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As applications, we provide a method for constructing maximal and minimal van der Geer--van der Vlugt curves, and show that every such curve arises from this construction.","weakest_assumption":"Factorization of the relevant additive polynomials yields a uniform description of the Frobenius eigenvalues that does not reintroduce the many auxiliary choices present in the quotient approach."}},"verdict_id":"648129c4-9402-424e-b1cd-a4848ccfe1b0"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:712da64290def3f3819ba5a1416f5a86728b46a5114af1fd924db825553acb67","target":"record","created_at":"2026-05-20T00:02:38Z","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":"bd1ec37e4eab8b802846fac6d96bc7c7896fe3ef89922eeacf2ed40c5fefa36f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-16T00:42:22Z","title_canon_sha256":"54968d40271ee25357ad6617fed3027c2ba1a9034237f3a6349c8819a72f9241"},"schema_version":"1.0","source":{"id":"2605.16729","kind":"arxiv","version":1}},"canonical_sha256":"59d3817025e04a2f26271662972352064e900bef92ec3367e2b73459e7be3b6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59d3817025e04a2f26271662972352064e900bef92ec3367e2b73459e7be3b6b","first_computed_at":"2026-05-20T00:02:38.772400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:38.772400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wKp2uCKt3sbnSWFK/Zd+foiIYYuDEUIN3gxUsuShic/8ccIlSbQ+ovDc1irZrQdXvAfHjVZTaZF3lXaAlrvOAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:38.773168Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16729","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:712da64290def3f3819ba5a1416f5a86728b46a5114af1fd924db825553acb67","sha256:1730434d22caec91c9cfaca60bac76f06ef468bf695d3bf510e25a288869b92b"],"state_sha256":"5dacfe3af2cd55514e8b8be7ba3eb2d6053aacf9d4c9a3691b18bf938fe0068a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5rJPlIiD+nBnU5mGXY/qgzhuXmikAvxagiHPRJV+W00pDHBBszfsEYhwH8Z+WhBHk1OWQDKRJ7Qa7CZSTXGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:52:30.071207Z","bundle_sha256":"1b589c18e5ca395d17dbc288c260aafa875808a29a39d999a336a4b3a5a3ef04"}}