{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:M7GDQEAPCNU65D2UWJD6KM6326","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":"5e5a3cc301f7d1405680b01e7b99e451ee262e98dcfdc21d92e6c59014bb1861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-12T18:43:16Z","title_canon_sha256":"96b76a8d01d2a61650ef0b5c03efbd56a153f64c9f74981417d5c9d0282abb0d"},"schema_version":"1.0","source":{"id":"1807.04782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04782","created_at":"2026-05-18T00:10:51Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04782v1","created_at":"2026-05-18T00:10:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04782","created_at":"2026-05-18T00:10:51Z"},{"alias_kind":"pith_short_12","alias_value":"M7GDQEAPCNU6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M7GDQEAPCNU65D2U","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M7GDQEAP","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:77250a0c10c338425237461db51df2727cc3f05fea88a6f5b490d8286f206702","target":"graph","created_at":"2026-05-18T00:10:51Z","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":"In this paper we consider the curves $H_{k,t}^{(p)} : y^{p^k}+y=x^{p^{kt}+1}$ over $\\mathbb F_p$ and and find an exact formula for the number of $\\mathbb F_{p^n}$-rational points on $H_{k,t}^{(p)}$ for all integers $n\\ge 1$. We also give the condition when the $L$-polynomial of a Hermitian curve divides the $L$-polynomial of another over $\\mathbb F_p$.","authors_text":"Emrah Sercan Y{\\i}lmaz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-12T18:43:16Z","title":"Number of Rational points of the Generalized Hermitian Curves over $\\mathbb F_{p^n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04782","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":"sha256:823e08234399f04094f8dec3fc0828480dce180a9cae2305011d555c837d63eb","target":"record","created_at":"2026-05-18T00:10:51Z","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":"5e5a3cc301f7d1405680b01e7b99e451ee262e98dcfdc21d92e6c59014bb1861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-12T18:43:16Z","title_canon_sha256":"96b76a8d01d2a61650ef0b5c03efbd56a153f64c9f74981417d5c9d0282abb0d"},"schema_version":"1.0","source":{"id":"1807.04782","kind":"arxiv","version":1}},"canonical_sha256":"67cc38100f1369ee8f54b247e533dbd799782462dc1d81c126c6f32b9b87313e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67cc38100f1369ee8f54b247e533dbd799782462dc1d81c126c6f32b9b87313e","first_computed_at":"2026-05-18T00:10:51.448074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:51.448074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6j9kfG7nSXszDlWAvkuFzEFL4svhYonz+X/acterAMBjXIbfcqVoK5n9oPoVa9v3Xl92mEQ841e1a7VabOhMAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:51.448639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:823e08234399f04094f8dec3fc0828480dce180a9cae2305011d555c837d63eb","sha256:77250a0c10c338425237461db51df2727cc3f05fea88a6f5b490d8286f206702"],"state_sha256":"908f3f99e65771f164656fe9de12a31d0a64c8e1564c1d615f069d65d478be18"}