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Thus the Hardy--Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \\[ p_k(n) \\sim \\frac{\\alpha_k}{n^{(3k+1)/(2k+2)}} \\exp\\!\\Big(\\beta_k\\, n^{1/(k+1)}\\Big), \\qquad n\\to\\infty, \\] where $\\alpha_k$ and~$\\beta_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for str"},"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":"2602.18575","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-02-20T19:32:11Z","cross_cats_sorted":["math.CV","math.NT"],"title_canon_sha256":"8757ddf1ae3f4d8ac5a816032785369d56afa06dd2275e63ae39cdd45e63110b","abstract_canon_sha256":"38d423c3b0b345102a3e64c788899d4999dc7c6a490c29c98605ddfd9e925580"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:21.026799Z","signature_b64":"9TvwDJGDG9EIjFG+5rqwYr6Jay6DCmgxaKzG7h7qJr1IQ/xA24r/tayqGYfqrXlOYPTWqJiXji4ahYbIkIm6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfee0fba4e89737380340c2c78f302aed4f5b3e7ab7ad99cdae50c8f4a6da35c","last_reissued_at":"2026-06-19T16:11:21.026364Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:21.026364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Power Partitions and Hayman Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The generating function for partitions into k-th powers is strongly Gaussian in the Báez-Duarte sense.","cross_cats":["math.CV","math.NT"],"primary_cat":"math.PR","authors_text":"Jos\\'e L. 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