{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HSW6A7HXBX24BHRLRAW2UBEGPL","short_pith_number":"pith:HSW6A7HX","schema_version":"1.0","canonical_sha256":"3cade07cf70df5c09e2b882daa04867ae64c184779cfd029110cef98bc80a86b","source":{"kind":"arxiv","id":"1304.4819","version":2},"attestation_state":"computed","paper":{"title":"Matching-Vector Families and LDCs Over Large Modulo","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Guangda Hu, Zeev Dvir","submitted_at":"2013-04-17T13:30:23Z","abstract_excerpt":"We prove new upper bounds on the size of families of vectors in $\\Z_m^n$ with restricted modular inner products, when $m$ is a large integer. More formally, if $\\vec{u}_1,\\ldots,\\vec{u}_t \\in \\Z_m^n$ and $\\vec{v}_1,\\ldots,\\vec{v}_t \\in \\Z_m^n$ satisfy $\\langle\\vec{u}_i,\\vec{v}_i\\rangle\\equiv0\\pmod m$ and $\\langle\\vec{u}_i,\\vec{v}_j\\rangle\\not\\equiv0\\pmod m$ for all $i\\neq j\\in[t]$, we prove that $t \\leq O(m^{n/2+8.47})$. This improves a recent bound of $t \\leq m^{n/2 + O(\\log(m))}$ by \\cite{BDL13} and is the best possible up to the constant 8.47 when $m$ is sufficiently larger than $n$.\n  The "},"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":"1304.4819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-17T13:30:23Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"c14b97f3b80da3f1966aa49742b033a83d740f0b8587dfac5c203137b1b59dd9","abstract_canon_sha256":"006e5611a517aafa253da3111fdc7eaa6e4193e942e3bc907071c53d3057d5c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:42.210617Z","signature_b64":"5/jMw7ZkklILFKQov26B8i6wIyFceyR8osndO0zkgAYpxx2IAOEq6P5kAJfeuXoCwIePMIs4hR+op+hh0BqgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cade07cf70df5c09e2b882daa04867ae64c184779cfd029110cef98bc80a86b","last_reissued_at":"2026-05-18T03:27:42.209962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:42.209962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matching-Vector Families and LDCs Over Large Modulo","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.CO","authors_text":"Guangda Hu, Zeev Dvir","submitted_at":"2013-04-17T13:30:23Z","abstract_excerpt":"We prove new upper bounds on the size of families of vectors in $\\Z_m^n$ with restricted modular inner products, when $m$ is a large integer. More formally, if $\\vec{u}_1,\\ldots,\\vec{u}_t \\in \\Z_m^n$ and $\\vec{v}_1,\\ldots,\\vec{v}_t \\in \\Z_m^n$ satisfy $\\langle\\vec{u}_i,\\vec{v}_i\\rangle\\equiv0\\pmod m$ and $\\langle\\vec{u}_i,\\vec{v}_j\\rangle\\not\\equiv0\\pmod m$ for all $i\\neq j\\in[t]$, we prove that $t \\leq O(m^{n/2+8.47})$. This improves a recent bound of $t \\leq m^{n/2 + O(\\log(m))}$ by \\cite{BDL13} and is the best possible up to the constant 8.47 when $m$ is sufficiently larger than $n$.\n  The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4819","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":"1304.4819","created_at":"2026-05-18T03:27:42.210093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4819v2","created_at":"2026-05-18T03:27:42.210093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4819","created_at":"2026-05-18T03:27:42.210093+00:00"},{"alias_kind":"pith_short_12","alias_value":"HSW6A7HXBX24","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HSW6A7HXBX24BHRL","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HSW6A7HX","created_at":"2026-05-18T12:27:46.883200+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/HSW6A7HXBX24BHRLRAW2UBEGPL","json":"https://pith.science/pith/HSW6A7HXBX24BHRLRAW2UBEGPL.json","graph_json":"https://pith.science/api/pith-number/HSW6A7HXBX24BHRLRAW2UBEGPL/graph.json","events_json":"https://pith.science/api/pith-number/HSW6A7HXBX24BHRLRAW2UBEGPL/events.json","paper":"https://pith.science/paper/HSW6A7HX"},"agent_actions":{"view_html":"https://pith.science/pith/HSW6A7HXBX24BHRLRAW2UBEGPL","download_json":"https://pith.science/pith/HSW6A7HXBX24BHRLRAW2UBEGPL.json","view_paper":"https://pith.science/paper/HSW6A7HX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4819&json=true","fetch_graph":"https://pith.science/api/pith-number/HSW6A7HXBX24BHRLRAW2UBEGPL/graph.json","fetch_events":"https://pith.science/api/pith-number/HSW6A7HXBX24BHRLRAW2UBEGPL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HSW6A7HXBX24BHRLRAW2UBEGPL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HSW6A7HXBX24BHRLRAW2UBEGPL/action/storage_attestation","attest_author":"https://pith.science/pith/HSW6A7HXBX24BHRLRAW2UBEGPL/action/author_attestation","sign_citation":"https://pith.science/pith/HSW6A7HXBX24BHRLRAW2UBEGPL/action/citation_signature","submit_replication":"https://pith.science/pith/HSW6A7HXBX24BHRLRAW2UBEGPL/action/replication_record"}},"created_at":"2026-05-18T03:27:42.210093+00:00","updated_at":"2026-05-18T03:27:42.210093+00:00"}