Pith Number

pith:TTAUM3WL

pith:2026:TTAUM3WLXBDUYA7ELKCB4N7IRE

not attested not anchored not stored refs resolved

Polynomial Maximization Method with Fractional Polynomial Basis: A Frequentist Bridge to Bayesian Fractional Polynomials

Serhii Zabolotnii

PMM-FP extends polynomial maximization to fractional bases and delivers a closed-form variance-reduction factor of 1 minus gamma_3 squared over 2 plus gamma_4 relative to ordinary least squares for asymmetric non-Gaussian errors.

arxiv:2605.16846 v1 · 2026-05-16 · stat.ME

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\pithnumber{TTAUM3WLXBDUYA7ELKCB4N7IRE}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

The main result is the closed-form variance-reduction coefficient g_2=1-gamma_3^2/(2+gamma_4) relative to OLS-FP for asymmetric non-Gaussian errors, formalised in Lean 4 and validated by Monte Carlo.

C2weakest assumption

The extension to fractional-polynomial bases is developed under appropriate moment conditions for the positive and full FP power sets.

C3one line summary

PMM-FP extends polynomial maximization to fractional polynomial bases and derives a closed-form variance-reduction coefficient g2 for asymmetric non-Gaussian errors, formalized in Lean 4 and checked via Monte Carlo.

References

30 extracted · 30 resolved · 3 Pith anchors

[1] Kunchenko, Yuriy P. , title =. 2002 , isbn = 2002

[2] and Warsza, Zygmunt L 2018

[3] and Warsza, Zygmunt L 2019

[4] Zabolotnii, Serhii and Tkachenko, Oleksandr and Warsza, Zygmunt L. , title =. Automation 2022: New Solutions and Technologies for Automation, Robotics and Measurement Techniques , series =. 2022 , doi 2022

[5] Zabolotnii, Serhii and Tkachenko, Oleksandr and Warsza, Zygmunt L. , title =. Automation 2023: Key Challenges in Automation, Robotics and Measurement Techniques , series =. 2023 , doi = 2023

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:25.896543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cc1466ecbb8474c03e45a841e37e88922a5a3020a881641ca1497d3f11d1589

Aliases

arxiv: 2605.16846 · arxiv_version: 2605.16846v1 · doi: 10.48550/arxiv.2605.16846 · pith_short_12: TTAUM3WLXBDU · pith_short_16: TTAUM3WLXBDUYA7E · pith_short_8: TTAUM3WL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TTAUM3WLXBDUYA7ELKCB4N7IRE \
  | 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: 9cc1466ecbb8474c03e45a841e37e88922a5a3020a881641ca1497d3f11d1589

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "34cd783b80d9e5f9a8ca54e8e2dca1e4047db73b0d2e76a8f4c70bba499e6f03",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-16T07:07:26Z",
    "title_canon_sha256": "492e9e28a5be61402ecb0867af382cba9e44ab32a97c9c1848ffc48338819d9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16846",
    "kind": "arxiv",
    "version": 1
  }
}