{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SHGYCK6PG5HWEYIH6LAIVMGTDY","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":"504aa1a09a66dfa592a2771be051cec69e4146ba0014548c2a9c30e455a9985f","cross_cats_sorted":["hep-th","math.CA","math.MP","math.RT","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-05-22T15:43:58Z","title_canon_sha256":"68fc47049cc22aaec3f7e30c492edb66a69485e43d30d5dbab4a869f51a2e906"},"schema_version":"1.0","source":{"id":"2505.16803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.16803","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.16803v1","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.16803","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_12","alias_value":"SHGYCK6PG5HW","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_16","alias_value":"SHGYCK6PG5HWEYIH","created_at":"2026-07-05T11:23:28Z"},{"alias_kind":"pith_short_8","alias_value":"SHGYCK6P","created_at":"2026-07-05T11:23:28Z"}],"graph_snapshots":[{"event_id":"sha256:0bbc8de63409f2e5e546d750d7ecfa7ffe0bb3637a09a61e5b671c5e622e3022","target":"graph","created_at":"2026-07-05T11:23:28Z","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/2505.16803/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In recent years, the Fourier series (Zak transform) structure of the Painlev\\'e I tau function has emerged in multiple contexts. Its main building block admits several conjectural interpretations, such as the partition function of an Argyres-Douglas gauge theory, the topological recursion partition function for the Weierstrass elliptic curve, and a 1-point conformal block on the Riemann sphere with an irregular insertion of rank $\\frac52$. We review and further develop a mathematical framework for these constructions, and formulate conjectures on their equivalence. In particular, we give a sim","authors_text":"Kohei Iwaki, Nikolai Iorgov, Oleg Lisovyy, Yurii Zhuravlov","cross_cats":["hep-th","math.CA","math.MP","math.RT","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-05-22T15:43:58Z","title":"Many-faced Painlev\\'e I: irregular conformal blocks, topological recursion, and holomorphic anomaly approaches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16803","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":"sha256:99ffeb469ea0033c6ca38529f547bdc189e42375d9cb94a9c6917ed73fc3b00d","target":"record","created_at":"2026-07-05T11:23:28Z","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":"504aa1a09a66dfa592a2771be051cec69e4146ba0014548c2a9c30e455a9985f","cross_cats_sorted":["hep-th","math.CA","math.MP","math.RT","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-05-22T15:43:58Z","title_canon_sha256":"68fc47049cc22aaec3f7e30c492edb66a69485e43d30d5dbab4a869f51a2e906"},"schema_version":"1.0","source":{"id":"2505.16803","kind":"arxiv","version":1}},"canonical_sha256":"91cd812bcf374f626107f2c08ab0d31e3e2e34cf0365ac5c7566cc01c47a1f2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91cd812bcf374f626107f2c08ab0d31e3e2e34cf0365ac5c7566cc01c47a1f2b","first_computed_at":"2026-07-05T11:23:28.405515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:23:28.405515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J55J6xkQ5kTiBeLgF5r6CpmuUgi3mf46QkVIldif4Xmy5MhKqdrzYqmlV2ydz/Bori+TZb8MhCNpFpDRFTqfBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:23:28.406020Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.16803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99ffeb469ea0033c6ca38529f547bdc189e42375d9cb94a9c6917ed73fc3b00d","sha256:0bbc8de63409f2e5e546d750d7ecfa7ffe0bb3637a09a61e5b671c5e622e3022"],"state_sha256":"d272b0f907265449da0bec5b21864402861144ade17ad36f0b7528b6796b099c"}