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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","authors_text":"Jos\\'e L. Fern\\'andez, V\\'ictor J. Maci\\'a","cross_cats":["math.CV","math.NT"],"headline":"The generating function for partitions into k-th powers is strongly Gaussian in the Báez-Duarte sense.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-02-20T19:32:11Z","title":"Power Partitions and Hayman Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.18575","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-15T20:32:06.864710Z","id":"6b2f1442-732c-498d-96df-f4c28863a483","model_set":{"reader":"grok-4.3"},"one_line_summary":"The generating function of k-th power partitions is strongly Gaussian, so the asymptotic p_k(n) ~ alpha_k n^(-(3k+1)/(2k+2)) exp(beta_k n^{1/(k+1)}) follows from Hayman's theorem via mean and variance approximations.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The generating function for partitions into k-th powers is strongly Gaussian in the Báez-Duarte sense.","strongest_claim":"We prove that the generating function of partitions into k-th powers is strongly Gaussian in the sense of Báez-Duarte.","weakest_assumption":"The bounds of Tenenbaum, Wu and Li on the generating function are strong enough to verify the Gaussianity criterion for Khinchin families."}},"verdict_id":"6b2f1442-732c-498d-96df-f4c28863a483"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8f323eaf36c85b404d7f49db729b80aa7e587e97392e7fa65e9db283b98672d7","target":"record","created_at":"2026-06-19T16:11:21Z","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":"38d423c3b0b345102a3e64c788899d4999dc7c6a490c29c98605ddfd9e925580","cross_cats_sorted":["math.CV","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-02-20T19:32:11Z","title_canon_sha256":"8757ddf1ae3f4d8ac5a816032785369d56afa06dd2275e63ae39cdd45e63110b"},"schema_version":"1.0","source":{"id":"2602.18575","kind":"arxiv","version":3}},"canonical_sha256":"dfee0fba4e89737380340c2c78f302aed4f5b3e7ab7ad99cdae50c8f4a6da35c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfee0fba4e89737380340c2c78f302aed4f5b3e7ab7ad99cdae50c8f4a6da35c","first_computed_at":"2026-06-19T16:11:21.026364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:21.026364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9TvwDJGDG9EIjFG+5rqwYr6Jay6DCmgxaKzG7h7qJr1IQ/xA24r/tayqGYfqrXlOYPTWqJiXji4ahYbIkIm6AA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:21.026799Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.18575","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f323eaf36c85b404d7f49db729b80aa7e587e97392e7fa65e9db283b98672d7","sha256:7509807156671df2ac782fedfc361808339c64f0a7ee819134211d892fcb56bd"],"state_sha256":"69aa417bf1a0e27fa1dedc6b1ef9c62774bec47c5b361579bc0613eceeaa7a01"}