{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YEQAJ4IRCNNYTQT2FAUTPS2TY7","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":"f6306efd7dd5e8e8d9fc85c351937ffe16a3e1e17433a4bef186d234e7e45696","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T12:08:36Z","title_canon_sha256":"76f372f1bf62f8f5b399585d959b1b4cc2058462d57daddf0f2059de16d9074c"},"schema_version":"1.0","source":{"id":"1507.04538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04538","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04538v1","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04538","created_at":"2026-05-18T00:30:22Z"},{"alias_kind":"pith_short_12","alias_value":"YEQAJ4IRCNNY","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YEQAJ4IRCNNYTQT2","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YEQAJ4IR","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:a04bd90fc6136ad10f8415b15a13d3446f6acaddd0670a1aa36b6230ae611a72","target":"graph","created_at":"2026-05-18T00:30:22Z","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 use a continued fraction approach to compare two statistical ensembles of quadrangulations with a boundary, both controlled by two parameters. In the first ensemble, the quadrangulations are bicolored and the parameters control their numbers of vertices of both colors. In the second ensemble, the parameters control instead the number of vertices which are local maxima for the distance to a given vertex, and the number of those which are not. Both ensembles may be described either by their (bivariate) generating functions at fixed boundary length or, after some standard slice decomposition, ","authors_text":"Emmanuel Guitter, \\'Eric Fusy","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T12:08:36Z","title":"Comparing two statistical ensembles of quadrangulations: a continued fraction approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04538","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":"sha256:6387dd39577815e94be7f83623401ea5fa11b24551bd96d9514ceb1ceba5a405","target":"record","created_at":"2026-05-18T00:30:22Z","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":"f6306efd7dd5e8e8d9fc85c351937ffe16a3e1e17433a4bef186d234e7e45696","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-16T12:08:36Z","title_canon_sha256":"76f372f1bf62f8f5b399585d959b1b4cc2058462d57daddf0f2059de16d9074c"},"schema_version":"1.0","source":{"id":"1507.04538","kind":"arxiv","version":1}},"canonical_sha256":"c12004f111135b89c27a282937cb53c7d75f3b68605cad846a39ad6ecc208e09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c12004f111135b89c27a282937cb53c7d75f3b68605cad846a39ad6ecc208e09","first_computed_at":"2026-05-18T00:30:22.773233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:22.773233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cWfbhWHuQ9qN8quAYaxwZZpeyZMkzhCBdn9UJUic4bNFcdVw4ql3jh+jEZdF7rTKI3bLYr/gCKcOSiXEyOltAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:22.773868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6387dd39577815e94be7f83623401ea5fa11b24551bd96d9514ceb1ceba5a405","sha256:a04bd90fc6136ad10f8415b15a13d3446f6acaddd0670a1aa36b6230ae611a72"],"state_sha256":"ed5d8f5f112f12edfb133facce4958ae4a8c4f9d804467c97139ac03a33ef26b"}