{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:O62B4PMGK3OIITJE44TAIW4QFL","short_pith_number":"pith:O62B4PMG","canonical_record":{"source":{"id":"0910.4695","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-10-25T18:51:27Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a2d30f69456d92c126407f95cd67d3605c48499331b3c02e062d4bd91020f199","abstract_canon_sha256":"85c1e5386b3b3d9987cdb13643411d0b350ec9cb664461553ac2c16b84a0baf2"},"schema_version":"1.0"},"canonical_sha256":"77b41e3d8656dc844d24e726045b902ae56ed5b1c1b6ef5ecc9fc9b558d3f7bd","source":{"kind":"arxiv","id":"0910.4695","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.4695","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"0910.4695v2","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4695","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"O62B4PMGK3OI","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"O62B4PMGK3OIITJE","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"O62B4PMG","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:O62B4PMGK3OIITJE44TAIW4QFL","target":"record","payload":{"canonical_record":{"source":{"id":"0910.4695","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-10-25T18:51:27Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a2d30f69456d92c126407f95cd67d3605c48499331b3c02e062d4bd91020f199","abstract_canon_sha256":"85c1e5386b3b3d9987cdb13643411d0b350ec9cb664461553ac2c16b84a0baf2"},"schema_version":"1.0"},"canonical_sha256":"77b41e3d8656dc844d24e726045b902ae56ed5b1c1b6ef5ecc9fc9b558d3f7bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:54.583578Z","signature_b64":"L86KsHhpQw/a+lCbHXnxaQdaFnkMKs8Ha0G08uvZ/vcUg2n68ojYL4RAT9wnP0S6AgjarxjPLzsWwyrwrtbRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77b41e3d8656dc844d24e726045b902ae56ed5b1c1b6ef5ecc9fc9b558d3f7bd","last_reissued_at":"2026-05-18T01:22:54.583084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:54.583084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.4695","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oJK7yv60xvdPgb16pAtNZzLFud0BHzeB3l6qPGB8vPbn4CFdptrnR+SWEDgIt1x+FmvQrw0/VevBmvqo4y75Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:38:43.631631Z"},"content_sha256":"f3b55107c5d7d257947f8a166684ac320ff83b57cfdfa4601f263ada525b62e3","schema_version":"1.0","event_id":"sha256:f3b55107c5d7d257947f8a166684ac320ff83b57cfdfa4601f263ada525b62e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:O62B4PMGK3OIITJE44TAIW4QFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-direct Galois covers of the affine line","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Bo-Hae Im, Ekin Ozman, Katherine Stevenson, Laura Hall-Seelig, Linda Gruendken, Rachel Pries","submitted_at":"2009-10-25T18:51:27Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $p>0$. Let $G$ be $Z/\\ell Z$ semi-direct product $Z/pZ$ where $\\ell$ is a prime distinct from $p$. In this paper, we study Galois covers $\\psi:Z \\to P^1_k$ ramified only over $\\infty$ with Galois group $G$. We find the minimal genus of a curve $Z$ that admits such a cover and show that it depends only on $\\ell$, $p$, and the order $a$ of $\\ell$ modulo $p$. We also prove that the number of curves $Z$ of this minimal genus which admit such a cover is at most $(p-1)/a$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4695","kind":"arxiv","version":2},"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":"2026-05-18T01:22:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bql/1IHOo7zYwwD3WW4lLaHFsr7Vrmqq5d9zHMnMeEkle8PvcxTHzR1CrDxuhSpz/OgVrJwW4p1xz79ujeswBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:38:43.632283Z"},"content_sha256":"5e217b16d7a8bf7b0fec22da6194cf0253f47a981a70cb8af9ac61fd1efee87f","schema_version":"1.0","event_id":"sha256:5e217b16d7a8bf7b0fec22da6194cf0253f47a981a70cb8af9ac61fd1efee87f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O62B4PMGK3OIITJE44TAIW4QFL/bundle.json","state_url":"https://pith.science/pith/O62B4PMGK3OIITJE44TAIW4QFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