{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OHJA6FTAAMQ4Z3CEE725VZSNJK","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":"1210fa0cc5adf9341edab0fba14a897407be1a1b821798c13c2a3a6acb8f3e2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-08T13:14:19Z","title_canon_sha256":"9ea307ff10491a19d9af75a723b68bd3740eb6399252e3ce0469ff004daafb30"},"schema_version":"1.0","source":{"id":"1004.1326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1326","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1326v1","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1326","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"OHJA6FTAAMQ4","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OHJA6FTAAMQ4Z3CE","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OHJA6FTA","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:81d4e5720c4c3f0cc02df9b8c60cf11c78d234b6e193d4c8ecf299c53167843c","target":"graph","created_at":"2026-05-18T02:58:02Z","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 x be a point in R^2 with irrational slope and let \\Gamma denote the lattice SL(2,Z) acting linearly on R^2. Then, the orbit \\Gamma x is dense in R^2. We give efective results on the approximation of a point y in R^2 by points of the form \\gamma x, where \\gamma belongs to \\Gamma, in terms of the size of \\gamma.","authors_text":"Arnaldo Nogueira, Michel Laurent","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-08T13:14:19Z","title":"Approximation to points in the plane by SL(2,Z)-orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1326","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":"sha256:077ff89f4ae1c823e46cf6118efed9d2392363550ed3758fb247710019b94896","target":"record","created_at":"2026-05-18T02:58:02Z","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":"1210fa0cc5adf9341edab0fba14a897407be1a1b821798c13c2a3a6acb8f3e2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-08T13:14:19Z","title_canon_sha256":"9ea307ff10491a19d9af75a723b68bd3740eb6399252e3ce0469ff004daafb30"},"schema_version":"1.0","source":{"id":"1004.1326","kind":"arxiv","version":1}},"canonical_sha256":"71d20f16600321ccec4427f5dae64d4a904094179f1b5698f2637ec142681506","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71d20f16600321ccec4427f5dae64d4a904094179f1b5698f2637ec142681506","first_computed_at":"2026-05-18T02:58:02.284122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:02.284122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8dGTRxmAHmErAHWU/aSBqJBLez69JsyGxquVva+uCQMy7fcIRnG84liwiw+2VVyiBU6tQ0/nYp1549KVqDRXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:02.284713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:077ff89f4ae1c823e46cf6118efed9d2392363550ed3758fb247710019b94896","sha256:81d4e5720c4c3f0cc02df9b8c60cf11c78d234b6e193d4c8ecf299c53167843c"],"state_sha256":"d8c152d528c5b07683f5cd2213a2bddab12b50c26bcd87408ac5202516eda8a0"}