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For $1\\le \\ell\\le (p-1)/2$, define \\[ \\ex_{\\Cay}(C_{2\\ell+1},\\Z_p)=\\max\\{|S|: S=-S,\\ 0\\notin S,\\ \\Cay(\\Z_p,S)\\text{ contains no }C_{2\\ell+1}\\}. \\] Confirming a conjecture of Cashman and Kelley, we prove that if $p=2\\ell+1$, then $\\ex_{\\Cay}(C_{2\\ell+1},\\Z_p)=0$, while if $p>2\\ell+1$, then \\[ \\ex_{\\Cay}(C_{2\\ell+1},\\Z_p)=2\\floor{\\frac{p+2\\ell+1}{2(2\\ell+1)}}. \\] The proof combines a sharp additiv","authors_text":"Kai Yang, Wei Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T11:04:15Z","title":"Odd cycles in symmetric Cayley graphs on prime cyclic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24426","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:902be66ef7334316870b3713cca30f6da507db9eaba834436f37cc11482f5b05","target":"record","created_at":"2026-06-24T01:15:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fe9fcca4e07d243ee648daffdeeb9d0553177fe8bfeb6f0b3c6b4d015d8bc17c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-23T11:04:15Z","title_canon_sha256":"849c772a8e1eb7adead9c3b23fd2c03729b6fe6e8ea0fb782dbdfd81680715fe"},"schema_version":"1.0","source":{"id":"2606.24426","kind":"arxiv","version":1}},"canonical_sha256":"aebadbd3540345846a131f5f607c9cc4b35c647292a9416392cd0d40e5bc83fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aebadbd3540345846a131f5f607c9cc4b35c647292a9416392cd0d40e5bc83fc","first_computed_at":"2026-06-24T01:15:30.102634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:30.102634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"omZ1f+C3ncg1ghGCBIv0kzXnvv+Y8AczzPXe3gM7+dClYJJarpM0mBnprxLJkUCougy2UNBygngoUC9e8ADxDQ==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:30.102987Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:902be66ef7334316870b3713cca30f6da507db9eaba834436f37cc11482f5b05","sha256:53db676a0a325f84cc502deef45bd9a8812da3839982424be689d64354cff9a5"],"state_sha256":"52497152cbd06f7219d962ab22ba3fd5715ad01290f908c214cc527a11f8a9bc"}