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First, we construct rooted SLE$_\\kappa$ loop measures in the Riemann sphere $\\widehat{\\mathbb C}$, which satisfy M\\\"obius covariance, conformal Markov property, reversibility, and space-time homogeneity, when the loop is parametrized by its $(1+\\frac \\kappa 8)$-dimensional Minkowski content. Second, by integrating rooted SLE$_\\kappa$ loop measures, we construct the unrooted SLE$_\\kappa$ loop measure in $\\widehat{\\mathbb C}$, which satisfies M\\\"obius inv"},"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":"1702.08026","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T12:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"4b7171f77f9d223a86fb1c6c65cdabf8592d9c6af5345c5a7e1f6c16e74235af","abstract_canon_sha256":"53f653ccc26a97e6eb7d47c078cfa8ba76372cab21ce334a552396063d806b32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:02.196081Z","signature_b64":"OlKAiypN4dUp1PYcnPrPAiHJrxnDXtlcPkMIQ5OXFI5qG1/qz1qgMqbRVnfH/XDzkcetfMR32ykGu9bUCxaFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a58bbd35bc8fd117bb12e785692c163a0cc34f7f51e8f274a27ab8db2ea3128","last_reissued_at":"2026-05-18T00:33:02.195546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:02.195546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SLE Loop Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dapeng Zhan","submitted_at":"2017-02-26T12:40:59Z","abstract_excerpt":"We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLE$_\\kappa$ loop measures for $\\kappa\\in(0,8)$. 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