Pith Number

pith:7UEZCPRR

pith:2026:7UEZCPRRZ72Y5TFBJR223KHD3D

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A Separation Method for Quartic Positivity and the Valid Region of Gram-Charlier densities

ByoungSeon Choi, Jung Chan Lee, Taehun Kim

A separation method supplies necessary and sufficient conditions for a quartic polynomial to stay positive everywhere, which then yields simpler analytic expressions for the valid region of Gram-Charlier densities.

arxiv:2603.00073 v2 · 2026-02-12 · cs.SC

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Claims

C1strongest claim

necessary and sufficient conditions for the positivity of a quartic polynomial are derived through a separation method. Based on these conditions, more concise analytic expressions for the positivity of the Gram-Charlier density are proposed.

C2weakest assumption

The separation method fully captures all cases of positivity for the specific quartic polynomials that arise from the Gram-Charlier expansion, without missing boundary cases or requiring additional restrictions.

C3one line summary

A separation method for quartic positivity produces more concise analytic conditions for the valid region of Gram-Charlier densities.

Receipt and verification

First computed	2026-05-17T23:38:59.844062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd09913e31cff58ecca14c75ada8e3d8ebbf849fafb03c4be4a8668f04208ea8

Aliases

arxiv: 2603.00073 · arxiv_version: 2603.00073v2 · doi: 10.48550/arxiv.2603.00073 · pith_short_12: 7UEZCPRRZ72Y · pith_short_16: 7UEZCPRRZ72Y5TFB · pith_short_8: 7UEZCPRR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7UEZCPRRZ72Y5TFBJR223KHD3D \
  | 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: fd09913e31cff58ecca14c75ada8e3d8ebbf849fafb03c4be4a8668f04208ea8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d6859c591cca7a4d07914ccaf66966ee8ee05b3f15003a56a54b8befe075db6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.SC",
    "submitted_at": "2026-02-12T04:48:27Z",
    "title_canon_sha256": "90d93d1c29de6e6e13386af09a453d223ba64e437fd88a2432de5f133c53ce0b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.00073",
    "kind": "arxiv",
    "version": 2
  }
}