{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TSK4MFYISN4AOOKVFA4WTEUUSB","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":"5a12e6f7f1e6fada25e67c2bb66e288a67269d6573f58c665faa5594fb704935","cross_cats_sorted":["math.DG","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-11-20T01:49:42Z","title_canon_sha256":"35338195873b04ee1ff3cee6da55b1b6b025ee2843cf35bef65b5e6e0e467ed3"},"schema_version":"1.0","source":{"id":"2411.12971","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12971","created_at":"2026-06-09T01:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12971v2","created_at":"2026-06-09T01:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12971","created_at":"2026-06-09T01:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"TSK4MFYISN4A","created_at":"2026-06-09T01:05:04Z"},{"alias_kind":"pith_short_16","alias_value":"TSK4MFYISN4AOOKV","created_at":"2026-06-09T01:05:04Z"},{"alias_kind":"pith_short_8","alias_value":"TSK4MFYI","created_at":"2026-06-09T01:05:04Z"}],"graph_snapshots":[{"event_id":"sha256:a558bb29f4f927d58d32dfd105507c6661a70c296f827367771fd53c517287a8","target":"graph","created_at":"2026-06-09T01:05:04Z","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/2411.12971/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{M}_g$ be the moduli space of hyperbolic surfaces of genus $g$ endowed with the Weil-Petersson metric. We view the regularized determinant $\\log \\det(\\Delta_{X})$ of Laplacian as a function on $\\mathcal{M}_g$ and show that there exists a universal constant $E>0$ such that as $g\\to \\infty$,\n  (1) the expected value of $\\left|\\frac{\\log \\det(\\Delta_{X})}{4\\pi(g-1)}-E \\right|$ over $\\mathcal{M}_g$ has rate of decay $g^{-\\delta}$ for some uniform constant $\\delta \\in (0,1)$;\n  (2) the expected value of $\\left|\\frac{\\log \\det(\\Delta_{X})}{4\\pi(g-1)}\\right|^\\beta$ over $\\mathcal{M}_g$ a","authors_text":"Yunhui Wu, Yuxin He","cross_cats":["math.DG","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-11-20T01:49:42Z","title":"Averages of determinants of Laplacians over moduli spaces for large genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12971","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":"sha256:78fa620d7d06e31a4579ded87e52bf4d2c77f449139227cf4cf83cc571bab490","target":"record","created_at":"2026-06-09T01:05:04Z","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":"5a12e6f7f1e6fada25e67c2bb66e288a67269d6573f58c665faa5594fb704935","cross_cats_sorted":["math.DG","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2024-11-20T01:49:42Z","title_canon_sha256":"35338195873b04ee1ff3cee6da55b1b6b025ee2843cf35bef65b5e6e0e467ed3"},"schema_version":"1.0","source":{"id":"2411.12971","kind":"arxiv","version":2}},"canonical_sha256":"9c95c6170893780739552839699294905674d37655ccf24b84386403ed517f1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c95c6170893780739552839699294905674d37655ccf24b84386403ed517f1b","first_computed_at":"2026-06-09T01:05:04.232652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:04.232652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hEyBO7T0bUpgbg4+CJAqUGcVip/XMSlOz8gmU3pNiehwIrM9ZVd7+ieLPIK4LzN6jdJuhWBZpaY7nGTxd8CDCw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:04.233164Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.12971","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78fa620d7d06e31a4579ded87e52bf4d2c77f449139227cf4cf83cc571bab490","sha256:a558bb29f4f927d58d32dfd105507c6661a70c296f827367771fd53c517287a8"],"state_sha256":"4d1df2c79693585374f782eade6d9c0bfe619c69488ba90cec2af5b996a3672e"}