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We prove that the type with respect to the order is related to certain multi-zeta values and that this type belongs to the interval\n  [\\pi/(p\\sin(\\pi/p)),\\pi/(p\\sin(\\pi/p)\\cos(\\pi/p))],\n  which also contains the conjectured value. This proves that the conjecture about type is asymptotically correct as p\\to\\inft"},"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":"1509.06540","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-22T10:21:55Z","cross_cats_sorted":[],"title_canon_sha256":"ba41dc7f596222c0d55354c160e1498f1f6fda633ea9f4b93350248a94dacfd1","abstract_canon_sha256":"e9e134dc833f8f2f1bc1050440f5ff0c957fd63a5646e3a75258225465f7beb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.292455Z","signature_b64":"fthCipHYnCBnZ2C2bpMZ/HhGNoMVowCBgkWpz1UTVZ9l1KchxkOLXBeQi+c5qcC0mRhOknNqExdJHFDR52ykDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2097910783cbc91d6cb216519db142324743ba4cc42ea5d3464ed6f01ce9e60","last_reissued_at":"2026-05-18T00:52:02.291782Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.291782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric moment problems and a conjecture of Valent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Christian Berg, Ryszard Szwarc","submitted_at":"2015-09-22T10:21:55Z","abstract_excerpt":"In 1998 G. Valent made conjectures about the order and type of certain indeterminate Stieltjes moment problems associated with birth and death processes having polynomial birth and death rates of degree p\\ge 3. Romanov recently proved that the order is 1/p as conjectured, see \\cite{Ro}. We prove that the type with respect to the order is related to certain multi-zeta values and that this type belongs to the interval\n  [\\pi/(p\\sin(\\pi/p)),\\pi/(p\\sin(\\pi/p)\\cos(\\pi/p))],\n  which also contains the conjectured value. 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