{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7ONHP66PWJM2AERWZYZSP3LQP5","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":"50037aa4b211e2114b3a6072de620977452f7053ed0b3426a8099201844dec96","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-12-14T14:24:05Z","title_canon_sha256":"2ffcd13ba5b9dc727c22402508c05de01acf1375484b01f5183cbab8f26ee14f"},"schema_version":"1.0","source":{"id":"1912.06855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.06855","created_at":"2026-07-05T00:26:16Z"},{"alias_kind":"arxiv_version","alias_value":"1912.06855v1","created_at":"2026-07-05T00:26:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.06855","created_at":"2026-07-05T00:26:16Z"},{"alias_kind":"pith_short_12","alias_value":"7ONHP66PWJM2","created_at":"2026-07-05T00:26:16Z"},{"alias_kind":"pith_short_16","alias_value":"7ONHP66PWJM2AERW","created_at":"2026-07-05T00:26:16Z"},{"alias_kind":"pith_short_8","alias_value":"7ONHP66P","created_at":"2026-07-05T00:26:16Z"}],"graph_snapshots":[{"event_id":"sha256:18bda1dae1cbe0e70b37ff1103ba8d9aab55c922397761efd33ab48f7a390d8d","target":"graph","created_at":"2026-07-05T00:26:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.06855/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general map-mobile bijection, we compute the three-point function of quadrangulations, before discussing the connection with continued fractions. Chapter 2 presents the slice decomposition, a unified bijective approach that applies notably to irreducible maps. Chapter 3 concerns the $O(n)$ loop model on planar maps: by a combinatorial decomposition, we obtain the phase diagr","authors_text":"J\\'er\\'emie Bouttier","cross_cats":["math.CO","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-12-14T14:24:05Z","title":"Planar maps and random partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.06855","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:d9f0aecb2e912ef03bacdda2d787b704e6218fafac752060f8c443fa414d50ba","target":"record","created_at":"2026-07-05T00:26:16Z","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":"50037aa4b211e2114b3a6072de620977452f7053ed0b3426a8099201844dec96","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-12-14T14:24:05Z","title_canon_sha256":"2ffcd13ba5b9dc727c22402508c05de01acf1375484b01f5183cbab8f26ee14f"},"schema_version":"1.0","source":{"id":"1912.06855","kind":"arxiv","version":1}},"canonical_sha256":"fb9a77fbcfb259a01236ce3327ed707f78f26763a225e4ca48128e2809ec5e60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb9a77fbcfb259a01236ce3327ed707f78f26763a225e4ca48128e2809ec5e60","first_computed_at":"2026-07-05T00:26:16.071929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:26:16.071929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HKM90P4Fuis1PdneCt6GaKOtuXNEbG3ybl+Ig2OE1EGyo4msKVtZIftVM9Eo2+J8B3atxueZ+ZZO9CHbBfqjAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:26:16.072302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.06855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9f0aecb2e912ef03bacdda2d787b704e6218fafac752060f8c443fa414d50ba","sha256:18bda1dae1cbe0e70b37ff1103ba8d9aab55c922397761efd33ab48f7a390d8d"],"state_sha256":"cd1fd80858eb52aedf809fdcd051933c1a5d37113569f6e7f8a9f71483bd4038"}