2026-05-18T04:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"VVGNGTMUXE45","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VVGNGTMUXE45YTR7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VVGNGTMU","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:ec8ce1a60b790728f0d755e4687280a0ad508a164c0915210dec113afc36d95e","target":"graph","created_at":"2026-05-18T04:33:59Z","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":"Let $\\Theta = (\\theta_1,\\theta_2,\\theta_3)\\in \\mathbb{R}^3$. Suppose that $1,\\theta_1,\\theta_2,\\theta_3$ are linearly independent over $\\mathbb{Z}$. For Diophantine exponents $$ \\alpha(\\Theta) = \\sup \\{\\gamma >0:\\,\\,\\, \\limsup_{t\\to +\\infty} t^\\gamma \\psi_\\Theta (t) <+\\infty \\} ,$$ $$\\beta(\\Theta) = \\sup \\{\\gamma >0:\\,\\,\\, \\liminf_{t\\to +\\infty} t^\\gamma \\psi_\\Theta (t) <+\\infty\\} $$ we prove $$ \\beta (\\Theta) \\ge {1/2} ({\\alpha (\\Theta)}/{1-\\alpha(\\Theta)} +\\sqrt{{\\alpha(\\Theta)}/{1-\\alpha(\\Theta)})^2 +{4\\alpha(\\Theta)}/{1-\\alpha(\\Theta)}}) \\alpha (\\Theta) $$","authors_text":"Nikolay Moshchevitin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-06T08:23:25Z","title":"Exponents for three-dimensional simultaneous Diophantine approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0987","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:cb2f79e695ce5191575a01adbf48757d8ec73c3c495782ec3003eec1423e7601","target":"record","created_at":"2026-05-18T04:33:59Z","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":"a971d385a735b6981323f02a99ef107812bc41c1f7e02e545720bc63b71d9092","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-09-06T08:23:25Z","title_canon_sha256":"0e061ab19f37dc7124f2d5d25337477a3c1c9713a08fef5dfeccfb720dd0268b"},"schema_version":"1.0","source":{"id":"1009.0987","kind":"arxiv","version":2}},"canonical_sha256":"ad4cd34d94b939dc4e3fe01c0609495a5a8511f76f920096e6cd9c2d1447f47c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad4cd34d94b939dc4e3fe01c0609495a5a8511f76f920096e6cd9c2d1447f47c","first_computed_at":"2026-05-18T04:33:59.623488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:59.623488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nfgmy4BfiioAaCXbIgERG6xKnjGNBVmiHDnAo5lIqZJI5Tc6Nz27x4f9V9P41fbZThq6NAr/JgY8ezvehujmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:59.624203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0987","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb2f79e695ce5191575a01adbf48757d8ec73c3c495782ec3003eec1423e7601","sha256:ec8ce1a60b790728f0d755e4687280a0ad508a164c0915210dec113afc36d95e"],"state_sha256":"1461e2960839ad0e2f83dbff2fc65a64eda053567206797b6ef69a2ffd5fccaf"}