{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AKGILLV2GOBPLYMZCKYS6SZINH","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":"97048d3179c3fd87c3fec8b2c65045a86bc7c0eee64266a36ae6481754f764c6","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-09-05T20:28:29Z","title_canon_sha256":"a2c5b4411f46bedeeaff3ade0cbbb2ba095123152c3376f1d917bbe0fbade2fc"},"schema_version":"1.0","source":{"id":"2509.05487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05487","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05487v1","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05487","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"AKGILLV2GOBP","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"AKGILLV2GOBPLYMZ","created_at":"2026-07-05T12:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"AKGILLV2","created_at":"2026-07-05T12:05:48Z"}],"graph_snapshots":[{"event_id":"sha256:1bc769014f518975574f89075a8dfc755885765be74ce4bf68aa30c23cda51c0","target":"graph","created_at":"2026-07-05T12:05:48Z","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/2509.05487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a hyperpfaffian formulation for correlation functions in $\\beta$-ensembles of $M \\times M$ random matrices when $\\beta = L^2$ is an even square integer. More specifically, to the $m$th correlation function $R_m : \\R^m \\rightarrow [0, \\infty)$ we associate the $L$-vector valued function $\\omega_m : \\R^m \\rightarrow \\Lambda^L \\R^{L(M-m)}$ such that $R_m(\\mathbf y)$ is given by the Vandermonde determinant in $y_1, \\ldots, y_M$ times the hyperpfaffian of $\\omega_m.$ The partition function of the ensemble was previously shown to be the hyperpfaffian of a {\\it Gram} $L$-form $\\omega$ in $\\La","authors_text":"Christopher D. Sinclair, Jonathan M. Wells","cross_cats":["math.CO","math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05487","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:d5525728caa71eb4bc77fa38bce44df53c80f81d4410c057e1e4d3fb1dfef139","target":"record","created_at":"2026-07-05T12:05:48Z","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":"97048d3179c3fd87c3fec8b2c65045a86bc7c0eee64266a36ae6481754f764c6","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-09-05T20:28:29Z","title_canon_sha256":"a2c5b4411f46bedeeaff3ade0cbbb2ba095123152c3376f1d917bbe0fbade2fc"},"schema_version":"1.0","source":{"id":"2509.05487","kind":"arxiv","version":1}},"canonical_sha256":"028c85aeba3382f5e19912b12f4b2869decf330e2860116d199de205a1cdc6a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"028c85aeba3382f5e19912b12f4b2869decf330e2860116d199de205a1cdc6a6","first_computed_at":"2026-07-05T12:05:48.410907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:48.410907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nbEhvLFTjsEvkFhtoLv8KcbYUxKcgacc6We+b4SHUr9kW79GiPCjSAZvEz577yeWlSmcuKF3j+KrQEW/hJD2BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:48.411392Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.05487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5525728caa71eb4bc77fa38bce44df53c80f81d4410c057e1e4d3fb1dfef139","sha256:1bc769014f518975574f89075a8dfc755885765be74ce4bf68aa30c23cda51c0"],"state_sha256":"3db3123e5dc9ebde6f0be38a0e7a568d8a89f569274cb20a6d33e8e6dd9f0d01"}