Pith Number

pith:WTZCTPJW

pith:2026:WTZCTPJWRDTE4M7F7L6I2FFGUW

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Exact density-functional theory as parallel ensemble variational hierarchies: from Lieb's formulation to Kohn-Sham theory

Nan Sheng

Exact density-functional theory emerges as two parallel ensemble variational hierarchies linked by the Kohn-Sham mapping on a shared density class.

arxiv:2603.23399 v4 · 2026-03-24 · physics.chem-ph · math-ph · math.MP

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Claims

C1strongest claim

Exact density-functional theory is reconstructed here from its convex variational structure as two parallel exact ensemble hierarchies: an interacting hierarchy rooted in Lieb's ensemble formulation and a noninteracting hierarchy rooted in the exact noninteracting ensemble theory. The Kohn-Sham construction links the two on a common admissible density class.

C2weakest assumption

That the convex variational structure of the energy functional admits exact parallel ensemble hierarchies for both interacting and noninteracting systems whose densities coincide under the Kohn-Sham mapping without additional constraints that would invalidate the claimed consequences for fractional occupations and derivative discontinuities.

C3one line summary

Exact DFT is reorganized as parallel interacting and noninteracting ensemble variational hierarchies whose geometry produces fractional particle numbers, piecewise linearity, and the derivative discontinuity as direct consequences.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

A density-functional perspective on force fields

Receipt and verification

First computed	2026-06-09T02:07:24.683724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4f229bd3688e64e33e5fafc8d14a6a5a09dc3545feca4ebc9857e6a2fb3c4b6

Aliases

arxiv: 2603.23399 · arxiv_version: 2603.23399v4 · doi: 10.48550/arxiv.2603.23399 · pith_short_12: WTZCTPJWRDTE · pith_short_16: WTZCTPJWRDTE4M7F · pith_short_8: WTZCTPJW

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WTZCTPJWRDTE4M7F7L6I2FFGUW \
  | 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: b4f229bd3688e64e33e5fafc8d14a6a5a09dc3545feca4ebc9857e6a2fb3c4b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ee67b21bfa5bd2a8b536e6c772286defc359acad7e68caa833121ae55a202b3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.chem-ph",
    "submitted_at": "2026-03-24T16:35:25Z",
    "title_canon_sha256": "454ca0623ee85b374e00c4a82944996d9619271eb3b1eb13d7d1f5cb791fe794"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.23399",
    "kind": "arxiv",
    "version": 4
  }
}