{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DNNDQNEQYZILRN4KJYYMPQ36MU","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":"0ce56651a8445c2cac7460d7d1fc97f85e84957020156a459ada794c7a330f47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-22T20:56:40Z","title_canon_sha256":"e8bf653c20e8f14845e90157c75c36d56c1cbf57d11d1d199a5b7aa574a3b8da"},"schema_version":"1.0","source":{"id":"1301.5311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5311","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5311v1","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5311","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"DNNDQNEQYZIL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DNNDQNEQYZILRN4K","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DNNDQNEQ","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:7a71ec769f2edb973e8404d619bc0797534e5711cb1b1cae5f0c84d72d120042","target":"graph","created_at":"2026-05-18T03:35:52Z","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 Bernoulli percolations on random lattices of the half-plane obtained as local limit of uniform planar triangulations or quadrangulations. Using the characteristic spatial Markov property or peeling process of these random lattices we prove a surprisingly simple universal formula for the critical threshold for bond and face percolations on these graphs. Our techniques also permit us to compute off-critical and critical exponents related to percolation clusters such as the volume and the perimeter.","authors_text":"Nicolas Curien, Omer Angel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-22T20:56:40Z","title":"Percolations on random maps I: half-plane models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5311","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":"sha256:7146042852dfc059f4652ea567935cddbae68477c56e3ba9acac2cd488be9532","target":"record","created_at":"2026-05-18T03:35:52Z","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":"0ce56651a8445c2cac7460d7d1fc97f85e84957020156a459ada794c7a330f47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-22T20:56:40Z","title_canon_sha256":"e8bf653c20e8f14845e90157c75c36d56c1cbf57d11d1d199a5b7aa574a3b8da"},"schema_version":"1.0","source":{"id":"1301.5311","kind":"arxiv","version":1}},"canonical_sha256":"1b5a383490c650b8b78a4e30c7c37e651d9c8362ead860b288df9a65b63158e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b5a383490c650b8b78a4e30c7c37e651d9c8362ead860b288df9a65b63158e0","first_computed_at":"2026-05-18T03:35:52.289640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:52.289640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fimXpbiQI3FL1E5sCx8yheEErZdykE22P4kFA3XjYDEmRirAVaCVUA80OQn3ci1XrUdGBQKWrnfKgWhPSE0gAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:52.290785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7146042852dfc059f4652ea567935cddbae68477c56e3ba9acac2cd488be9532","sha256:7a71ec769f2edb973e8404d619bc0797534e5711cb1b1cae5f0c84d72d120042"],"state_sha256":"c82c60893e82c2149c57a2164d7cb64ef1980f8c2d39041bd5a2bcf324cee1ad"}