{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Q3SWBH2DD5GXK2PQTEYPKSWBIP","short_pith_number":"pith:Q3SWBH2D","canonical_record":{"source":{"id":"1605.00311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-01T21:32:50Z","cross_cats_sorted":["math.NT","math.PR"],"title_canon_sha256":"4999c21a3859f60525dad599edb426f0eff7c53bd176c24517ad12eeda167de4","abstract_canon_sha256":"69e9fac66c3a35e1e230f1b7b6fcb86a8d6d4c80bd934312123b4727591334c6"},"schema_version":"1.0"},"canonical_sha256":"86e5609f431f4d7569f09930f54ac143e661ae5459eaa866e9defe02bc46c4e6","source":{"kind":"arxiv","id":"1605.00311","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00311","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00311v1","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00311","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"Q3SWBH2DD5GX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q3SWBH2DD5GXK2PQ","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q3SWBH2D","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Q3SWBH2DD5GXK2PQTEYPKSWBIP","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-01T21:32:50Z","cross_cats_sorted":["math.NT","math.PR"],"title_canon_sha256":"4999c21a3859f60525dad599edb426f0eff7c53bd176c24517ad12eeda167de4","abstract_canon_sha256":"69e9fac66c3a35e1e230f1b7b6fcb86a8d6d4c80bd934312123b4727591334c6"},"schema_version":"1.0"},"canonical_sha256":"86e5609f431f4d7569f09930f54ac143e661ae5459eaa866e9defe02bc46c4e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:56.212543Z","signature_b64":"E8/IVlFd6d/x1/PQTsPWAsjpAxpdj8Q9rF8xXBc86yG6PV7p8zp8GASs3InF2A/dXQ8eEcGTrLLmKXSr7nVrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86e5609f431f4d7569f09930f54ac143e661ae5459eaa866e9defe02bc46c4e6","last_reissued_at":"2026-05-18T01:15:56.211908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:56.211908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00311","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":"2026-05-18T01:15:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KrTtfkaNd1PzNe2NDP/QmB28mYrURGZLP7Npiq8kNBaG+b8yHtC7toFcQaEcRX+bdf/LBWp9bYuCb9iF4FIkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:14:25.281581Z"},"content_sha256":"3503ee64c90445f06e4a80f7e7075b8368f0e24c55dbe736d8d57894a291a545","schema_version":"1.0","event_id":"sha256:3503ee64c90445f06e4a80f7e7075b8368f0e24c55dbe736d8d57894a291a545"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Q3SWBH2DD5GXK2PQTEYPKSWBIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central limit theorems for simultaneous Diophantine approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.PR"],"primary_cat":"math.DS","authors_text":"Bassam Fayad, Dmitry Dolgopyat, Ilya Vinogradov","submitted_at":"2016-05-01T21:32:50Z","abstract_excerpt":"We study the distribution modulo $1$ of the values taken on the integers of $r$ linear forms in $d$ variables with random coefficients. We obtain quenched and annealed central limit theorems for the number of simultaneous hits into shrinking targets of radii $n^{-\\frac{r}{d}}$. By the Khintchine-Groshev theorem on Diophantine approximations, $\\frac{r}{d}$ is the critical exponent for the infinite number of hits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00311","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":"2026-05-18T01:15:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IW7szBNamR/3h4fFs3twnXHBexAz/m8k0aLW40Cz5CaFI2gnxuTbUUuaIWq6Hu4dS8QH2AbBk+dCcfBPNm+uDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:14:25.282234Z"},"content_sha256":"041ba11e556939d7bd17b527ceb1c756e04b8202e746f4682bb442ca993c7cd5","schema_version":"1.0","event_id":"sha256:041ba11e556939d7bd17b527ceb1c756e04b8202e746f4682bb442ca993c7cd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3SWBH2DD5GXK2PQTEYPKSWBIP/bundle.json","state_url":"https://pith.science/pith/Q3SWBH2DD5GXK2PQTEYPKSWBIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3SWBH2DD5GXK2PQTEYPKSWBIP/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":"2026-05-30T16:14:25Z","links":{"resolver":"https://pith.science/pith/Q3SWBH2DD5GXK2PQTEYPKSWBIP","bundle":"https://pith.science/pith/Q3SWBH2DD5GXK2PQTEYPKSWBIP/bundle.json","state":"https://pith.science/pith/Q3SWBH2DD5GXK2PQTEYPKSWBIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3SWBH2DD5GXK2PQTEYPKSWBIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q3SWBH2DD5GXK2PQTEYPKSWBIP","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":"69e9fac66c3a35e1e230f1b7b6fcb86a8d6d4c80bd934312123b4727591334c6","cross_cats_sorted":["math.NT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-01T21:32:50Z","title_canon_sha256":"4999c21a3859f60525dad599edb426f0eff7c53bd176c24517ad12eeda167de4"},"schema_version":"1.0","source":{"id":"1605.00311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00311","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00311v1","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00311","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"Q3SWBH2DD5GX","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q3SWBH2DD5GXK2PQ","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q3SWBH2D","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:041ba11e556939d7bd17b527ceb1c756e04b8202e746f4682bb442ca993c7cd5","target":"graph","created_at":"2026-05-18T01:15:56Z","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 study the distribution modulo $1$ of the values taken on the integers of $r$ linear forms in $d$ variables with random coefficients. We obtain quenched and annealed central limit theorems for the number of simultaneous hits into shrinking targets of radii $n^{-\\frac{r}{d}}$. By the Khintchine-Groshev theorem on Diophantine approximations, $\\frac{r}{d}$ is the critical exponent for the infinite number of hits.","authors_text":"Bassam Fayad, Dmitry Dolgopyat, Ilya Vinogradov","cross_cats":["math.NT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-01T21:32:50Z","title":"Central limit theorems for simultaneous Diophantine approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00311","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":"sha256:3503ee64c90445f06e4a80f7e7075b8368f0e24c55dbe736d8d57894a291a545","target":"record","created_at":"2026-05-18T01:15:56Z","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":"69e9fac66c3a35e1e230f1b7b6fcb86a8d6d4c80bd934312123b4727591334c6","cross_cats_sorted":["math.NT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-01T21:32:50Z","title_canon_sha256":"4999c21a3859f60525dad599edb426f0eff7c53bd176c24517ad12eeda167de4"},"schema_version":"1.0","source":{"id":"1605.00311","kind":"arxiv","version":1}},"canonical_sha256":"86e5609f431f4d7569f09930f54ac143e661ae5459eaa866e9defe02bc46c4e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86e5609f431f4d7569f09930f54ac143e661ae5459eaa866e9defe02bc46c4e6","first_computed_at":"2026-05-18T01:15:56.211908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:56.211908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E8/IVlFd6d/x1/PQTsPWAsjpAxpdj8Q9rF8xXBc86yG6PV7p8zp8GASs3InF2A/dXQ8eEcGTrLLmKXSr7nVrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:56.212543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3503ee64c90445f06e4a80f7e7075b8368f0e24c55dbe736d8d57894a291a545","sha256:041ba11e556939d7bd17b527ceb1c756e04b8202e746f4682bb442ca993c7cd5"],"state_sha256":"9dfb04db6be9d3f72957daefbe8db5da1fc6d36f684c38e707a8eef599bd3063"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OtOdlKOQhFqAAtP4fy22yvG3InJ3GmFlIc5D44XompqtPWkabZr7F1BdDdKpetFBMYovY+3rjhOLD6OlFhp/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:14:25.285449Z","bundle_sha256":"a7582031174c930fe7863a0ffb69700378e033029ed974a506ca67bba1b13c15"}}