{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U4QRD4D42DTY7V63YASJS6TNSP","short_pith_number":"pith:U4QRD4D4","canonical_record":{"source":{"id":"1304.4842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-17T14:40:05Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"25f907157f8efaf720941f1239115c215b2d6733dde0e9b05d0cd6c2531dbdc7","abstract_canon_sha256":"b7c3e93c3e721721bb9dd246b0daa8c2dacfec299fbcfa7ead7524c1131da8e7"},"schema_version":"1.0"},"canonical_sha256":"a72111f07cd0e78fd7dbc024997a6d93c0c2aa61b4ad40c3c0cf228433bade2b","source":{"kind":"arxiv","id":"1304.4842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4842","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4842v1","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4842","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"U4QRD4D42DTY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4QRD4D42DTY7V63","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4QRD4D4","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U4QRD4D42DTY7V63YASJS6TNSP","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-17T14:40:05Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"25f907157f8efaf720941f1239115c215b2d6733dde0e9b05d0cd6c2531dbdc7","abstract_canon_sha256":"b7c3e93c3e721721bb9dd246b0daa8c2dacfec299fbcfa7ead7524c1131da8e7"},"schema_version":"1.0"},"canonical_sha256":"a72111f07cd0e78fd7dbc024997a6d93c0c2aa61b4ad40c3c0cf228433bade2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:43.513185Z","signature_b64":"43laqYXYTb/KHGrqVsmiksW7u3eQ+Nc2U4/3UBAJV90OUoq+FFMn4X5MONF7vgQ6YTMQU8gh5nVgRbQGfRRsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a72111f07cd0e78fd7dbc024997a6d93c0c2aa61b4ad40c3c0cf228433bade2b","last_reissued_at":"2026-05-18T03:27:43.512461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:43.512461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4842","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7JRXtIWuIdRmzuvkUpaoJStrMMNDu/0arnP5tz4ej5UKsm2iwY9GiYgrdptsb1IacL8bOIxE52stfLsSwqzhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T14:06:18.897709Z"},"content_sha256":"e536e2286950bc6f370cf2495d44d9e800b27da10e0595ce58d31053f4372755","schema_version":"1.0","event_id":"sha256:e536e2286950bc6f370cf2495d44d9e800b27da10e0595ce58d31053f4372755"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U4QRD4D42DTY7V63YASJS6TNSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on Diophatine approximation in $\\rm{SL}_2(\\mathbb{R})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Nikolay Moshchevitin","submitted_at":"2013-04-17T14:40:05Z","abstract_excerpt":"We prove a quantitative version of the following statement: the unipotent flow orbit of a typical lattice in $\\rm{SL}_2(\\mathbb{R})/\\rm{SL}_2(\\mathbb{Z})$ is dense. Our quantitative result uses A. Weil's bounds for Kloostermann sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4842","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JLULfgDU372nBp4yl/lUJvOUjqwA4TzfivaiKOq82CqP1zwg8fXaE331YXBnuSR1szDjNRauUieeLzMLXjiJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T14:06:18.898452Z"},"content_sha256":"66d6e310e1bf9283ec4d741002cd93170e970b1addb143248dd62b2c3cdf97df","schema_version":"1.0","event_id":"sha256:66d6e310e1bf9283ec4d741002cd93170e970b1addb143248dd62b2c3cdf97df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4QRD4D42DTY7V63YASJS6TNSP/bundle.json","state_url":"https://pith.science/pith/U4QRD4D42DTY7V63YASJS6TNSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4QRD4D42DTY7V63YASJS6TNSP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T14:06:18Z","links":{"resolver":"https://pith.science/pith/U4QRD4D42DTY7V63YASJS6TNSP","bundle":"https://pith.science/pith/U4QRD4D42DTY7V63YASJS6TNSP/bundle.json","state":"https://pith.science/pith/U4QRD4D42DTY7V63YASJS6TNSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4QRD4D42DTY7V63YASJS6TNSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U4QRD4D42DTY7V63YASJS6TNSP","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":"b7c3e93c3e721721bb9dd246b0daa8c2dacfec299fbcfa7ead7524c1131da8e7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-17T14:40:05Z","title_canon_sha256":"25f907157f8efaf720941f1239115c215b2d6733dde0e9b05d0cd6c2531dbdc7"},"schema_version":"1.0","source":{"id":"1304.4842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4842","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4842v1","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4842","created_at":"2026-05-18T03:27:43Z"},{"alias_kind":"pith_short_12","alias_value":"U4QRD4D42DTY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4QRD4D42DTY7V63","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4QRD4D4","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:66d6e310e1bf9283ec4d741002cd93170e970b1addb143248dd62b2c3cdf97df","target":"graph","created_at":"2026-05-18T03:27:43Z","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 prove a quantitative version of the following statement: the unipotent flow orbit of a typical lattice in $\\rm{SL}_2(\\mathbb{R})/\\rm{SL}_2(\\mathbb{Z})$ is dense. Our quantitative result uses A. Weil's bounds for Kloostermann sums.","authors_text":"Nikolay Moshchevitin","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-17T14:40:05Z","title":"A note on Diophatine approximation in $\\rm{SL}_2(\\mathbb{R})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4842","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:e536e2286950bc6f370cf2495d44d9e800b27da10e0595ce58d31053f4372755","target":"record","created_at":"2026-05-18T03:27:43Z","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":"b7c3e93c3e721721bb9dd246b0daa8c2dacfec299fbcfa7ead7524c1131da8e7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-17T14:40:05Z","title_canon_sha256":"25f907157f8efaf720941f1239115c215b2d6733dde0e9b05d0cd6c2531dbdc7"},"schema_version":"1.0","source":{"id":"1304.4842","kind":"arxiv","version":1}},"canonical_sha256":"a72111f07cd0e78fd7dbc024997a6d93c0c2aa61b4ad40c3c0cf228433bade2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a72111f07cd0e78fd7dbc024997a6d93c0c2aa61b4ad40c3c0cf228433bade2b","first_computed_at":"2026-05-18T03:27:43.512461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:43.512461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"43laqYXYTb/KHGrqVsmiksW7u3eQ+Nc2U4/3UBAJV90OUoq+FFMn4X5MONF7vgQ6YTMQU8gh5nVgRbQGfRRsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:43.513185Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e536e2286950bc6f370cf2495d44d9e800b27da10e0595ce58d31053f4372755","sha256:66d6e310e1bf9283ec4d741002cd93170e970b1addb143248dd62b2c3cdf97df"],"state_sha256":"6bc25884a85c2700bc96e5288c8d3e115a011a55f10c30c20026f4fa8a569a61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6WJrLVpylMd1YqvdLUq10rWF18LZX7YrCzFrMTtXwQ8JzRuBRwXqGOX8T2V/OWHcydefB1wITLMC89LbN1QDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T14:06:18.907248Z","bundle_sha256":"fd6af36c6bcc46f7150d5b5058a96617dcb242b81f70fb1f4e5a16e9cba203ce"}}