{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3LL2HIC4OMS7IJSCAGW42VGZJ3","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":"fddfecc721a1522705bf1b405aa209c30626c497f2fa62e1baebfd96ca4db0d3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-23T14:39:48Z","title_canon_sha256":"6d601ccc87324415b917bf202a363ec34cb12e5d9d722ae9692df40da58239b2"},"schema_version":"1.0","source":{"id":"1702.07230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07230","created_at":"2026-05-18T00:50:07Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07230v1","created_at":"2026-05-18T00:50:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07230","created_at":"2026-05-18T00:50:07Z"},{"alias_kind":"pith_short_12","alias_value":"3LL2HIC4OMS7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LL2HIC4OMS7IJSC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LL2HIC4","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:cf17889b61a4191dd8b686877a8a4ebc4f62342d3f41d2bf55a69b91a8ddb285","target":"graph","created_at":"2026-05-18T00:50:07Z","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":"The partition function of the Penner matrix model for both positive and negative values of the coupling constant can be explicitly written in terms of the Barnes G function. In this paper we show that for negative values of the coupling constant this partition function can also be represented as the product of an holomorphic matrix integral by a nontrivial oscillatory function of n. We show that the planar limit of the free energy with 't Hooft sequences does not exist. Therefore we use a certain modification that uses Kuijlaars-McLaughlin sequences instead of 't Hooft sequences and leads to a","authors_text":"Elena Medina, Gabriel \\'Alvarez, Luis Mart\\'inez Alonso","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-23T14:39:48Z","title":"Phase space and phase transitions in the Penner matrix model with negative coupling constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07230","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:a8d26ec774a8c7de046fd2600ea604ddcc517725f93dabe301164d4406582817","target":"record","created_at":"2026-05-18T00:50:07Z","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":"fddfecc721a1522705bf1b405aa209c30626c497f2fa62e1baebfd96ca4db0d3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-23T14:39:48Z","title_canon_sha256":"6d601ccc87324415b917bf202a363ec34cb12e5d9d722ae9692df40da58239b2"},"schema_version":"1.0","source":{"id":"1702.07230","kind":"arxiv","version":1}},"canonical_sha256":"dad7a3a05c7325f4264201adcd54d94edddca44da7587333affe1d88d1a6840f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dad7a3a05c7325f4264201adcd54d94edddca44da7587333affe1d88d1a6840f","first_computed_at":"2026-05-18T00:50:07.801876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:07.801876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9cuXGozq1l/aqEwOopRibK7W3DX29DUcTWle8AXJbpcLuiw3w4+6BdSXdNhcKvyIMhhMi6eveqvHoDoVCvyWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:07.802539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.07230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8d26ec774a8c7de046fd2600ea604ddcc517725f93dabe301164d4406582817","sha256:cf17889b61a4191dd8b686877a8a4ebc4f62342d3f41d2bf55a69b91a8ddb285"],"state_sha256":"09a86d56401dc8e83b5e6ccfed48d190da6dc531d2b3e2dc3a60a68f5ef4d031"}