{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:STJORQKWKEWTIRBR5UNIW52RJ7","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":"a2b49ae8c0bfa83738282b616e2270173fdc580062cbd46f520cf55c5d19b525","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-05-22T21:29:31Z","title_canon_sha256":"fce94bfd3a9bfedf0244e7bda13a1e4a0b266bb2c8f5b13fdcaf7f4a76eaef9a"},"schema_version":"1.0","source":{"id":"2605.24237","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24237","created_at":"2026-05-26T01:02:54Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24237v1","created_at":"2026-05-26T01:02:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24237","created_at":"2026-05-26T01:02:54Z"},{"alias_kind":"pith_short_12","alias_value":"STJORQKWKEWT","created_at":"2026-05-26T01:02:54Z"},{"alias_kind":"pith_short_16","alias_value":"STJORQKWKEWTIRBR","created_at":"2026-05-26T01:02:54Z"},{"alias_kind":"pith_short_8","alias_value":"STJORQKW","created_at":"2026-05-26T01:02:54Z"}],"graph_snapshots":[{"event_id":"sha256:205531eb5571136f438876b0ecfc1e96c1f4873d75644a6771979aa5bda65188","target":"graph","created_at":"2026-05-26T01:02:54Z","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/2605.24237/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The genus--g Fuss--Catalan (FC) number counts the number of ways to obtain a genus-g surface by identifying the edges of a pn--gon via p-valent hyperedges. For p=2 these are the genus--g Catalan numbers which are generated as the trace correlations in the Gaussian matrix model (GUE). Here we construct a simple two-matrix model which generates the higher-genus Fuss--Catalan numbers for any p as the coefficients of its 1/N-expansion. We obtain exact sum rules and an explicit formula for the higher-genus Fuss--Catalan numbers which generalises the Harer--Zagier formula to p>2. We discuss the rela","authors_text":"Anatol Kirillov, Ivan Kostov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-05-22T21:29:31Z","title":"A Matrix Model for Higher-Genus Fuss--Catalan Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24237","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":"sha256:47a92882c6123f5cd43af52f52eac393ce5529c3576471503e58aa7d85128b4a","target":"record","created_at":"2026-05-26T01:02:54Z","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":"a2b49ae8c0bfa83738282b616e2270173fdc580062cbd46f520cf55c5d19b525","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-05-22T21:29:31Z","title_canon_sha256":"fce94bfd3a9bfedf0244e7bda13a1e4a0b266bb2c8f5b13fdcaf7f4a76eaef9a"},"schema_version":"1.0","source":{"id":"2605.24237","kind":"arxiv","version":1}},"canonical_sha256":"94d2e8c156512d344431ed1a8b77514fe44efd342d58d41e4100baf81cda3689","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94d2e8c156512d344431ed1a8b77514fe44efd342d58d41e4100baf81cda3689","first_computed_at":"2026-05-26T01:02:54.190157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:02:54.190157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yEaEBeoXrPwNODk2QuSOK0u3/710qoyAShFBPUWAHWFfHNfQ4i7R27t7sdxpR98Vjo1eY74+00czJSmFTAodAg==","signature_status":"signed_v1","signed_at":"2026-05-26T01:02:54.190845Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24237","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47a92882c6123f5cd43af52f52eac393ce5529c3576471503e58aa7d85128b4a","sha256:205531eb5571136f438876b0ecfc1e96c1f4873d75644a6771979aa5bda65188"],"state_sha256":"7aa48f20e386444b0fdb0410beb283ebf221d24856528d33235e9001d17015ba"}