{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T7MSZ2OS6R2YKE5WVA5676CWJP","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":"f0359f89481323114a5b2721079ac4fb83218eca056c737c5ff23e968255983e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T09:37:19Z","title_canon_sha256":"228b60898195d01ff522462ab229d2c19162301fc34d193577fe5aa917c754a5"},"schema_version":"1.0","source":{"id":"1403.3514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3514","created_at":"2026-05-18T01:36:38Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3514v1","created_at":"2026-05-18T01:36:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3514","created_at":"2026-05-18T01:36:38Z"},{"alias_kind":"pith_short_12","alias_value":"T7MSZ2OS6R2Y","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T7MSZ2OS6R2YKE5W","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T7MSZ2OS","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:f85165235d41e056603da2b974246a0f1047caa4d3bab0dd2e5f4354999e66f7","target":"graph","created_at":"2026-05-18T01:36:38Z","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 compute the distance-dependent three-point function of general planar maps and of bipartite planar maps, i.e., the generating function of these maps with three marked vertices at prescribed pairwise distances. Explicit expressions are given for maps counted by their number of edges only, or by both their numbers of edges and faces. A few limiting cases and applications are discussed.","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":"2014-03-14T09:37:19Z","title":"The three-point function of general planar maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3514","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":"sha256:549b0f8c2e144ffbbe21ed697ecb1f8852263b1decc45e7b9b3dd828d23e49c6","target":"record","created_at":"2026-05-18T01:36:38Z","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":"f0359f89481323114a5b2721079ac4fb83218eca056c737c5ff23e968255983e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T09:37:19Z","title_canon_sha256":"228b60898195d01ff522462ab229d2c19162301fc34d193577fe5aa917c754a5"},"schema_version":"1.0","source":{"id":"1403.3514","kind":"arxiv","version":1}},"canonical_sha256":"9fd92ce9d2f4758513b6a83beff8564bc097af2ddab9d0fa097938698b2fe707","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fd92ce9d2f4758513b6a83beff8564bc097af2ddab9d0fa097938698b2fe707","first_computed_at":"2026-05-18T01:36:38.929970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:38.929970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Bu2h3CFED1LK6sMoK2LBbbTetqJ0K0Uqro1Vi8oIosFlevCOg0L9S2RIDg1grZJHkkELj1Mb5wi0n8daPM5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:38.930849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:549b0f8c2e144ffbbe21ed697ecb1f8852263b1decc45e7b9b3dd828d23e49c6","sha256:f85165235d41e056603da2b974246a0f1047caa4d3bab0dd2e5f4354999e66f7"],"state_sha256":"78b3804320c4c700b5f458f91dd5edf03e20a4de5b7f795d23fc062f7619e776"}