{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AEDZSUF25ZXGWEEVWMKBPLZ3E6","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":"6ce5c8aac7e151c971849bb8411061930f0ebe7b4228b52a74c14c4233bfb6e1","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-01-30T18:35:20Z","title_canon_sha256":"5532e9a097dacc45026d6c23bdb9c964cc895f6cd5887ad97222d4696e7f74ec"},"schema_version":"1.0","source":{"id":"2301.13157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.13157","created_at":"2026-07-05T10:49:02Z"},{"alias_kind":"arxiv_version","alias_value":"2301.13157v2","created_at":"2026-07-05T10:49:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.13157","created_at":"2026-07-05T10:49:02Z"},{"alias_kind":"pith_short_12","alias_value":"AEDZSUF25ZXG","created_at":"2026-07-05T10:49:02Z"},{"alias_kind":"pith_short_16","alias_value":"AEDZSUF25ZXGWEEV","created_at":"2026-07-05T10:49:02Z"},{"alias_kind":"pith_short_8","alias_value":"AEDZSUF2","created_at":"2026-07-05T10:49:02Z"}],"graph_snapshots":[{"event_id":"sha256:01a8175470d857f76610f820401d1e55952c75623c371ef80d50fd5eaa217ca2","target":"graph","created_at":"2026-07-05T10:49:02Z","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/2301.13157/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a smooth, projective, and geometrically connected curve defined over a finite field $\\mathbb{F}_q$ of characteristic $p$ different from $2$ and $S\\subseteq X$ a subset of closed points. Let $\\overline{X}$ and $\\overline{S}$ be their base changes to an algebraic closure of $\\mathbb{F}_q$. We study the number of $\\ell$-adic local systems $(\\ell\\neq p)$ in rank $2$ over $\\overline{X}-\\overline{S}$ with all possible prescribed tame local monodromies fixed by $k$-fold iterated action of Frobenius endomorphism for every $k\\geq 1$. In all cases, we confirm conjectures of Deligne predicting","authors_text":"Hongjie Yu","cross_cats":["math.NT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-01-30T18:35:20Z","title":"Rank 2 $\\ell$-adic local systems and Higgs bundles over a curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.13157","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:eae217ef8d89eb7024feaf4117d30989921b6de89d43f6f11012922e41d7ef0e","target":"record","created_at":"2026-07-05T10:49:02Z","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":"6ce5c8aac7e151c971849bb8411061930f0ebe7b4228b52a74c14c4233bfb6e1","cross_cats_sorted":["math.NT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-01-30T18:35:20Z","title_canon_sha256":"5532e9a097dacc45026d6c23bdb9c964cc895f6cd5887ad97222d4696e7f74ec"},"schema_version":"1.0","source":{"id":"2301.13157","kind":"arxiv","version":2}},"canonical_sha256":"01079950baee6e6b1095b31417af3b27bb0cef1c31f5b51d622fb768d1c920d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01079950baee6e6b1095b31417af3b27bb0cef1c31f5b51d622fb768d1c920d3","first_computed_at":"2026-07-05T10:49:02.335878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:49:02.335878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sMoGDJO7HAxejFKXiICEMQoxBb00xMCORWEg2+SIyLj81eEYaKfmVZznnOWbs7FhYdenNIdBdOusmmqe/vAjCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:49:02.336487Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.13157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eae217ef8d89eb7024feaf4117d30989921b6de89d43f6f11012922e41d7ef0e","sha256:01a8175470d857f76610f820401d1e55952c75623c371ef80d50fd5eaa217ca2"],"state_sha256":"1562051d16c648025a90ac40b43c3213fa6f7cc768c49d854a4e41eaeef98d9b"}