{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PLVGOU54CVGJLGMU63QBQ3JYAH","short_pith_number":"pith:PLVGOU54","schema_version":"1.0","canonical_sha256":"7aea6753bc154c959994f6e0186d3801d3b808d5a8df965d5a61d62206da9f3d","source":{"kind":"arxiv","id":"1703.00609","version":2},"attestation_state":"computed","paper":{"title":"The generalized k-resultant modulus set problem in finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"David Covert, Doowon Koh, Youngjin Pi","submitted_at":"2017-03-02T04:18:43Z","abstract_excerpt":"Let $\\mathbb F_q^d$ be the $d$-dimensional vector space over the finite field $\\mathbb F_q$ with $q$ elements. Given $k$ sets $E_j\\subset \\mathbb F_q^d$ for $j=1,2,\\ldots, k$, the generalized $k$-resultant modulus set, denoted by $\\Delta_k(E_1,E_2, \\ldots, E_k)$, is defined by $$ \\Delta_k(E_1,E_2, \\ldots, E_k)=\\left\\{\\|{\\bf x}^1+{\\bf x}^2+\\cdots+{\\bf x}^k\\|\\in \\mathbb F_q:{\\bf x}^j\\in E_j,\\, j=1,2,\\ldots, k\\right\\},$$ where $\\|{\\bf y}\\|={\\bf y}_1^2+ \\cdots + {\\bf y}_d^2$ for ${\\bf y}=({\\bf y}_1, \\ldots, {\\bf y}_d)\\in \\mathbb F_q^d.$ We prove that if $\\prod\\limits_{j=1}^3 |E_j| \\ge C q^{3\\left("},"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":"1703.00609","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-02T04:18:43Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"f189945ee32467ffa19cd2882c1eae2ad3589803307834770e95990f4a092205","abstract_canon_sha256":"0e294d81663fbec1c9cfdb3dca1d2250ff0fcc385164a0caa152f333b15bfc55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:13.275533Z","signature_b64":"LUuwbuEv2HUWvDxA1GT6ZwMZViLKs/vbVFm3eriIlOFWvZdkQTtsOkSb2pq0hr+q0vrFTIXhD3wbwmhWb3L8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7aea6753bc154c959994f6e0186d3801d3b808d5a8df965d5a61d62206da9f3d","last_reissued_at":"2026-05-18T00:40:13.274839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:13.274839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The generalized k-resultant modulus set problem in finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"David Covert, Doowon Koh, Youngjin Pi","submitted_at":"2017-03-02T04:18:43Z","abstract_excerpt":"Let $\\mathbb F_q^d$ be the $d$-dimensional vector space over the finite field $\\mathbb F_q$ with $q$ elements. Given $k$ sets $E_j\\subset \\mathbb F_q^d$ for $j=1,2,\\ldots, k$, the generalized $k$-resultant modulus set, denoted by $\\Delta_k(E_1,E_2, \\ldots, E_k)$, is defined by $$ \\Delta_k(E_1,E_2, \\ldots, E_k)=\\left\\{\\|{\\bf x}^1+{\\bf x}^2+\\cdots+{\\bf x}^k\\|\\in \\mathbb F_q:{\\bf x}^j\\in E_j,\\, j=1,2,\\ldots, k\\right\\},$$ where $\\|{\\bf y}\\|={\\bf y}_1^2+ \\cdots + {\\bf y}_d^2$ for ${\\bf y}=({\\bf y}_1, \\ldots, {\\bf y}_d)\\in \\mathbb F_q^d.$ We prove that if $\\prod\\limits_{j=1}^3 |E_j| \\ge C q^{3\\left("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00609","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":"1703.00609","created_at":"2026-05-18T00:40:13.274953+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.00609v2","created_at":"2026-05-18T00:40:13.274953+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00609","created_at":"2026-05-18T00:40:13.274953+00:00"},{"alias_kind":"pith_short_12","alias_value":"PLVGOU54CVGJ","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PLVGOU54CVGJLGMU","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PLVGOU54","created_at":"2026-05-18T12:31:37.085036+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/PLVGOU54CVGJLGMU63QBQ3JYAH","json":"https://pith.science/pith/PLVGOU54CVGJLGMU63QBQ3JYAH.json","graph_json":"https://pith.science/api/pith-number/PLVGOU54CVGJLGMU63QBQ3JYAH/graph.json","events_json":"https://pith.science/api/pith-number/PLVGOU54CVGJLGMU63QBQ3JYAH/events.json","paper":"https://pith.science/paper/PLVGOU54"},"agent_actions":{"view_html":"https://pith.science/pith/PLVGOU54CVGJLGMU63QBQ3JYAH","download_json":"https://pith.science/pith/PLVGOU54CVGJLGMU63QBQ3JYAH.json","view_paper":"https://pith.science/paper/PLVGOU54","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.00609&json=true","fetch_graph":"https://pith.science/api/pith-number/PLVGOU54CVGJLGMU63QBQ3JYAH/graph.json","fetch_events":"https://pith.science/api/pith-number/PLVGOU54CVGJLGMU63QBQ3JYAH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PLVGOU54CVGJLGMU63QBQ3JYAH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PLVGOU54CVGJLGMU63QBQ3JYAH/action/storage_attestation","attest_author":"https://pith.science/pith/PLVGOU54CVGJLGMU63QBQ3JYAH/action/author_attestation","sign_citation":"https://pith.science/pith/PLVGOU54CVGJLGMU63QBQ3JYAH/action/citation_signature","submit_replication":"https://pith.science/pith/PLVGOU54CVGJLGMU63QBQ3JYAH/action/replication_record"}},"created_at":"2026-05-18T00:40:13.274953+00:00","updated_at":"2026-05-18T00:40:13.274953+00:00"}