{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YWU42QHD5KQAFRNTG3YKPSYSXV","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":"a225dbe3c52e899644de96719578773f3c377556e03718d86e8113d7ee463e05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-25T14:55:58Z","title_canon_sha256":"e29694cee1e28da3118f3a60e8c5f00e29dd4e22b8a406544cc6fc41a85e5a61"},"schema_version":"1.0","source":{"id":"1901.08897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.08897","created_at":"2026-05-17T23:55:31Z"},{"alias_kind":"arxiv_version","alias_value":"1901.08897v1","created_at":"2026-05-17T23:55:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08897","created_at":"2026-05-17T23:55:31Z"},{"alias_kind":"pith_short_12","alias_value":"YWU42QHD5KQA","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YWU42QHD5KQAFRNT","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YWU42QHD","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:89138ec18a9a981968c7a12eafc3974b493039c43f8a2bda10fe66849549a5f9","target":"graph","created_at":"2026-05-17T23:55:31Z","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"},"paper":{"abstract_excerpt":"The second generalized GK maximal curves $\\mathcal{GK}_{2,n}$ are maximal curves over finite fields with $q^{2n}$ elements, where $q$ is a prime power and $n \\geq 3$ an odd integer, constructed by Beelen and Montanucci. In this paper we determine the structure of the Weierstrass semigroup $H(P)$ where $P$ is an arbitrary $\\mathbb{F}_{q^2}$-rational point of $\\mathcal{GK}_{2,n}$. We show that these points are Weierstrass points and the Frobenius dimension of $\\mathcal{GK}_{2,n}$ is computed. A new proof of the fact that the first and the second generalized GK curves are not isomorphic for any $","authors_text":"Maria Montanucci, Vicenzo Pallozzi Lavorante","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-25T14:55:58Z","title":"AG codes from the second generalization of the GK maximal curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08897","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":"sha256:8c8daacb44a7c038f5c0862ca0a504c88302cf93c403bc18fdeabfab3d769397","target":"record","created_at":"2026-05-17T23:55:31Z","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":"a225dbe3c52e899644de96719578773f3c377556e03718d86e8113d7ee463e05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-25T14:55:58Z","title_canon_sha256":"e29694cee1e28da3118f3a60e8c5f00e29dd4e22b8a406544cc6fc41a85e5a61"},"schema_version":"1.0","source":{"id":"1901.08897","kind":"arxiv","version":1}},"canonical_sha256":"c5a9cd40e3eaa002c5b336f0a7cb12bd4f8650416e66d0ba94e9d3717797d2e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5a9cd40e3eaa002c5b336f0a7cb12bd4f8650416e66d0ba94e9d3717797d2e0","first_computed_at":"2026-05-17T23:55:31.213583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:31.213583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bJswuRTmiX9HPg8U1/Ey6QLhWGYIZpfEGDBDCLe0jSCk3nKg2YNd1kymU9Vz3mqyIdzVxCU9pyH+QYzy8aRABw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:31.213973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.08897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c8daacb44a7c038f5c0862ca0a504c88302cf93c403bc18fdeabfab3d769397","sha256:89138ec18a9a981968c7a12eafc3974b493039c43f8a2bda10fe66849549a5f9"],"state_sha256":"efa45268474e69fe27cba1c289eba1b4f94ce7133e8a2cfd0eddca708eb06806"}