{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FMQQA3A4ONZWLQPITMCJWAUXLA","short_pith_number":"pith:FMQQA3A4","canonical_record":{"source":{"id":"1608.04338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-15T17:40:34Z","cross_cats_sorted":[],"title_canon_sha256":"15eef083cfecfea0a4ca1c37f3f6730ae5e69de8827a03661da2b03949563a5b","abstract_canon_sha256":"b01931c0f128fed493893932931f3d35755b04a6e122afd9589bd7f794e54610"},"schema_version":"1.0"},"canonical_sha256":"2b21006c1c737365c1e89b049b0297582241feb0ae2fe7b5b14bfd7920a3fcdb","source":{"kind":"arxiv","id":"1608.04338","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04338","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04338v1","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04338","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"pith_short_12","alias_value":"FMQQA3A4ONZW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FMQQA3A4ONZWLQPI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FMQQA3A4","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FMQQA3A4ONZWLQPITMCJWAUXLA","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-15T17:40:34Z","cross_cats_sorted":[],"title_canon_sha256":"15eef083cfecfea0a4ca1c37f3f6730ae5e69de8827a03661da2b03949563a5b","abstract_canon_sha256":"b01931c0f128fed493893932931f3d35755b04a6e122afd9589bd7f794e54610"},"schema_version":"1.0"},"canonical_sha256":"2b21006c1c737365c1e89b049b0297582241feb0ae2fe7b5b14bfd7920a3fcdb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:03.764875Z","signature_b64":"6jS5nZ/WL+Gvyr/dbyDgU0ag/rviAg26gdwRWnLuBjHJWCizqLsOQnWKOqfq6LxrvgxcnnXcAtFi6ANntHkqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b21006c1c737365c1e89b049b0297582241feb0ae2fe7b5b14bfd7920a3fcdb","last_reissued_at":"2026-05-18T01:09:03.764460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:03.764460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04338","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HoKd3eVLsmFTCNI50FNdconHG4ZSEgqRewk1dFP3KvGJ9rGWB6mV+rSnFLHhKvh0neYJyOU8i/O7nr+aDq43DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:54:29.353215Z"},"content_sha256":"8a595a732e5a622245e18257326eb57295cadf5ba997a35a2a49ee16e2462ac2","schema_version":"1.0","event_id":"sha256:8a595a732e5a622245e18257326eb57295cadf5ba997a35a2a49ee16e2462ac2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FMQQA3A4ONZWLQPITMCJWAUXLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On generalizations of Fermat curves over finite fields and their automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nazar Arakelian, Pietro Speziali","submitted_at":"2016-08-15T17:40:34Z","abstract_excerpt":"Let $\\mathcal{X}$ be an irreducible algebraic curve defined over a finite field $\\mathbb{F}_q$ of characteristic $p>2$. Assume that the $\\mathbb{F}_q$-automorphism group of $\\mathcal{X}$ admits as an automorphism group the direct product of two cyclic groups $C_m$ and $C_n$ of orders $m$ and $n$ prime to $p$ such that both quotient curves $\\mathcal{X}/C_n$ and $\\mathcal{X}/C_m$ are rational. In this paper, we provide a complete classification of such curves, as well as a characterization of their full automorphism groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04338","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6WlNoFLYM6FE4G7ohRfv19hzvc9Br3dDGG9fCCEEV8BbvWh8K6/QGv6RsL3zNPKpQmFW+OcTatG9emv5ULZMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:54:29.353574Z"},"content_sha256":"1336d115265a0f20dddab499b151cdec39e39aaf5043b4d33af00af8a977d834","schema_version":"1.0","event_id":"sha256:1336d115265a0f20dddab499b151cdec39e39aaf5043b4d33af00af8a977d834"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMQQA3A4ONZWLQPITMCJWAUXLA/bundle.json","state_url":"https://pith.science/pith/FMQQA3A4ONZWLQPITMCJWAUXLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMQQA3A4ONZWLQPITMCJWAUXLA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T19:54:29Z","links":{"resolver":"https://pith.science/pith/FMQQA3A4ONZWLQPITMCJWAUXLA","bundle":"https://pith.science/pith/FMQQA3A4ONZWLQPITMCJWAUXLA/bundle.json","state":"https://pith.science/pith/FMQQA3A4ONZWLQPITMCJWAUXLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMQQA3A4ONZWLQPITMCJWAUXLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FMQQA3A4ONZWLQPITMCJWAUXLA","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":"b01931c0f128fed493893932931f3d35755b04a6e122afd9589bd7f794e54610","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-15T17:40:34Z","title_canon_sha256":"15eef083cfecfea0a4ca1c37f3f6730ae5e69de8827a03661da2b03949563a5b"},"schema_version":"1.0","source":{"id":"1608.04338","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04338","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04338v1","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04338","created_at":"2026-05-18T01:09:03Z"},{"alias_kind":"pith_short_12","alias_value":"FMQQA3A4ONZW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FMQQA3A4ONZWLQPI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FMQQA3A4","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:1336d115265a0f20dddab499b151cdec39e39aaf5043b4d33af00af8a977d834","target":"graph","created_at":"2026-05-18T01:09:03Z","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 $\\mathcal{X}$ be an irreducible algebraic curve defined over a finite field $\\mathbb{F}_q$ of characteristic $p>2$. Assume that the $\\mathbb{F}_q$-automorphism group of $\\mathcal{X}$ admits as an automorphism group the direct product of two cyclic groups $C_m$ and $C_n$ of orders $m$ and $n$ prime to $p$ such that both quotient curves $\\mathcal{X}/C_n$ and $\\mathcal{X}/C_m$ are rational. In this paper, we provide a complete classification of such curves, as well as a characterization of their full automorphism groups.","authors_text":"Nazar Arakelian, Pietro Speziali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-15T17:40:34Z","title":"On generalizations of Fermat curves over finite fields and their automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04338","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":"sha256:8a595a732e5a622245e18257326eb57295cadf5ba997a35a2a49ee16e2462ac2","target":"record","created_at":"2026-05-18T01:09:03Z","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":"b01931c0f128fed493893932931f3d35755b04a6e122afd9589bd7f794e54610","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-15T17:40:34Z","title_canon_sha256":"15eef083cfecfea0a4ca1c37f3f6730ae5e69de8827a03661da2b03949563a5b"},"schema_version":"1.0","source":{"id":"1608.04338","kind":"arxiv","version":1}},"canonical_sha256":"2b21006c1c737365c1e89b049b0297582241feb0ae2fe7b5b14bfd7920a3fcdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b21006c1c737365c1e89b049b0297582241feb0ae2fe7b5b14bfd7920a3fcdb","first_computed_at":"2026-05-18T01:09:03.764460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:03.764460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6jS5nZ/WL+Gvyr/dbyDgU0ag/rviAg26gdwRWnLuBjHJWCizqLsOQnWKOqfq6LxrvgxcnnXcAtFi6ANntHkqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:03.764875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04338","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a595a732e5a622245e18257326eb57295cadf5ba997a35a2a49ee16e2462ac2","sha256:1336d115265a0f20dddab499b151cdec39e39aaf5043b4d33af00af8a977d834"],"state_sha256":"55ec77c7052f350f85dbfa56831874ac3f91512fcee6dc1ef64f8e458b1a7a04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSdDb/BgGk5ZnaBms/jsXsFj2iDUtQ6K570tN3ckObuc+RcuEnqaLnCyRJPa/zAwvmxJ/xcwGdc3OI6u/8+TAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:54:29.355889Z","bundle_sha256":"12b31212b8911578df8090a767fbdc8c031a220e54b8d382cff3fa52fb03616e"}}