O62B4PMGK3OIITJE44TAIW4QFL/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":"2026-05-29T17:38:43Z","links":{"resolver":"https://pith.science/pith/O62B4PMGK3OIITJE44TAIW4QFL","bundle":"https://pith.science/pith/O62B4PMGK3OIITJE44TAIW4QFL/bundle.json","state":"https://pith.science/pith/O62B4PMGK3OIITJE44TAIW4QFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O62B4PMGK3OIITJE44TAIW4QFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:O62B4PMGK3OIITJE44TAIW4QFL","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":"85c1e5386b3b3d9987cdb13643411d0b350ec9cb664461553ac2c16b84a0baf2","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-10-25T18:51:27Z","title_canon_sha256":"a2d30f69456d92c126407f95cd67d3605c48499331b3c02e062d4bd91020f199"},"schema_version":"1.0","source":{"id":"0910.4695","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.4695","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"arxiv_version","alias_value":"0910.4695v2","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4695","created_at":"2026-05-18T01:22:54Z"},{"alias_kind":"pith_short_12","alias_value":"O62B4PMGK3OI","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"O62B4PMGK3OIITJE","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"O62B4PMG","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:5e217b16d7a8bf7b0fec22da6194cf0253f47a981a70cb8af9ac61fd1efee87f","target":"graph","created_at":"2026-05-18T01:22:54Z","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 $k$ be an algebraically closed field of characteristic $p>0$. Let $G$ be $Z/\\ell Z$ semi-direct product $Z/pZ$ where $\\ell$ is a prime distinct from $p$. In this paper, we study Galois covers $\\psi:Z \\to P^1_k$ ramified only over $\\infty$ with Galois group $G$. We find the minimal genus of a curve $Z$ that admits such a cover and show that it depends only on $\\ell$, $p$, and the order $a$ of $\\ell$ modulo $p$. We also prove that the number of curves $Z$ of this minimal genus which admit such a cover is at most $(p-1)/a$.","authors_text":"Bo-Hae Im, Ekin Ozman, Katherine Stevenson, Laura Hall-Seelig, Linda Gruendken, Rachel Pries","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-10-25T18:51:27Z","title":"Semi-direct Galois covers of the affine line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4695","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:f3b55107c5d7d257947f8a166684ac320ff83b57cfdfa4601f263ada525b62e3","target":"record","created_at":"2026-05-18T01:22:54Z","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":"85c1e5386b3b3d9987cdb13643411d0b350ec9cb664461553ac2c16b84a0baf2","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-10-25T18:51:27Z","title_canon_sha256":"a2d30f69456d92c126407f95cd67d3605c48499331b3c02e062d4bd91020f199"},"schema_version":"1.0","source":{"id":"0910.4695","kind":"arxiv","version":2}},"canonical_sha256":"77b41e3d8656dc844d24e726045b902ae56ed5b1c1b6ef5ecc9fc9b558d3f7bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77b41e3d8656dc844d24e726045b902ae56ed5b1c1b6ef5ecc9fc9b558d3f7bd","first_computed_at":"2026-05-18T01:22:54.583084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:54.583084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L86KsHhpQw/a+lCbHXnxaQdaFnkMKs8Ha0G08uvZ/vcUg2n68ojYL4RAT9wnP0S6AgjarxjPLzsWwyrwrtbRAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:54.583578Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.4695","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3b55107c5d7d257947f8a166684ac320ff83b57cfdfa4601f263ada525b62e3","sha256:5e217b16d7a8bf7b0fec22da6194cf0253f47a981a70cb8af9ac61fd1efee87f"],"state_sha256":"9b60fcf00bb16bc536138e214c82dfc450bfbbffbeb6cdb9747dab024b66d88e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z+L790D55hjDaAY9ci5C7vqkumlu++lqm8lbkO8BBmHuCvzcP5vf15nc3p9Zi8DklOMSKtub1n9Dzw6kNySNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:38:43.635840Z","bundle_sha256":"66cff93efc0eefe4854358db2f42876f990b135d7d9941575844b33f4a491036"}}