{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JZ4T6H2QWIHBVIRWRALFEMK6S6","short_pith_number":"pith:JZ4T6H2Q","schema_version":"1.0","canonical_sha256":"4e793f1f50b20e1aa236881652315e97aff2d762bc6fd92fd87a9eb355e61e7e","source":{"kind":"arxiv","id":"1105.4842","version":2},"attestation_state":"computed","paper":{"title":"Uniqueness and universality of the Brownian map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Le Gall","submitted_at":"2011-05-24T17:34:48Z","abstract_excerpt":"We consider a random planar map $M_n$ which is uniformly distributed over the class of all rooted q-angulations with n faces. We let $\\mathbf{m}_n$ be the vertex set of $M_n$, which is equipped with the graph distance $d_\\mathrm{gr}$. Both when $q\\geq4$ is an even integer and when q=3, there exists a positive constant $c_q$ such that the rescaled metric spaces $(\\mathbf{m}_n,c_qn^{-1/4}d_\\mathrm{gr})$ converge in distribution in the Gromov-Hausdorff sense, toward a universal limit called the Brownian map. The particular case of triangulations solves a question of Schramm."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.4842","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-24T17:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"46f6d9cf010a02ee132efc8e438cdef1660f95ea97a675d989fe4cefe19c0e7b","abstract_canon_sha256":"492b9d87eb9160a0ea6c1cdfa28e7c15177871c2d047099888d034039da792a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:35.554056Z","signature_b64":"AFWYfkTXYDWNSR/GuKpZKzR989uum2SdWGp8UduCxU9zE0JtUypJCB2ZpEGZ6Z4l2KBhjYYQdQtMPfMZ/DOOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e793f1f50b20e1aa236881652315e97aff2d762bc6fd92fd87a9eb355e61e7e","last_reissued_at":"2026-05-18T03:17:35.553574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:35.553574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness and universality of the Brownian map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Le Gall","submitted_at":"2011-05-24T17:34:48Z","abstract_excerpt":"We consider a random planar map $M_n$ which is uniformly distributed over the class of all rooted q-angulations with n faces. We let $\\mathbf{m}_n$ be the vertex set of $M_n$, which is equipped with the graph distance $d_\\mathrm{gr}$. Both when $q\\geq4$ is an even integer and when q=3, there exists a positive constant $c_q$ such that the rescaled metric spaces $(\\mathbf{m}_n,c_qn^{-1/4}d_\\mathrm{gr})$ converge in distribution in the Gromov-Hausdorff sense, toward a universal limit called the Brownian map. The particular case of triangulations solves a question of Schramm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4842","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.4842","created_at":"2026-05-18T03:17:35.553651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.4842v2","created_at":"2026-05-18T03:17:35.553651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4842","created_at":"2026-05-18T03:17:35.553651+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZ4T6H2QWIHB","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZ4T6H2QWIHBVIRW","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZ4T6H2Q","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.05573","citing_title":"Random surfaces and Liouville quantum gravity","ref_index":47,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6","json":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6.json","graph_json":"https://pith.science/api/pith-number/JZ4T6H2QWIHBVIRWRALFEMK6S6/graph.json","events_json":"https://pith.science/api/pith-number/JZ4T6H2QWIHBVIRWRALFEMK6S6/events.json","paper":"https://pith.science/paper/JZ4T6H2Q"},"agent_actions":{"view_html":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6","download_json":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6.json","view_paper":"https://pith.science/paper/JZ4T6H2Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.4842&json=true","fetch_graph":"https://pith.science/api/pith-number/JZ4T6H2QWIHBVIRWRALFEMK6S6/graph.json","fetch_events":"https://pith.science/api/pith-number/JZ4T6H2QWIHBVIRWRALFEMK6S6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6/action/storage_attestation","attest_author":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6/action/author_attestation","sign_citation":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6/action/citation_signature","submit_replication":"https://pith.science/pith/JZ4T6H2QWIHBVIRWRALFEMK6S6/action/replication_record"}},"created_at":"2026-05-18T03:17:35.553651+00:00","updated_at":"2026-05-18T03:17:35.553651+00:00"}