{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SU55XRS5JCEE5XXXT2QTYYPUNN","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":"3afa708ed4ade1bc8401b3ad805da5e75d4b349f9c4d3d407bfbc2c86385d094","cross_cats_sorted":["hep-th","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-11T14:29:23Z","title_canon_sha256":"1429ff095ff351bc009f82e18557c5723d126002f2d862c29f10d5187300ec91"},"schema_version":"1.0","source":{"id":"1307.3123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3123","created_at":"2026-05-18T03:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3123v2","created_at":"2026-05-18T03:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3123","created_at":"2026-05-18T03:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"SU55XRS5JCEE","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SU55XRS5JCEE5XXX","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SU55XRS5","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:cb7c189cf179b144f39ec6ebfcd6f102283512fae531c970868803a3550cfb6d","target":"graph","created_at":"2026-05-18T03:04:08Z","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":"Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point process. We show that this measure can be expressed as: (1) a sum over 3-spanning-trees partitions of the edges of the Delaunay triangulations; (2) the volume form of a K\\\"ahler metric over the space of Delaunay triangulations, whose prepotential has a simple formulation in term of ideal tessellations of the 3d hyperbolic space; (3) a discretized version (involv","authors_text":"Bertrand Eynard, Francois David","cross_cats":["hep-th","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-11T14:29:23Z","title":"Planar maps, circle patterns and 2d gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3123","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:ba82b486d8ac816b8fc502fff395967b296a7e12ba8b61a7b9e66905a387ab15","target":"record","created_at":"2026-05-18T03:04:08Z","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":"3afa708ed4ade1bc8401b3ad805da5e75d4b349f9c4d3d407bfbc2c86385d094","cross_cats_sorted":["hep-th","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-11T14:29:23Z","title_canon_sha256":"1429ff095ff351bc009f82e18557c5723d126002f2d862c29f10d5187300ec91"},"schema_version":"1.0","source":{"id":"1307.3123","kind":"arxiv","version":2}},"canonical_sha256":"953bdbc65d48884edef79ea13c61f46b5e4e68f039bdcc71822eb4f4e3036127","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"953bdbc65d48884edef79ea13c61f46b5e4e68f039bdcc71822eb4f4e3036127","first_computed_at":"2026-05-18T03:04:08.313439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:08.313439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wAFhv+xbGMbsdnx6nkm333HPaqn7HTwWoC7xrJAva28z7z/tsI51BtrR3rzgl9nZi9kwaF9ZEhAfuKgfXMXfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:08.313916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba82b486d8ac816b8fc502fff395967b296a7e12ba8b61a7b9e66905a387ab15","sha256:cb7c189cf179b144f39ec6ebfcd6f102283512fae531c970868803a3550cfb6d"],"state_sha256":"c9722ad8d20b601a20b10a3ed27423b47e9b7d31829d77c236a5624e238e9fe2"}