{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZCWOIHFJF5F2HFYFIKWYFB643G","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b8a3d12d4e4f064d1159324ec3a6da7752b94b1955adba4b2d5b032edfbbc6de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-04T06:53:28Z","title_canon_sha256":"a3a34368aad0e9ea145d1d555b79e87e91a42345d7dedd5d35065f181af2af7f"},"schema_version":"1.0","source":{"id":"2608.03220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03220","created_at":"2026-08-05T00:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03220v1","created_at":"2026-08-05T00:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03220","created_at":"2026-08-05T00:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZCWOIHFJF5F2","created_at":"2026-08-05T00:46:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZCWOIHFJF5F2HFYF","created_at":"2026-08-05T00:46:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZCWOIHFJ","created_at":"2026-08-05T00:46:18Z"}],"graph_snapshots":[{"event_id":"sha256:beb418e7f7909d227b89740259c1e70231d32d7c8996abc7ce6c5cbd9bfdb8cf","target":"graph","created_at":"2026-08-05T00:46:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.03220/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Aggarwal, Dadush, Regev, and Stephens-Davidowitz (ADRS; STOC 2015) sample $2^{n/2}$ discrete Gaussians at an arbitrary parameter in $2^{n+o(n)}$ time, and above smoothing in $2^{n/2+o(n)}$ time. They ask whether the latter bound suffices for one sample at an arbitrary parameter. We answer this question affirmatively: for every rank-$n$ lattice $L\\subseteq\\R^n$ specified by a rational basis and every rational $s^2>0$, we produce one sample from $D_{L,s}$ within statistical distance $\\exp(-\\Omega(n^3))$ in expected $2^{n/2+o(n)}$ time and $2^{n/2+o(n)}$ space on every execution. The algorithm sa","authors_text":"Jiseung Kim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-04T06:53:28Z","title":"One Discrete Gaussian Sample in $2^{n/2+o(n)}$ Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03220","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:f4c1316950c1efdeb19a2e947808a7a63db60ccfbe4a7d024aebad4fd305c81e","target":"record","created_at":"2026-08-05T00:46:18Z","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":"b8a3d12d4e4f064d1159324ec3a6da7752b94b1955adba4b2d5b032edfbbc6de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-04T06:53:28Z","title_canon_sha256":"a3a34368aad0e9ea145d1d555b79e87e91a42345d7dedd5d35065f181af2af7f"},"schema_version":"1.0","source":{"id":"2608.03220","kind":"arxiv","version":1}},"canonical_sha256":"c8ace41ca92f4ba3970542ad8287dcd9b393a59d9ea8a4e735f0a020297533bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8ace41ca92f4ba3970542ad8287dcd9b393a59d9ea8a4e735f0a020297533bf","first_computed_at":"2026-08-05T00:46:18.670500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-05T00:46:18.670500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ccpGFd3XjJWxY73MkwMtJ/pyAtViokH/iDS9KaKzcziDelDKASZFWHJm2g5Ik2X6jdOLwvwCbfrbm7dYynqCw==","signature_status":"signed_v1","signed_at":"2026-08-05T00:46:18.673298Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.03220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4c1316950c1efdeb19a2e947808a7a63db60ccfbe4a7d024aebad4fd305c81e","sha256:beb418e7f7909d227b89740259c1e70231d32d7c8996abc7ce6c5cbd9bfdb8cf","sha256:ac018bf1c5446038567c79b4264952531c59643a41c96b585200dd9cc1ac1ce4"],"state_sha256":"2548fc9b8f62edba590031a1675d1f673ab0748bb3946e7406e468ab9d16e71e"}