{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:K6HD36RPTOEKJ4W7IQILSHIVG3","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":"872c6245dacfbcffc2fc4b00c6ce09d35fed1525b3cac100628ba50dc4d198a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-04T23:30:48Z","title_canon_sha256":"9aa001641899d8bc8d887b3cce318fda7f4b32dbfd0d6fd3657aa78142f8f45d"},"schema_version":"1.0","source":{"id":"1309.1207","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1207","created_at":"2026-05-18T01:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1207v3","created_at":"2026-05-18T01:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1207","created_at":"2026-05-18T01:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"K6HD36RPTOEK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"K6HD36RPTOEKJ4W7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"K6HD36RP","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:939cef44141486d1935ab7edaab4364c1d9c6bdecb423a621c33db18c851a19b","target":"graph","created_at":"2026-05-18T01:47:49Z","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 study the scaling limit of planar loop erased random walk (LERW) on the percolation cluster, with occupation probability $p\\geq p_c$. We numerically demonstrate that the scaling limit of planar LERW$_p$ curves, for all $p>p_c$, can be described by Schramm-Loewner Evolution (SLE) with a single parameter $\\kappa$ which is close to normal LERW in Euclidean lattice. However our results reveal that the LERW on critical incipient percolation clusters is compatible with SLE, but with another diffusivity coefficient $\\kappa$. Several geometrical tests are applied to ascertain this. All calculations","authors_text":"E. Daryaei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-04T23:30:48Z","title":"Loop erased random walk on a percolation cluster is compatible with Schramm-Loewner evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1207","kind":"arxiv","version":3},"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":"sha256:5e4fb9887eb078793fd9d9816248b8f0c36660c7b7a8ab627ed71193e933bd0c","target":"record","created_at":"2026-05-18T01:47:49Z","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":"872c6245dacfbcffc2fc4b00c6ce09d35fed1525b3cac100628ba50dc4d198a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-04T23:30:48Z","title_canon_sha256":"9aa001641899d8bc8d887b3cce318fda7f4b32dbfd0d6fd3657aa78142f8f45d"},"schema_version":"1.0","source":{"id":"1309.1207","kind":"arxiv","version":3}},"canonical_sha256":"578e3dfa2f9b88a4f2df4410b91d1536c9ba3008cdfadc457c1705adad601436","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"578e3dfa2f9b88a4f2df4410b91d1536c9ba3008cdfadc457c1705adad601436","first_computed_at":"2026-05-18T01:47:49.648630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:47:49.648630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oURqm8KlHWNB4+WsEiuprtkYuGgZEupJdc//JXpr7uSRhGB/UX6V2amDpo6adQtpCqit/wL2rpv4pEtFKpcqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:47:49.649098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1207","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e4fb9887eb078793fd9d9816248b8f0c36660c7b7a8ab627ed71193e933bd0c","sha256:939cef44141486d1935ab7edaab4364c1d9c6bdecb423a621c33db18c851a19b"],"state_sha256":"cca052465f8bf6cfe57d4bc47091195af7a67fe6169f086997fddb39a5c4a198"}