{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ABC3552RKZ3CSVAGRQ53DTO7TP","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":"c0cbaefbd0862ca0f0b952db7c851cb0b82a0d208f395f8039be6641b059b1e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-29T22:12:33Z","title_canon_sha256":"376854495963e3d1ab2acf90dcdfd839032df66af078a4b98a16518005bd6a1e"},"schema_version":"1.0","source":{"id":"1506.08881","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08881","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08881v2","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08881","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"pith_short_12","alias_value":"ABC3552RKZ3C","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ABC3552RKZ3CSVAG","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ABC3552R","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:d82bae68215446c8b7a2a0ae5971d6f6a933527f9c229aa065245d4440072e2d","target":"graph","created_at":"2026-05-18T01:35:22Z","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 consider the abelian sandpile model and the uniform spanning unicycle on random planar maps. We show that the sandpile density converges to 5/2 as the maps get large. For the spanning unicycle, we show that the length and area of the cycle converges to the hitting time and location of a simple random walk in the first quadrant. The calculations use the \"hamburger-cheeseburger\" construction of Fortuin--Kasteleyn random cluster configurations on random planar maps.","authors_text":"David B. Wilson, Xin Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-29T22:12:33Z","title":"Sandpiles and unicycles on random planar maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08881","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":"sha256:59e9eab66caeb856dc645f693eeaff5b7a6f7cca00a55a34de9a40a9690f60c8","target":"record","created_at":"2026-05-18T01:35:22Z","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":"c0cbaefbd0862ca0f0b952db7c851cb0b82a0d208f395f8039be6641b059b1e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-29T22:12:33Z","title_canon_sha256":"376854495963e3d1ab2acf90dcdfd839032df66af078a4b98a16518005bd6a1e"},"schema_version":"1.0","source":{"id":"1506.08881","kind":"arxiv","version":2}},"canonical_sha256":"0045bef75156762954068c3bb1cddf9be61fd9137f763549e9eff76dc713248d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0045bef75156762954068c3bb1cddf9be61fd9137f763549e9eff76dc713248d","first_computed_at":"2026-05-18T01:35:22.078951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:22.078951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fVnkx2AtVV609pHMyzN2VcjpX1PNAIPBUyblr5L3OVHWFNPSfJhPqOq2f0cwAPahpHXcI6QOMSZQLKiFniNYBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:22.079859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08881","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59e9eab66caeb856dc645f693eeaff5b7a6f7cca00a55a34de9a40a9690f60c8","sha256:d82bae68215446c8b7a2a0ae5971d6f6a933527f9c229aa065245d4440072e2d"],"state_sha256":"ed86cad086350762506dc098ad25a3bad16db422187e2c3056e7a056e4404def"}