Pith Number

pith:37XA7OSO

pith:2026:37XA7OSORFZXHABUBQWHR4YCV3

not attested not anchored not stored refs pending

Power Partitions and Hayman Functions

Jos\'e L. Fern\'andez, V\'ictor J. Maci\'a

The generating function for partitions into k-th powers is strongly Gaussian in the Báez-Duarte sense.

arxiv:2602.18575 v3 · 2026-02-20 · math.PR · math.CV · math.NT

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove that the generating function of partitions into k-th powers is strongly Gaussian in the sense of Báez-Duarte.

C2weakest assumption

The bounds of Tenenbaum, Wu and Li on the generating function are strong enough to verify the Gaussianity criterion for Khinchin families.

C3one 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.

Receipt and verification

First computed	2026-06-19T16:11:21.026364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfee0fba4e89737380340c2c78f302aed4f5b3e7ab7ad99cdae50c8f4a6da35c

Aliases

arxiv: 2602.18575 · arxiv_version: 2602.18575v3 · doi: 10.48550/arxiv.2602.18575 · pith_short_12: 37XA7OSORFZX · pith_short_16: 37XA7OSORFZXHABU · pith_short_8: 37XA7OSO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/37XA7OSORFZXHABUBQWHR4YCV3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: dfee0fba4e89737380340c2c78f302aed4f5b3e7ab7ad99cdae50c8f4a6da35c

Canonical record JSON

{
  "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
  }
}