{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FTD6ZENJOAG3CMLOEUMBRPQZDT","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":"e1539d039be98db0bbcc24c800f68fb7095fc1fae37cb7878ef4b498381480ce","cross_cats_sorted":["cond-mat.dis-nn","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-08-19T17:00:35Z","title_canon_sha256":"a84efecc830a4c7035d5033261c4b35ca82025806ece71f83fbe8c4dfd962396"},"schema_version":"1.0","source":{"id":"1708.05876","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05876","created_at":"2026-05-18T00:32:39Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05876v2","created_at":"2026-05-18T00:32:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05876","created_at":"2026-05-18T00:32:39Z"},{"alias_kind":"pith_short_12","alias_value":"FTD6ZENJOAG3","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FTD6ZENJOAG3CMLO","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FTD6ZENJ","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:07dd5d7caf3614e398d3c5b9230502991efb5ded8dd12c60cd03af2847289a61","target":"graph","created_at":"2026-05-18T00:32:39Z","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 use invasion percolation to compute numerical values for bond and site percolation thresholds $p_c$ (existence of an infinite cluster) and $p_u$ (uniqueness of the infinite cluster) of tesselations $\\{P,Q\\}$ of the hyperbolic plane, where $Q$ faces meet at each vertex and each face is a $P$-gon. Our values are accurate to six or seven decimal places, allowing us to explore their functional dependency on $P$ and $Q$ and to numerically compute critical exponents. We also prove rigorous upper and lower bounds for $p_c$ and $p_u$ that can be used to find the scaling of both thresholds as a func","authors_text":"Cristopher Moore, Stephan Mertens","cross_cats":["cond-mat.dis-nn","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-08-19T17:00:35Z","title":"Percolation Thresholds in Hyperbolic Lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05876","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":"sha256:6a0b0add51e34e93de4092dacd827f0cd704f6692609dc8c254454a2a4688397","target":"record","created_at":"2026-05-18T00:32:39Z","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":"e1539d039be98db0bbcc24c800f68fb7095fc1fae37cb7878ef4b498381480ce","cross_cats_sorted":["cond-mat.dis-nn","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-08-19T17:00:35Z","title_canon_sha256":"a84efecc830a4c7035d5033261c4b35ca82025806ece71f83fbe8c4dfd962396"},"schema_version":"1.0","source":{"id":"1708.05876","kind":"arxiv","version":2}},"canonical_sha256":"2cc7ec91a9700db1316e251818be191ce236c2a3ea4c330ba7feb871f59e4be6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cc7ec91a9700db1316e251818be191ce236c2a3ea4c330ba7feb871f59e4be6","first_computed_at":"2026-05-18T00:32:39.352613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:39.352613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"buCTlQDM1jgGOFvDGapWqHe/SkE/XiKtvkjTnXGJ56D/OWmCgxjLrO4VbvFnlJH6S2a6gjLE3KzsmpSW9Ya6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:39.353270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05876","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a0b0add51e34e93de4092dacd827f0cd704f6692609dc8c254454a2a4688397","sha256:07dd5d7caf3614e398d3c5b9230502991efb5ded8dd12c60cd03af2847289a61"],"state_sha256":"f55b9afb41f37da5b85f5a1642cf80f63b3fe27d9f09a2949d7f179cedd9a54d"}