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2=1) \\vee n=2k+1$ and $s(Ci_n(1,2,...,k))=\\lceil\\frac{n+2k-1}{2k}\\rceil+1$."},"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":"1111.0316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-01T21:05:32Z","cross_cats_sorted":[],"title_canon_sha256":"1f87825a5e675d5843e0bd4474e5633b8b1be6859b575ae57a8844ada635d662","abstract_canon_sha256":"6c9942e94c58bd7e68b47e8f5948ed500b21847ae9904e188c428739806b50f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:45.286334Z","signature_b64":"zZEcjnoLc0sIbCtgMpRVJcwUVOe0bNsSMEXSU30Lveivyi9vLfOknNCrFiKRQDIMZi7Sy7d8quJHBTeI30/QAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28baf1fb6fd431fab2a66739ae64999b7715821a715d873efe5519017e864dcd","last_reissued_at":"2026-05-18T04:09:45.285795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:45.285795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irregular 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