{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DJMLXU23ZD6RC65RFZ4FNEWBMO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"53f653ccc26a97e6eb7d47c078cfa8ba76372cab21ce334a552396063d806b32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T12:40:59Z","title_canon_sha256":"4b7171f77f9d223a86fb1c6c65cdabf8592d9c6af5345c5a7e1f6c16e74235af"},"schema_version":"1.0","source":{"id":"1702.08026","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08026","created_at":"2026-05-18T00:33:02Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08026v4","created_at":"2026-05-18T00:33:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08026","created_at":"2026-05-18T00:33:02Z"},{"alias_kind":"pith_short_12","alias_value":"DJMLXU23ZD6R","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DJMLXU23ZD6RC65R","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DJMLXU23","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:f6071cf209f0b6141863ade00f7277999d28762f070cfa4a888975cabd3b566f","target":"graph","created_at":"2026-05-18T00:33:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLE$_\\kappa$ loop measures for $\\kappa\\in(0,8)$. 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","authors_text":"Dapeng Zhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T12:40:59Z","title":"SLE Loop Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08026","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f94778fced2940986ae927f20698422f11f9a85849e806abe296069d924a4afa","target":"record","created_at":"2026-05-18T00:33:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"53f653ccc26a97e6eb7d47c078cfa8ba76372cab21ce334a552396063d806b32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-26T12:40:59Z","title_canon_sha256":"4b7171f77f9d223a86fb1c6c65cdabf8592d9c6af5345c5a7e1f6c16e74235af"},"schema_version":"1.0","source":{"id":"1702.08026","kind":"arxiv","version":4}},"canonical_sha256":"1a58bbd35bc8fd117bb12e785692c163a0cc34f7f51e8f274a27ab8db2ea3128","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a58bbd35bc8fd117bb12e785692c163a0cc34f7f51e8f274a27ab8db2ea3128","first_computed_at":"2026-05-18T00:33:02.195546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:02.195546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OlKAiypN4dUp1PYcnPrPAiHJrxnDXtlcPkMIQ5OXFI5qG1/qz1qgMqbRVnfH/XDzkcetfMR32ykGu9bUCxaFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:02.196081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08026","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f94778fced2940986ae927f20698422f11f9a85849e806abe296069d924a4afa","sha256:f6071cf209f0b6141863ade00f7277999d28762f070cfa4a888975cabd3b566f"],"state_sha256":"8fa9047fcac5c62643f94912826a5af2c4923b7132a655f13e1dd7b33cc0165e"}