Pith Number

pith:BFZ5LPQB

pith:2026:BFZ5LPQBVGN53HD3YZGQOESWIU

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Two Approximate Solutions of the Ornstein-Zernike (OZ) Integral Equation

Jianzhong Wu

The work re-derives analytical solutions to the OZ equation for hard spheres under PY and MSA approximations and obtains closed-form expressions for the equation of state and activity coefficients.

arxiv:2604.03963 v2 · 2026-04-05 · math-ph · math.MP

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Claims

C1strongest claim

This work presents a comprehensive derivation of analytical solutions to the OZ integral equation under the hard-sphere model, including applications of the PY approximation for both single- and multi-component systems, as well as the MSA for systems of charged hard spheres, leading to explicit expressions for the equation of state and activity coefficients.

C2weakest assumption

The Percus-Yevick and Mean Spherical approximations remain sufficiently accurate for the hard-sphere and charged hard-sphere systems considered, and the Fourier and complex-analysis techniques correctly invert the integral equation without hidden singularities.

C3one line summary

The work re-derives analytical solutions to the OZ equation for hard spheres under PY and MSA approximations and obtains closed-form expressions for the equation of state and activity coefficients.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-09T02:08:41.658210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0973d5be01a99bdd9c7bc64d07125645240e2b89b68cafa7b63bcc5656af208e

Aliases

arxiv: 2604.03963 · arxiv_version: 2604.03963v2 · doi: 10.48550/arxiv.2604.03963 · pith_short_12: BFZ5LPQBVGN5 · pith_short_16: BFZ5LPQBVGN53HD3 · pith_short_8: BFZ5LPQB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BFZ5LPQBVGN53HD3YZGQOESWIU \
  | 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: 0973d5be01a99bdd9c7bc64d07125645240e2b89b68cafa7b63bcc5656af208e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c364577aa2c627d521b4be12a6818139dcf9da0a980b69e1229612035d49777",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-04-05T04:50:57Z",
    "title_canon_sha256": "779ed12b8bfaa3656aedfa24041a4592f2d4e0afca036b5bc25132a941642cc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.03963",
    "kind": "arxiv",
    "version": 2
  }
}