Pith Number

pith:MNDFQQX3

pith:2026:MNDFQQX36BRK3I3ZKAWMXUJIAM

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Universality of the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models

Hyunsuk Choo, Ji Oon Lee, Yoochan Han

Fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models converge to universal Gaussian limits in the high-temperature regime.

arxiv:2605.07050 v2 · 2026-05-07 · math.PR · math-ph · math.MP · math.ST · stat.TH

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4 Citations 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

We prove that the limiting laws of the fluctuations are Gaussian under suitable assumptions, and the result is universal in the sense that it does not depend on the distribution of the disorder or the prior except that the means and the variances of the limiting laws depend on a few parameters of the model.

C2weakest assumption

The models operate in the high temperature/subcritical regime and satisfy suitable assumptions on the disorder and prior distributions that enable the multigraph expansion to yield Gaussian limits.

C3one line summary

Fluctuations in free energy and log-likelihood ratio for generalized SK and spiked Wigner models are Gaussian and universal in the high-temperature regime.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-25T02:01:22.522771Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63465842fbf062ada379502ccbd128033704da901881e517cec3d270fd87595d

Aliases

arxiv: 2605.07050 · arxiv_version: 2605.07050v2 · doi: 10.48550/arxiv.2605.07050 · pith_short_12: MNDFQQX36BRK · pith_short_16: MNDFQQX36BRK3I3Z · pith_short_8: MNDFQQX3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MNDFQQX36BRK3I3ZKAWMXUJIAM \
  | 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: 63465842fbf062ada379502ccbd128033704da901881e517cec3d270fd87595d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e410236e6ae3cae9707b3fc33411621e439b265035647cfc22f9749b9b4fd80",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-07T23:59:32Z",
    "title_canon_sha256": "d82c125db0c7bd2a5e7cf41f7216246d2dbb89249efe18355f92e469307836dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.07050",
    "kind": "arxiv",
    "version": 2
  }
}