{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CBXV7T4P65YYYCLWEQSHZRNTLC","short_pith_number":"pith:CBXV7T4P","canonical_record":{"source":{"id":"1706.09218","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-28T11:18:36Z","cross_cats_sorted":["math.DS","math.PR"],"title_canon_sha256":"f131102596f20a5f5fb63d1194b82ff78e304b54365d27179995098637c5ea01","abstract_canon_sha256":"a593f521d8e19e80b6d243f1638c1e2ceb404cc5e316c12807b60ea2fac73ae2"},"schema_version":"1.0"},"canonical_sha256":"106f5fcf8ff7718c097624247cc5b358bcd20b738593ccf703480d7740821a15","source":{"kind":"arxiv","id":"1706.09218","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09218","created_at":"2026-05-18T00:34:37Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09218v2","created_at":"2026-05-18T00:34:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09218","created_at":"2026-05-18T00:34:37Z"},{"alias_kind":"pith_short_12","alias_value":"CBXV7T4P65YY","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CBXV7T4P65YYYCLW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CBXV7T4P","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CBXV7T4P65YYYCLWEQSHZRNTLC","target":"record","payload":{"canonical_record":{"source":{"id":"1706.09218","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-28T11:18:36Z","cross_cats_sorted":["math.DS","math.PR"],"title_canon_sha256":"f131102596f20a5f5fb63d1194b82ff78e304b54365d27179995098637c5ea01","abstract_canon_sha256":"a593f521d8e19e80b6d243f1638c1e2ceb404cc5e316c12807b60ea2fac73ae2"},"schema_version":"1.0"},"canonical_sha256":"106f5fcf8ff7718c097624247cc5b358bcd20b738593ccf703480d7740821a15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:37.035801Z","signature_b64":"+sC+JISS63KPwycDvNO0lfiMZ0LmqOO7PY6uV/DOljCvFmnzpTgunkARe4xBN9G76uT0iqCgjREjA3KIkXm9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"106f5fcf8ff7718c097624247cc5b358bcd20b738593ccf703480d7740821a15","last_reissued_at":"2026-05-18T00:34:37.035325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:37.035325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.09218","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKj90jZoN5lvGRrHFBf7oNjbmmlQJ7cxgava5JlaFcTQGX6ASTP4XetGMRf92D4PaXphOGW4ltqNL8f5wFfMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:50:01.270688Z"},"content_sha256":"5bc3ae7f7cab73bc8ae1d31435edeef84824b4a231143eb765bcae824037ccc4","schema_version":"1.0","event_id":"sha256:5bc3ae7f7cab73bc8ae1d31435edeef84824b4a231143eb765bcae824037ccc4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CBXV7T4P65YYYCLWEQSHZRNTLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorems in the geometry of numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR"],"primary_cat":"math.NT","authors_text":"Alexander Gorodnik, Michael Bj\\\"orklund","submitted_at":"2017-06-28T11:18:36Z","abstract_excerpt":"We investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a Central Limit Theorem. Furthermore, we show that the Central Limit Theorem holds for the number of rational approximants for weighted Diophantine approximation in $\\mathbb{R}^d$. Our arguments exploit chaotic properties of the Cartan flow on the space of lattices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09218","kind":"arxiv","version":2},"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":"2026-05-18T00:34:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hwJNmG3r1a9wRrOt4ZN3IlgtEi/SKSKPxNvaWIBxQqR3BE1ZxnJKNGUNyUkXs9Vk8h2BwCks9tlaRqoGq3kEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T04:50:01.271340Z"},"content_sha256":"717b5e6efb283b3fd6573f0281085b41294d8e47444e1e4385054102faab28a5","schema_version":"1.0","event_id":"sha256:717b5e6efb283b3fd6573f0281085b41294d8e47444e1e4385054102faab28a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBXV7T4P65YYYCLWEQSHZRNTLC/bundle.json","state_url":"https://pith.science/pith/CBXV7T4P65YYYCLWEQSHZRNTLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBXV7T4P65YYYCLWEQSHZRNTLC/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":"2026-06-10T04:50:01Z","links":{"resolver":"https://pith.science/pith/CBXV7T4P65YYYCLWEQSHZRNTLC","bundle":"https://pith.science/pith/CBXV7T4P65YYYCLWEQSHZRNTLC/bundle.json","state":"https://pith.science/pith/CBXV7T4P65YYYCLWEQSHZRNTLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBXV7T4P65YYYCLWEQSHZRNTLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CBXV7T4P65YYYCLWEQSHZRNTLC","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":"a593f521d8e19e80b6d243f1638c1e2ceb404cc5e316c12807b60ea2fac73ae2","cross_cats_sorted":["math.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-28T11:18:36Z","title_canon_sha256":"f131102596f20a5f5fb63d1194b82ff78e304b54365d27179995098637c5ea01"},"schema_version":"1.0","source":{"id":"1706.09218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09218","created_at":"2026-05-18T00:34:37Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09218v2","created_at":"2026-05-18T00:34:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09218","created_at":"2026-05-18T00:34:37Z"},{"alias_kind":"pith_short_12","alias_value":"CBXV7T4P65YY","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CBXV7T4P65YYYCLW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CBXV7T4P","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:717b5e6efb283b3fd6573f0281085b41294d8e47444e1e4385054102faab28a5","target":"graph","created_at":"2026-05-18T00:34:37Z","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 investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a Central Limit Theorem. Furthermore, we show that the Central Limit Theorem holds for the number of rational approximants for weighted Diophantine approximation in $\\mathbb{R}^d$. Our arguments exploit chaotic properties of the Cartan flow on the space of lattices.","authors_text":"Alexander Gorodnik, Michael Bj\\\"orklund","cross_cats":["math.DS","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-28T11:18:36Z","title":"Central limit theorems in the geometry of numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09218","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":"sha256:5bc3ae7f7cab73bc8ae1d31435edeef84824b4a231143eb765bcae824037ccc4","target":"record","created_at":"2026-05-18T00:34:37Z","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":"a593f521d8e19e80b6d243f1638c1e2ceb404cc5e316c12807b60ea2fac73ae2","cross_cats_sorted":["math.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-28T11:18:36Z","title_canon_sha256":"f131102596f20a5f5fb63d1194b82ff78e304b54365d27179995098637c5ea01"},"schema_version":"1.0","source":{"id":"1706.09218","kind":"arxiv","version":2}},"canonical_sha256":"106f5fcf8ff7718c097624247cc5b358bcd20b738593ccf703480d7740821a15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"106f5fcf8ff7718c097624247cc5b358bcd20b738593ccf703480d7740821a15","first_computed_at":"2026-05-18T00:34:37.035325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:37.035325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+sC+JISS63KPwycDvNO0lfiMZ0LmqOO7PY6uV/DOljCvFmnzpTgunkARe4xBN9G76uT0iqCgjREjA3KIkXm9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:37.035801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bc3ae7f7cab73bc8ae1d31435edeef84824b4a231143eb765bcae824037ccc4","sha256:717b5e6efb283b3fd6573f0281085b41294d8e47444e1e4385054102faab28a5"],"state_sha256":"d3ed681cd15ba7b5a029e5b3773f1252d687423383486df59d75c367fa4f9131"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bsBhvb2KofWjIl2J0TkOCKZFKoBYX0pNv0qPhBOGj5rWY32RlLbJ8oW3aDJEqMK25T2eUnyXF5iEX68ssZdhAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T04:50:01.275172Z","bundle_sha256":"f096aa3c1078cc90a6a70c2349db2b1f443ee1a505359b6d9092178847fef94c"}}