{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:774HSAKY2RPRRD7VK5EUA3DJUR","short_pith_number":"pith:774HSAKY","schema_version":"1.0","canonical_sha256":"fff8790158d45f188ff55749406c69a46efc0efbe67f4e63085d5a98f95d4be6","source":{"kind":"arxiv","id":"1905.01873","version":1},"attestation_state":"computed","paper":{"title":"Scaling limits for random triangulations on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"cs.DM","authors_text":"Benjamin L\\'ev\\^eque, Cong Bang Huynh, Vincent Beffara","submitted_at":"2019-05-06T08:23:23Z","abstract_excerpt":"We study the scaling limit of essentially simple triangulations on the torus. We consider, for every $n\\geq 1$, a uniformly random triangulation $G_n$ over the set of (appropriately rooted) essentially simple triangulations on the torus with $n$ vertices. We view $G_n$ as a metric space by endowing its set of vertices with the graph distance denoted by $d_{G_n}$ and show that the random metric space $(V(G_n),n^{-1/4}d_{G_n})$ converges in distribution in the Gromov-Hausdorff sense when $n$ goes to infinity, at least along subsequences, toward a random metric space. One of the crucial steps in "},"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":"1905.01873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-05-06T08:23:23Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"c683e24d64f6afee2002218653ddfa682db75043ef349442ba0bb3b35c64ef17","abstract_canon_sha256":"7d2c6757088cda2ab8236cfb144ee5389f0c368219beebbd40b4f50750b94112"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:57.169356Z","signature_b64":"hGqjc5Ou6+jWJ2RxoPPa1et5tI5CJWta+3oqvYUYZG/q+O5rNSgK8xOy7Mz1ANa6OplAQ5Lceqp6EZ77JIcXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fff8790158d45f188ff55749406c69a46efc0efbe67f4e63085d5a98f95d4be6","last_reissued_at":"2026-05-17T23:46:57.168731Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:57.168731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling limits for random triangulations on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"cs.DM","authors_text":"Benjamin L\\'ev\\^eque, Cong Bang Huynh, Vincent Beffara","submitted_at":"2019-05-06T08:23:23Z","abstract_excerpt":"We study the scaling limit of essentially simple triangulations on the torus. We consider, for every $n\\geq 1$, a uniformly random triangulation $G_n$ over the set of (appropriately rooted) essentially simple triangulations on the torus with $n$ vertices. We view $G_n$ as a metric space by endowing its set of vertices with the graph distance denoted by $d_{G_n}$ and show that the random metric space $(V(G_n),n^{-1/4}d_{G_n})$ converges in distribution in the Gromov-Hausdorff sense when $n$ goes to infinity, at least along subsequences, toward a random metric space. One of the crucial steps in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01873","kind":"arxiv","version":1},"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":"1905.01873","created_at":"2026-05-17T23:46:57.168845+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.01873v1","created_at":"2026-05-17T23:46:57.168845+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01873","created_at":"2026-05-17T23:46:57.168845+00:00"},{"alias_kind":"pith_short_12","alias_value":"774HSAKY2RPR","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"774HSAKY2RPRRD7V","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"774HSAKY","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR","json":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR.json","graph_json":"https://pith.science/api/pith-number/774HSAKY2RPRRD7VK5EUA3DJUR/graph.json","events_json":"https://pith.science/api/pith-number/774HSAKY2RPRRD7VK5EUA3DJUR/events.json","paper":"https://pith.science/paper/774HSAKY"},"agent_actions":{"view_html":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR","download_json":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR.json","view_paper":"https://pith.science/paper/774HSAKY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.01873&json=true","fetch_graph":"https://pith.science/api/pith-number/774HSAKY2RPRRD7VK5EUA3DJUR/graph.json","fetch_events":"https://pith.science/api/pith-number/774HSAKY2RPRRD7VK5EUA3DJUR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR/action/storage_attestation","attest_author":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR/action/author_attestation","sign_citation":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR/action/citation_signature","submit_replication":"https://pith.science/pith/774HSAKY2RPRRD7VK5EUA3DJUR/action/replication_record"}},"created_at":"2026-05-17T23:46:57.168845+00:00","updated_at":"2026-05-17T23:46:57.168845+00:00"}