{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DFHL6DHO6ER4RMEPNVKUBWNTKF","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":"5b8177bccae386ddd9170a89771730547e4887a6eabde9276f855a9f6189efbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-06T13:37:42Z","title_canon_sha256":"bd66d1efb7e76c01723bb6f091af7bcf6c82e48e16022cfab886d9eeb1039906"},"schema_version":"1.0","source":{"id":"2607.05075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05075","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05075v1","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05075","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"DFHL6DHO6ER4","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"DFHL6DHO6ER4RMEP","created_at":"2026-07-07T03:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"DFHL6DHO","created_at":"2026-07-07T03:19:15Z"}],"graph_snapshots":[{"event_id":"sha256:794db327ba7f826c5022bfb935ba94958aa825bf494474a729c14865720312ea","target":"graph","created_at":"2026-07-07T03:19:15Z","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/2607.05075/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We complete the classification of exceptional rational functions of degree 5 over any finite field $\\mathbb{F}_{q}$ of characteristic different from 2 and 5, up to M\\\"obius equivalence. Our approach employs the arithmetic and geometric monodromy groups, combined with the ramification structure of the associated cover and the Riemann-Hurwitz formula. The cyclic monodromy case yields precisely monomials and R\\'edei functions, while the dihedral case is resolved by analysing its inertia groups and branch points; this leads to Dickson polynomials and a non-polynomial family arising from rational 5","authors_text":"Xiang Fan, Zhichao Tang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-06T13:37:42Z","title":"Exceptional rational functions of degree 5 over finite fields: classification by monodromy, ramification, and the Riemann-Hurwitz formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05075","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:a69010409d5c3991fdf59b05d9d5abe2dc1cb10114ff431399364d0f7e08369b","target":"record","created_at":"2026-07-07T03:19:15Z","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":"5b8177bccae386ddd9170a89771730547e4887a6eabde9276f855a9f6189efbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-06T13:37:42Z","title_canon_sha256":"bd66d1efb7e76c01723bb6f091af7bcf6c82e48e16022cfab886d9eeb1039906"},"schema_version":"1.0","source":{"id":"2607.05075","kind":"arxiv","version":1}},"canonical_sha256":"194ebf0ceef123c8b08f6d5540d9b3514dc921d7f15612788df1067c776a8b34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"194ebf0ceef123c8b08f6d5540d9b3514dc921d7f15612788df1067c776a8b34","first_computed_at":"2026-07-07T03:19:15.274694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T03:19:15.274694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A/I9AKJxHuJSaAzS2e1441zQxMFmBpifYYD3kB7t1T7tLRGyL2X/3WsjjTsM+TF/eCTkl39DF9fLXcrATPHXAg==","signature_status":"signed_v1","signed_at":"2026-07-07T03:19:15.275356Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.05075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a69010409d5c3991fdf59b05d9d5abe2dc1cb10114ff431399364d0f7e08369b","sha256:794db327ba7f826c5022bfb935ba94958aa825bf494474a729c14865720312ea"],"state_sha256":"80d2b6889a7d75035b804627aa18e69bfe55940291f1bfa2b523b18839034013"}