{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DX7P7EIF6D4IIPT66LYIQ5X337","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":"4562f7d536ab393796d97c2da6ee9f39e36017f59403980ec25aefc13dd7ab8f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-04T20:49:53Z","title_canon_sha256":"46fa636a8402e1607afb6648766dc3c528df9229f78ba44c8a7a54729d9ffcee"},"schema_version":"1.0","source":{"id":"1312.1324","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1324","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1324v2","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1324","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"pith_short_12","alias_value":"DX7P7EIF6D4I","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DX7P7EIF6D4IIPT6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DX7P7EIF","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:909949b772e07e15d95a33909695c798e8b442c065910fa2e25b69a45d11a09d","target":"graph","created_at":"2026-05-18T03:00:00Z","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":"In this paper we mingle the Gaussian free field, the Schramm-Loewner evolution and the KPZ relation in a natural way, shedding new light on all of them. Our principal result shows that the level lines and the SLE$_\\kappa$ flow lines of the Gaussian free field do not satisfy the usual KPZ relation. In order to prove this, we have to make a technical detour: by a careful study of a certain diffusion process, we provide exact estimates of the exponential moments of winding of chordal SLE curves conditioned to pass nearby a fixed point. This extends previous results on winding of SLE curves by Sch","authors_text":"Juhan Aru","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-04T20:49:53Z","title":"KPZ relation does not hold for the level lines and the SLE$_\\kappa$ flow lines of the Gaussian free field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1324","kind":"arxiv","version":2},"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:f89f4b7e56c03977ea14f14a0ff489238fdcec7bc6136faa2a8c5f0baaa80031","target":"record","created_at":"2026-05-18T03:00:00Z","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":"4562f7d536ab393796d97c2da6ee9f39e36017f59403980ec25aefc13dd7ab8f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-04T20:49:53Z","title_canon_sha256":"46fa636a8402e1607afb6648766dc3c528df9229f78ba44c8a7a54729d9ffcee"},"schema_version":"1.0","source":{"id":"1312.1324","kind":"arxiv","version":2}},"canonical_sha256":"1dfeff9105f0f8843e7ef2f08876fbdfc003c4255886b00eb0f6b1dc7f4ed8b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dfeff9105f0f8843e7ef2f08876fbdfc003c4255886b00eb0f6b1dc7f4ed8b8","first_computed_at":"2026-05-18T03:00:00.328138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:00.328138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9q6qNjwZI1pUN7FYvEO764tqhlWWi6xLSrl81Lq3aMuoB99TBPIOLFvdwikgWoUwb4a+G9nXURvF1ebL8i8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:00.328960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1324","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f89f4b7e56c03977ea14f14a0ff489238fdcec7bc6136faa2a8c5f0baaa80031","sha256:909949b772e07e15d95a33909695c798e8b442c065910fa2e25b69a45d11a09d"],"state_sha256":"a4548990870b0af10f8e4b296a180ca1b9cabd1a48a4dce07285b9383ed6f559"}