{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PW2RSQDJ3UGAS2A55MAKIRLLPB","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":"0c394c0111d0516cad96dfb7d1a94b87d1990a11e83153e1837aac675f74f4e0","cross_cats_sorted":["cond-mat.stat-mech","math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-21T20:59:40Z","title_canon_sha256":"b33b822f82d0b7d61049d2756162d4c9c13eee0275e7425fb8cdce379239241b"},"schema_version":"1.0","source":{"id":"1012.4800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4800","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4800v1","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4800","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"pith_short_12","alias_value":"PW2RSQDJ3UGA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PW2RSQDJ3UGAS2A5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PW2RSQDJ","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:e57b383535bccaef5016c10476e43f07b8732290f0c40729d969e8f492b2fa19","target":"graph","created_at":"2026-05-18T02:04:19Z","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 conformally weld (via \"quantum zipping\") two boundary arcs of a Liouville quantum gravity random surface to generate a random curve called the Schramm-Loewner evolution (SLE). We develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under welding via SLE martingales. As an application, we construct the natural quantum length and boundary intersection measures on the SLE curve itself.","authors_text":"Bertrand Duplantier, Scott Sheffield","cross_cats":["cond-mat.stat-mech","math.CV","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-21T20:59:40Z","title":"Schramm Loewner Evolution and Liouville Quantum Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4800","kind":"arxiv","version":1},"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":"sha256:708f2cc3e97a468479027b9c911959c22e18092e6f1f244d5dc50bd3f862f0b4","target":"record","created_at":"2026-05-18T02:04:19Z","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":"0c394c0111d0516cad96dfb7d1a94b87d1990a11e83153e1837aac675f74f4e0","cross_cats_sorted":["cond-mat.stat-mech","math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-21T20:59:40Z","title_canon_sha256":"b33b822f82d0b7d61049d2756162d4c9c13eee0275e7425fb8cdce379239241b"},"schema_version":"1.0","source":{"id":"1012.4800","kind":"arxiv","version":1}},"canonical_sha256":"7db5194069dd0c09681deb00a4456b7858fe03e4e33171c77d79fc9e83be5f76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7db5194069dd0c09681deb00a4456b7858fe03e4e33171c77d79fc9e83be5f76","first_computed_at":"2026-05-18T02:04:19.014706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:19.014706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uXfNCjeL6WDR5iNp3cKnrBzaoH5cd6K1YuaDuyk9Uq681BYOjsOQZi+HhxM2lqnEy4FjbxkuDWMTHFIB8INPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:19.015407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:708f2cc3e97a468479027b9c911959c22e18092e6f1f244d5dc50bd3f862f0b4","sha256:e57b383535bccaef5016c10476e43f07b8732290f0c40729d969e8f492b2fa19"],"state_sha256":"1f74e7e092e7d11599ea2f0ebef58aba990f0ba184a9ee2378d444322561df0a"}