{"paper":{"title":"Renormalised two-point functions of CLE$_4$ gaskets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Renormalised probabilities that two points belong to the same or outermost CLE₄ gasket equal the two-point functions of the Ashkin-Teller scaling limit.","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Juhan Aru, Titus Lupu","submitted_at":"2026-04-16T15:20:38Z","abstract_excerpt":"We first consider nested CLE$_4$ in a simply-connected domain and compute some exact renormalised probabilities: the probability that two points belong to the same CLE$_4$ gasket and the probability that two points belong to the outermost CLE$_4$ gasket. The resulting conformally covariant formulas have a non-trivial modular dependence, expressed explicitly in terms of Jacobi theta functions.\n  We are guided by the conformal field theory of the Ashkin-Teller (AT) model, but our proofs are purely probabilistic using Brownian loop soups, gauge-twisted Gaussian free fields (GFFs) and the level li"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Renormalised probabilities that two points belong to the same or outermost CLE₄ gasket equal the two-point functions of the Ashkin-Teller scaling limit.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"218f89d9bdfb98ae24a4813d6674ee516270d1cf25ff287331f8f5903db52a03"},"source":{"id":"2604.15146","kind":"arxiv","version":2},"verdict":{"id":"88dbcae1-bab4-4c67-b238-001f880a51e2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T09:53:36.722909Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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).","pith_extraction_headline":"Renormalised probabilities that two points belong to the same or outermost CLE₄ gasket equal the two-point functions of the Ashkin-Teller scaling limit."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.15146/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}