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We prove that as one sends $\\kappa \\downarrow 4$ in the subcritical setting, the space-filling SLE$_\\kappa$ in a disk degenerates to the CLE$_4$ exploration introduced by Werner and Wu, along with a collection of i.i.d.\\ coin tosses inde"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2109.00275","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-09-01T09:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"6237f750716c00e415d565d05a54e98675d7a61882f2ba40ec767747b44d03e0","abstract_canon_sha256":"974b6a925a46db795a70b1fc9753c5eee0783696a6bf88d352266e13cb948e7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:53:25.154444Z","signature_b64":"yyy5usE9Btbp4PSpnxJCXJQN/+iSZQGIBT2Yyax9LLJJELx09eIpJfeAAjY3HbZsKfBesQb+h8n3+Cq9xObmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5542271486c5e97b284d6dcab1e5019aa536d94edfbf4d9092c9f91f215e5e1a","last_reissued_at":"2026-07-05T04:53:25.153965Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:53:25.153965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mating of trees for critical Liouville quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ellen Powell, Juhan Aru, Nina Holden, Xin Sun","submitted_at":"2021-09-01T09:39:02Z","abstract_excerpt":"In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be described by the mating of two continuum random trees. 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