{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:432JIIOZ4A5FZ34YBOZRYUT7AQ","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":"cc4a2fc5f04a238daaea11b52c5e1a1a613c6acb12ddf748615d05b5b48c33e5","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-13T21:17:32Z","title_canon_sha256":"2a580deb75f7b0052b833a0ecce9a659992c85d00d47a788f28b159dd0ec9d80"},"schema_version":"1.0","source":{"id":"1606.04143","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04143","created_at":"2026-05-18T00:59:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04143v2","created_at":"2026-05-18T00:59:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04143","created_at":"2026-05-18T00:59:41Z"},{"alias_kind":"pith_short_12","alias_value":"432JIIOZ4A5F","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"432JIIOZ4A5FZ34Y","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"432JIIOZ","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:c1629d76de74892ad4b7d0a32dc774d88061eb2df80b5182f063fcfce5e43b2f","target":"graph","created_at":"2026-05-18T00:59:41Z","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":"For Kummer extensions defined by $y^m = f (x)$, where $f (x)$ is a separable polynomial over the finite field $\\mathbb{F}_q$, we compute the number of Weierstrass gaps at two totally ramified places. For many totally ramified places we give a criterion to find pure gaps at these points and present families of pure gaps. We then apply our results to construct many points algebraic geometric codes with good parameters.","authors_text":"Daniele Bartoli, Giovanni Zini, Luciane Quoos","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-13T21:17:32Z","title":"Algebraic Geometric codes from Kummer Extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04143","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:df2bc13f6ef98efb74f6c446ad0e769e54c642d50e597418df38ee965644c2fa","target":"record","created_at":"2026-05-18T00:59:41Z","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":"cc4a2fc5f04a238daaea11b52c5e1a1a613c6acb12ddf748615d05b5b48c33e5","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-13T21:17:32Z","title_canon_sha256":"2a580deb75f7b0052b833a0ecce9a659992c85d00d47a788f28b159dd0ec9d80"},"schema_version":"1.0","source":{"id":"1606.04143","kind":"arxiv","version":2}},"canonical_sha256":"e6f49421d9e03a5cef980bb31c527f0414b318ffb64b01d28dbd4826d4a4cb64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6f49421d9e03a5cef980bb31c527f0414b318ffb64b01d28dbd4826d4a4cb64","first_computed_at":"2026-05-18T00:59:41.902554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:41.902554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J65HI9+L81LoXgV6kJZIOkSd3XnxPumigVk2oMlBvMmgnK7bDhsXlJhDe/h5k3jlDamExB4TDXuSVmo025rUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:41.903241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04143","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df2bc13f6ef98efb74f6c446ad0e769e54c642d50e597418df38ee965644c2fa","sha256:c1629d76de74892ad4b7d0a32dc774d88061eb2df80b5182f063fcfce5e43b2f"],"state_sha256":"204f72de2c865cb7c665eeaad4b275266e5d8edc56c7ff234b464cdcedb5da26"}