{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:KSCJZGQ5CT6HODNQRIYQETQRMT","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":"be62011ff9f171c97912a57eeede01e3b31bf715aa610e18cf2e72476dc691c4","cross_cats_sorted":["math.AG","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1998-11-25T09:05:37Z","title_canon_sha256":"2dddd81e17d893b4c271a97f9b625b40afca24a21ed8d413f25f7e9dda18fb0e"},"schema_version":"1.0","source":{"id":"math-ph/9811024","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9811024","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9811024v2","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9811024","created_at":"2026-05-18T04:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"KSCJZGQ5CT6H","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"KSCJZGQ5CT6HODNQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"KSCJZGQ5","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:420825be1c6d6789d3760895ff6423256ec22206df8e6cae3be200429cd54d85","target":"graph","created_at":"2026-05-18T04:39:51Z","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":"It is well known that there is a bijective correspondence between metric ribbon graphs and compact Riemann surfaces with meromorphic Strebel differentials. In this article, it is proved that Grothendieck's correspondence between dessins d'enfants and Belyi morphisms is a special case of this correspondence. For a metric ribbon graph with edge length 1, an algebraic curve over $\\bar Q$ and a Strebel differential on it is constructed. It is also shown that the critical trajectories of the measured foliation that is determined by the Strebel differential recover the original metric ribbon graph. ","authors_text":"Michael Penkava, Motohico Mulase","cross_cats":["math.AG","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"1998-11-25T09:05:37Z","title":"Ribbon Graphs, Quadratic Differentials on Riemann Surfaces, and Algebraic Curves Defined over $\\bar Q$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9811024","kind":"arxiv","version":2},"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":"sha256:93f059d167504720d5f61b8804785fe4084775c3d89c94325340dff1a782b863","target":"record","created_at":"2026-05-18T04:39:51Z","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":"be62011ff9f171c97912a57eeede01e3b31bf715aa610e18cf2e72476dc691c4","cross_cats_sorted":["math.AG","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1998-11-25T09:05:37Z","title_canon_sha256":"2dddd81e17d893b4c271a97f9b625b40afca24a21ed8d413f25f7e9dda18fb0e"},"schema_version":"1.0","source":{"id":"math-ph/9811024","kind":"arxiv","version":2}},"canonical_sha256":"54849c9a1d14fc770db08a31024e1164e2d5387ee5e56638422605c937d8d431","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54849c9a1d14fc770db08a31024e1164e2d5387ee5e56638422605c937d8d431","first_computed_at":"2026-05-18T04:39:51.566569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:51.566569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CnGIYa3IPzCtrgDRJ4UvhgQ64KNWIRW2hB26Kjd/McOMA58pz3BjIR113DEyuTAX0J2n/UuIX2QUcfdGXQwvDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:51.567134Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/9811024","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93f059d167504720d5f61b8804785fe4084775c3d89c94325340dff1a782b863","sha256:420825be1c6d6789d3760895ff6423256ec22206df8e6cae3be200429cd54d85"],"state_sha256":"4452e432347d80347d64221474ef8d50ce7997e9be9590f5a0aa54d305155dbe"}