{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UEARIHJ4QQSUEEL3OLXJH5KZEF","short_pith_number":"pith:UEARIHJ4","schema_version":"1.0","canonical_sha256":"a101141d3c842542117b72ee93f5592164eaa6cd48911ae6cd3009a573ee3bc4","source":{"kind":"arxiv","id":"1509.01326","version":2},"attestation_state":"computed","paper":{"title":"On the largest subsets avoiding the diameter of $(0,\\pm 1)$-vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiroshi Nozaki, Saori Adachi","submitted_at":"2015-09-04T02:01:47Z","abstract_excerpt":"Let $L_{mkl}\\subset \\mathbb{R}^{m+k+l}$ be the set of vectors which have $m$ of entries $-1$, $k$ of entries $0$, and $l$ of entries $1$. In this paper, we investigate the largest subset of $L_{mkl}$ whose diameter is smaller than that of $L_{mkl}$. The largest subsets for $m=1$, $l=2$, and any $k$ will be classified. From this result, we can classify the largest $4$-distance sets containing the Euclidean representation of the Johnson scheme $J(9,4)$. This was an open problem in Bannai, Sato, and Shigezumi (2012)."},"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":"1509.01326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-04T02:01:47Z","cross_cats_sorted":[],"title_canon_sha256":"2a124870f7ce1addee5c294f2eb32c4af46de9c0dedd4e7fd9aceb7acf30a7b1","abstract_canon_sha256":"b8c52d6674cab94547dc2cdd6e64b9bae98dc51c5590963c92efbec2a434b6bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:57.289807Z","signature_b64":"FiXfhLcyNea6NfwFyNb4rn+7gFKZliySUpms+2wI4kXVX+V7l1uUnk8VivE6MxFkFQAVhLTu2yuKmhY1IVdyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a101141d3c842542117b72ee93f5592164eaa6cd48911ae6cd3009a573ee3bc4","last_reissued_at":"2026-05-18T01:26:57.289180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:57.289180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the largest subsets avoiding the diameter of $(0,\\pm 1)$-vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiroshi Nozaki, Saori Adachi","submitted_at":"2015-09-04T02:01:47Z","abstract_excerpt":"Let $L_{mkl}\\subset \\mathbb{R}^{m+k+l}$ be the set of vectors which have $m$ of entries $-1$, $k$ of entries $0$, and $l$ of entries $1$. In this paper, we investigate the largest subset of $L_{mkl}$ whose diameter is smaller than that of $L_{mkl}$. The largest subsets for $m=1$, $l=2$, and any $k$ will be classified. From this result, we can classify the largest $4$-distance sets containing the Euclidean representation of the Johnson scheme $J(9,4)$. This was an open problem in Bannai, Sato, and Shigezumi (2012)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01326","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":"1509.01326","created_at":"2026-05-18T01:26:57.289274+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01326v2","created_at":"2026-05-18T01:26:57.289274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01326","created_at":"2026-05-18T01:26:57.289274+00:00"},{"alias_kind":"pith_short_12","alias_value":"UEARIHJ4QQSU","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UEARIHJ4QQSUEEL3","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UEARIHJ4","created_at":"2026-05-18T12:29:44.643036+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/UEARIHJ4QQSUEEL3OLXJH5KZEF","json":"https://pith.science/pith/UEARIHJ4QQSUEEL3OLXJH5KZEF.json","graph_json":"https://pith.science/api/pith-number/UEARIHJ4QQSUEEL3OLXJH5KZEF/graph.json","events_json":"https://pith.science/api/pith-number/UEARIHJ4QQSUEEL3OLXJH5KZEF/events.json","paper":"https://pith.science/paper/UEARIHJ4"},"agent_actions":{"view_html":"https://pith.science/pith/UEARIHJ4QQSUEEL3OLXJH5KZEF","download_json":"https://pith.science/pith/UEARIHJ4QQSUEEL3OLXJH5KZEF.json","view_paper":"https://pith.science/paper/UEARIHJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01326&json=true","fetch_graph":"https://pith.science/api/pith-number/UEARIHJ4QQSUEEL3OLXJH5KZEF/graph.json","fetch_events":"https://pith.science/api/pith-number/UEARIHJ4QQSUEEL3OLXJH5KZEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UEARIHJ4QQSUEEL3OLXJH5KZEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UEARIHJ4QQSUEEL3OLXJH5KZEF/action/storage_attestation","attest_author":"https://pith.science/pith/UEARIHJ4QQSUEEL3OLXJH5KZEF/action/author_attestation","sign_citation":"https://pith.science/pith/UEARIHJ4QQSUEEL3OLXJH5KZEF/action/citation_signature","submit_replication":"https://pith.science/pith/UEARIHJ4QQSUEEL3OLXJH5KZEF/action/replication_record"}},"created_at":"2026-05-18T01:26:57.289274+00:00","updated_at":"2026-05-18T01:26:57.289274+00:00"}