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For example, exploiting provable algebraic relations among MCVs, we show that \\[\\mathscr A_{1,5}=-\\frac{9[495L(\\chi_{-3},6)-30\\pi^{2}L(\\chi_{-3},4)-2\\pi^{4}L(\\chi_{-3},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":"2607.14646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-16T07:15:40Z","cross_cats_sorted":["hep-th","math.CO"],"title_canon_sha256":"f45569682c952be4350f70c8bddf1f84a37b892d7c5162f77989930ef5cd455a","abstract_canon_sha256":"d9840d18be88c0f046ebb85d54c2bcbd10d69228aad2cb6255756eda771f4dc0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:22.740258Z","signature_b64":"qiBWgbWfmkNBVo+iDrrO8b4Ih4FTsPkus58BSvwnbeH5mKoQtKSLxbNuTdHKlz4sYlUJQlLn+xF5UEyIDWyiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"389f1e3778350d2018d8e05e3c702e29cf8f945a9e7c602ad3b3b9e6ca08ddac","last_reissued_at":"2026-07-17T01:21:22.739376Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:22.739376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiple Clausen values and deformed Ap\\'ery-like series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.NT","authors_text":"Yajun Zhou, Zhi-Wei Sun","submitted_at":"2026-07-16T07:15:40Z","abstract_excerpt":"With generalized central binomial coefficients $ \\binom{2x}{x}:=\\frac{\\Gamma(2x+1)}{[\\Gamma(x+1)]^2}$ defined through Euler's gamma function, we represent deformed Ap\\'ery-like series \\[ \\mathscr A_{s,n}:=\\sum_{k=1}^\\infty\\left.\\!\\frac{\\partial^n}{\\partial x^n}\\frac{1}{x^s\\binom{2x}{x}}\\right|_{x=k} \\] by multiple Clausen values (MCVs), which belong to a special class of cyclotomic multiple zeta values (CMZVs) at level $3$. 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