Pith Number

pith:3LLGIJ32

pith:2026:3LLGIJ32N2CPFDVYOK2VBMTB22

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Renormalised two-point functions of CLE$_4$ gaskets

Juhan Aru, Titus Lupu

Renormalised probabilities that two points belong to the same or outermost CLE₄ gasket equal the two-point functions of the Ashkin-Teller scaling limit.

arxiv:2604.15146 v2 · 2026-04-16 · math.PR · math-ph · math.MP

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Claims

C1strongest claim

We consider nested CLE₄ in a simply-connected domain and compute the following renormalised probabilities: the probability that two points belong to the same CLE₄ gasket and the probability that two points belong to the outermost CLE₄ gasket. ... These quantities correspond to the two-point function of the conjectured scaling limit of the AT single spins on the critical line.

C2weakest assumption

That the renormalized probabilities computed from CLE4 gaskets and GFF two-valued sets exactly match the two-point functions of the conjectured scaling limit of the Ashkin-Teller single spins (invoked in the abstract to interpret the results).

C3one line summary

Renormalized two-point functions for CLE4 gaskets are computed probabilistically via loop soups and GFF, corresponding to Ashkin-Teller spin correlations and recovering Ising at the decoupling point.

Receipt and verification

First computed	2026-06-08T01:04:05.051506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dad664277a6e84f28eb872b550b261d68eb2cd6a1bec71e8f64f8986bb9d3cb7

Aliases

arxiv: 2604.15146 · arxiv_version: 2604.15146v2 · doi: 10.48550/arxiv.2604.15146 · pith_short_12: 3LLGIJ32N2CP · pith_short_16: 3LLGIJ32N2CPFDVY · pith_short_8: 3LLGIJ32

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/3LLGIJ32N2CPFDVYOK2VBMTB22 \
  | 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: dad664277a6e84f28eb872b550b261d68eb2cd6a1bec71e8f64f8986bb9d3cb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07f5af07edf9379b6e522df5bf1e2bd559e625e1cff7ea98b3031fcfdcd32dd0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-16T15:20:38Z",
    "title_canon_sha256": "4c09e5bb31c002c9f66ff5deba77ab890fb85381cfeafd761d4ca8af38d5eca6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.15146",
    "kind": "arxiv",
    "version": 2
  }
}