{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YMEC74I2IYS4YFOVZVUXWGYIE4","short_pith_number":"pith:YMEC74I2","schema_version":"1.0","canonical_sha256":"c3082ff11a4625cc15d5cd697b1b082728715b3ddd73db04e0d6cba0d0f12e91","source":{"kind":"arxiv","id":"1704.01295","version":1},"attestation_state":"computed","paper":{"title":"Proof of a conjecture of Kl{\\o}ve on permutation codes under the Chebychev distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Victor J. W. Guo, Yiting Yang","submitted_at":"2017-04-05T07:52:18Z","abstract_excerpt":"Let $d$ be a positive integer and $x$ a real number. Let $A_{d, x}$ be a $d\\times 2d$ matrix with its entries $$ a_{i,j}=\\left\\{ \\begin{array}{ll} x\\ \\ & \\mbox{for} \\ 1\\leqslant j\\leqslant d+1-i, 1\\ \\ & \\mbox{for} \\ d+2-i\\leqslant j\\leqslant d+i, 0\\ \\ & \\mbox{for} \\ d+1+i\\leqslant j\\leqslant 2d. \\end{array} \\right. $$ Further, let $R_d$ be a set of sequences of integers as follows: $$R_d=\\{(\\rho_1, \\rho_2,\\ldots, \\rho_d)|1\\leqslant \\rho_i\\leqslant d+i, 1\\leqslant i \\leqslant d,\\ \\mbox{and}\\ \\rho_r\\neq \\rho_s\\ \\mbox{for}\\ r\\neq s\\}.$$ and define $$\\Omega_d(x)=\\sum_{\\rho\\in R_d}a_{1,\\rho_1}a_{2,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.01295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-05T07:52:18Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"afabcedf6a9cdf25bf89b293e6199509b3f6c4f4e21bc4db78e07d3d88c7f54e","abstract_canon_sha256":"ec30d65da3d7c5cbb57df795b2c7bfaa2f82f0cad0656add05d7975912c5da23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:58.551274Z","signature_b64":"4Ki/Yz3Rt4g6j+KMkZFCjgMtEMkAcGnsphj/mZEI8Z3l5UM6G1ELcdTFW7s+6YFC4ltGfZgyPBNaB3A5xx8UAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3082ff11a4625cc15d5cd697b1b082728715b3ddd73db04e0d6cba0d0f12e91","last_reissued_at":"2026-05-18T00:46:58.550800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:58.550800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of a conjecture of Kl{\\o}ve on permutation codes under the Chebychev distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Victor J. W. Guo, Yiting Yang","submitted_at":"2017-04-05T07:52:18Z","abstract_excerpt":"Let $d$ be a positive integer and $x$ a real number. Let $A_{d, x}$ be a $d\\times 2d$ matrix with its entries $$ a_{i,j}=\\left\\{ \\begin{array}{ll} x\\ \\ & \\mbox{for} \\ 1\\leqslant j\\leqslant d+1-i, 1\\ \\ & \\mbox{for} \\ d+2-i\\leqslant j\\leqslant d+i, 0\\ \\ & \\mbox{for} \\ d+1+i\\leqslant j\\leqslant 2d. \\end{array} \\right. $$ Further, let $R_d$ be a set of sequences of integers as follows: $$R_d=\\{(\\rho_1, \\rho_2,\\ldots, \\rho_d)|1\\leqslant \\rho_i\\leqslant d+i, 1\\leqslant i \\leqslant d,\\ \\mbox{and}\\ \\rho_r\\neq \\rho_s\\ \\mbox{for}\\ r\\neq s\\}.$$ and define $$\\Omega_d(x)=\\sum_{\\rho\\in R_d}a_{1,\\rho_1}a_{2,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01295","kind":"arxiv","version":1},"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":"1704.01295","created_at":"2026-05-18T00:46:58.550869+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.01295v1","created_at":"2026-05-18T00:46:58.550869+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01295","created_at":"2026-05-18T00:46:58.550869+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMEC74I2IYS4","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMEC74I2IYS4YFOV","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMEC74I2","created_at":"2026-05-18T12:31:56.362134+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/YMEC74I2IYS4YFOVZVUXWGYIE4","json":"https://pith.science/pith/YMEC74I2IYS4YFOVZVUXWGYIE4.json","graph_json":"https://pith.science/api/pith-number/YMEC74I2IYS4YFOVZVUXWGYIE4/graph.json","events_json":"https://pith.science/api/pith-number/YMEC74I2IYS4YFOVZVUXWGYIE4/events.json","paper":"https://pith.science/paper/YMEC74I2"},"agent_actions":{"view_html":"https://pith.science/pith/YMEC74I2IYS4YFOVZVUXWGYIE4","download_json":"https://pith.science/pith/YMEC74I2IYS4YFOVZVUXWGYIE4.json","view_paper":"https://pith.science/paper/YMEC74I2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.01295&json=true","fetch_graph":"https://pith.science/api/pith-number/YMEC74I2IYS4YFOVZVUXWGYIE4/graph.json","fetch_events":"https://pith.science/api/pith-number/YMEC74I2IYS4YFOVZVUXWGYIE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMEC74I2IYS4YFOVZVUXWGYIE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMEC74I2IYS4YFOVZVUXWGYIE4/action/storage_attestation","attest_author":"https://pith.science/pith/YMEC74I2IYS4YFOVZVUXWGYIE4/action/author_attestation","sign_citation":"https://pith.science/pith/YMEC74I2IYS4YFOVZVUXWGYIE4/action/citation_signature","submit_replication":"https://pith.science/pith/YMEC74I2IYS4YFOVZVUXWGYIE4/action/replication_record"}},"created_at":"2026-05-18T00:46:58.550869+00:00","updated_at":"2026-05-18T00:46:58.550869+00:00"}