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After a seminal paper by Garcia, Stichtenoth and Xing, many papers have provided genera of quotients of $\\mathcal{H}_q$, but their complete determination is a challenging open problem. In this paper we determine completely the spectrum of genera of quotients of $\\mathcal{H}_q$ for any $q\\equiv1\\pmod4$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.04546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-11T15:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"b37ce52e4b114dc381963ee85ec2e147556235c8b1955401a5c68b6be7ae067d","abstract_canon_sha256":"ced12dd3938d8b8c31233d3c5a3cd23b844c164b2dc5bf5ac596c267b5d79e2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:33.442078Z","signature_b64":"v5+OBx78Ca6A2GnlY8U4F4JjF/v4QC7R55os3ALECf85bGb9J8ArXREPirTBgAu27iM3ajRm3Vu9DbqeK5HmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"733d4e34af5cf9cbe73c101bbec4115f5512ec6e658374216d13d1c5819326b7","last_reissued_at":"2026-05-18T00:13:33.441632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:33.441632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The complete list of genera of quotients of the $\\mathbb{F}_{q^2}$-maximal Hermitian curve for $q\\equiv1\\pmod{4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giovanni Zini, Maria Montanucci","submitted_at":"2018-06-11T15:39:38Z","abstract_excerpt":"Let $\\mathbb{F}_{q^2}$ be the finite field with $q^2$ elements. 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