{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SFXAI5S2BNRTZDPG5S4PECYUDY","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":"da0e2e6eff46a7b7fd5286950b3d479e999a1dafeeea535a267f5d2208030707","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-23T20:32:39Z","title_canon_sha256":"31c86ed8303eb155b0ab90abe388f94954f770831b1adcff8393958b9bbf3e48"},"schema_version":"1.0","source":{"id":"1905.09909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.09909","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"1905.09909v1","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09909","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"SFXAI5S2BNRT","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SFXAI5S2BNRTZDPG","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SFXAI5S2","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:cb85c2a75296f7ac325ddbd740258c2cca45194e8526a0703c2a4e1ecfb1dade","target":"graph","created_at":"2026-05-17T23:45:14Z","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":"Let $\\mathcal{G}$ be the projective plane curve defined over $\\mathbb{F}_q$ given by $$aX^nY^n-X^nZ^n-Y^nZ^n+bZ^{2n}=0,$$ where $ab\\notin\\{0,1\\}$, and for each $s\\in\\{2,\\ldots,n-1\\}$, let $\\mathcal{D}_s^{P_1,P_2}$ be the base-point-free linear series cut out on $\\mathcal{G}$ by the linear system of all curves of degree $s$ passing through the singular points $P_1=(1:0:0)$ and $P_2=(0:1:0)$ of $\\mathcal{G}$. The present work determines an upper bound for the number $N_q(\\mathcal{G})$ of $\\mathbb{F}_q$-rational points on the nonsingular model of $\\mathcal{G}$ in cases where $\\mathcal{D}_s^{P_1,P","authors_text":"Herivelto Borges, Mariana Coutinho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-23T20:32:39Z","title":"On some generalized Fermat curves and chords of an affinely regular polygon inscribed in a hyperbola"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09909","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":"sha256:657778e1229323c25938bcdc1ad96817791e9ce579c4152573dca53ebf516b30","target":"record","created_at":"2026-05-17T23:45:14Z","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":"da0e2e6eff46a7b7fd5286950b3d479e999a1dafeeea535a267f5d2208030707","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-23T20:32:39Z","title_canon_sha256":"31c86ed8303eb155b0ab90abe388f94954f770831b1adcff8393958b9bbf3e48"},"schema_version":"1.0","source":{"id":"1905.09909","kind":"arxiv","version":1}},"canonical_sha256":"916e04765a0b633c8de6ecb8f20b141e3ef5f649da85576107943b737014a130","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"916e04765a0b633c8de6ecb8f20b141e3ef5f649da85576107943b737014a130","first_computed_at":"2026-05-17T23:45:14.059834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:14.059834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iLnmdhsHhni4lBx1+hvYVlPYOM5CFW04G5mLgpy7JMsdQfrdoKqLy88NYW+HuZXd2UrsGgJKdGUgS3l8NRBRDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:14.060384Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.09909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:657778e1229323c25938bcdc1ad96817791e9ce579c4152573dca53ebf516b30","sha256:cb85c2a75296f7ac325ddbd740258c2cca45194e8526a0703c2a4e1ecfb1dade"],"state_sha256":"da68c02ea115676b4053d04b0f8772a4d0ed0d6889bd47286de5567113976ce7"}