{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2MYJF63MEXRX3WO7EGQJFFARSQ","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":"d69e4468220780d81cb4222ca36f4f171d2e5b98621b0c162c899d9ec9f73e8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-22T13:00:03Z","title_canon_sha256":"641f84f298fd25c3610e052ac239f6f452f16c43605e867c361bb6a76f0c4ca2"},"schema_version":"1.0","source":{"id":"1305.5114","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5114","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5114v3","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5114","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"pith_short_12","alias_value":"2MYJF63MEXRX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2MYJF63MEXRX3WO7","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2MYJF63M","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:7429a2c62e07fe88d865d1974a57630e1e27473ad5a4fb49981f8b2c103d4fda","target":"graph","created_at":"2026-05-18T02:29:32Z","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 spanning trees on Sierpinski graphs (i.e., finite approximations to the Sierpinski gasket) that are chosen uniformly at random. We construct a joint probability space for uniform spanning trees on every finite Sierpinski graph and show that this construction gives rise to a multi-type Galton-Watson tree. We derive a number of structural results, for instance on the degree distribution. The connection between uniform spanning trees and loop-erased random walk is then exploited to prove convergence of the latter to a continuous stochastic process. Some geometric properties of this limit","authors_text":"Elmar Teufl, Masato Shinoda, Stephan Wagner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-22T13:00:03Z","title":"Uniform spanning trees on Sierpinski graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5114","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":"sha256:3b8739403cfb2cc22065d2e59cdb7ffadd1c1170952e949e412a6654a93975a5","target":"record","created_at":"2026-05-18T02:29:32Z","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":"d69e4468220780d81cb4222ca36f4f171d2e5b98621b0c162c899d9ec9f73e8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-22T13:00:03Z","title_canon_sha256":"641f84f298fd25c3610e052ac239f6f452f16c43605e867c361bb6a76f0c4ca2"},"schema_version":"1.0","source":{"id":"1305.5114","kind":"arxiv","version":3}},"canonical_sha256":"d33092fb6c25e37dd9df21a0929411940026d02e13c14c606c6e666f2ba71429","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d33092fb6c25e37dd9df21a0929411940026d02e13c14c606c6e666f2ba71429","first_computed_at":"2026-05-18T02:29:32.420290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:32.420290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tiSQK2LjTWa32SY3j8iwZbp4abed5jc1xBSLPo+gW6gWGdeWB+bpBLu1rodoKY6XPevxYSsFdSwWmp+iz6wmCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:32.420723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5114","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b8739403cfb2cc22065d2e59cdb7ffadd1c1170952e949e412a6654a93975a5","sha256:7429a2c62e07fe88d865d1974a57630e1e27473ad5a4fb49981f8b2c103d4fda"],"state_sha256":"68a98eac2f93e83b80340b87c3357f093688cd3e2be14e1b1259fd65a7b8c83e"}