{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:X6YQ5USQEJIIXOSPSGJ7EUD54L","short_pith_number":"pith:X6YQ5USQ","schema_version":"1.0","canonical_sha256":"bfb10ed25022508bba4f9193f2507de2f7ee3fb438e6254aa2106a41e8727399","source":{"kind":"arxiv","id":"1308.2405","version":2},"attestation_state":"computed","paper":{"title":"A Note on Discrete Gaussian Combinations of Lattice Vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"cs.CR","authors_text":"Divesh Aggarwal, Oded Regev","submitted_at":"2013-08-11T16:13:31Z","abstract_excerpt":"We analyze the distribution of $\\sum_{i=1}^m v_i \\bx_i$ where $\\bx_1,...,\\bx_m$ are fixed vectors from some lattice $\\cL \\subset \\R^n$ (say $\\Z^n$) and $v_1,...,v_m$ are chosen independently from a discrete Gaussian distribution over $\\Z$. We show that under a natural constraint on $\\bx_1,...,\\bx_m$, if the $v_i$ are chosen from a wide enough Gaussian, the sum is statistically close to a discrete Gaussian over $\\cL$. We also analyze the case of $\\bx_1,...,\\bx_m$ that are themselves chosen from a discrete Gaussian distribution (and fixed).\n  Our results simplify and qualitatively improve upon a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.2405","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-08-11T16:13:31Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"81f5d9b34f42642b9da6d7b928cf6255fc646da48c9d2e59d9694f20d260c6f9","abstract_canon_sha256":"5323349c6fc7bb56f79bead72eb978173ee7c8547ec24056ee3af1f0c201343f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:46.818595Z","signature_b64":"3Zag+UQOQD5L4Lg1GtB4BFyn+/kQwISIShdlVxxiyRYsvouTX+d7ZayhmcWbmzo3T3+pVi6Uek9v9V6p2B9rDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfb10ed25022508bba4f9193f2507de2f7ee3fb438e6254aa2106a41e8727399","last_reissued_at":"2026-05-18T03:02:46.817881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:46.817881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Discrete Gaussian Combinations of Lattice Vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"cs.CR","authors_text":"Divesh Aggarwal, Oded Regev","submitted_at":"2013-08-11T16:13:31Z","abstract_excerpt":"We analyze the distribution of $\\sum_{i=1}^m v_i \\bx_i$ where $\\bx_1,...,\\bx_m$ are fixed vectors from some lattice $\\cL \\subset \\R^n$ (say $\\Z^n$) and $v_1,...,v_m$ are chosen independently from a discrete Gaussian distribution over $\\Z$. We show that under a natural constraint on $\\bx_1,...,\\bx_m$, if the $v_i$ are chosen from a wide enough Gaussian, the sum is statistically close to a discrete Gaussian over $\\cL$. We also analyze the case of $\\bx_1,...,\\bx_m$ that are themselves chosen from a discrete Gaussian distribution (and fixed).\n  Our results simplify and qualitatively improve upon a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2405","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1308.2405","created_at":"2026-05-18T03:02:46.817980+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.2405v2","created_at":"2026-05-18T03:02:46.817980+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2405","created_at":"2026-05-18T03:02:46.817980+00:00"},{"alias_kind":"pith_short_12","alias_value":"X6YQ5USQEJII","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"X6YQ5USQEJIIXOSP","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"X6YQ5USQ","created_at":"2026-05-18T12:28:06.772260+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L","json":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L.json","graph_json":"https://pith.science/api/pith-number/X6YQ5USQEJIIXOSPSGJ7EUD54L/graph.json","events_json":"https://pith.science/api/pith-number/X6YQ5USQEJIIXOSPSGJ7EUD54L/events.json","paper":"https://pith.science/paper/X6YQ5USQ"},"agent_actions":{"view_html":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L","download_json":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L.json","view_paper":"https://pith.science/paper/X6YQ5USQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.2405&json=true","fetch_graph":"https://pith.science/api/pith-number/X6YQ5USQEJIIXOSPSGJ7EUD54L/graph.json","fetch_events":"https://pith.science/api/pith-number/X6YQ5USQEJIIXOSPSGJ7EUD54L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L/action/storage_attestation","attest_author":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L/action/author_attestation","sign_citation":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L/action/citation_signature","submit_replication":"https://pith.science/pith/X6YQ5USQEJIIXOSPSGJ7EUD54L/action/replication_record"}},"created_at":"2026-05-18T03:02:46.817980+00:00","updated_at":"2026-05-18T03:02:46.817980+00:00"}