{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SZFJT3UMVA4VAMLV5Q64CPKDKM","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":"51c497a10af43aeed446a0204768a402b569c5b8377b1a9271d4bead9aa364ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-22T12:46:31Z","title_canon_sha256":"5d59a6b1523d83ed3ae032b814f5fd3134bbcde4005e893edf019721bad0a3cd"},"schema_version":"1.0","source":{"id":"1503.06420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06420","created_at":"2026-05-18T01:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06420v2","created_at":"2026-05-18T01:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06420","created_at":"2026-05-18T01:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"SZFJT3UMVA4V","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SZFJT3UMVA4VAMLV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SZFJT3UM","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:db50367d8f3867173c9fb41cae6c935aa183ea14a7031e2eb421988b361cbbe8","target":"graph","created_at":"2026-05-18T01:35:04Z","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 a field containing $\\mathbb{F}_q$. Let $\\psi$ be a rank $r$ Drinfeld $\\mathbb{F}_q[t]$-module determined by $\\psi_t(X) = tX+a_1X^q+\\cdots+a_{r-1}X^{q^{r-1}}+X^{q^r}$, where $t,a_1,\\ldots,a_{r-1}$ are algebraically independent over $k$. Let $n\\in\\mathbb{F}_q[T]$ be a monic polynomial. We show that the Galois group of $\\psi_n(X)$ over $k(t,a_1,\\ldots,a_{r-1})$ is isomorphic to $\\mathrm{GL}_r(\\mathbb{F}_q[t]/n\\mathbb{F}_q[t])$, settling a conjecture of Abhyankar. Along the way we obtain an explicit construction of Drinfeld moduli schemes of level $tn$.","authors_text":"Florian Breuer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-22T12:46:31Z","title":"Explicit Drinfeld moduli schemes and Abhyankar's generalized iteration conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06420","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":"sha256:7b1cbdd854bf61955c80cc8acf17e6173a116d4ff01de8324bdb86b49aef8ae5","target":"record","created_at":"2026-05-18T01:35:04Z","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":"51c497a10af43aeed446a0204768a402b569c5b8377b1a9271d4bead9aa364ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-22T12:46:31Z","title_canon_sha256":"5d59a6b1523d83ed3ae032b814f5fd3134bbcde4005e893edf019721bad0a3cd"},"schema_version":"1.0","source":{"id":"1503.06420","kind":"arxiv","version":2}},"canonical_sha256":"964a99ee8ca839503175ec3dc13d435325ea0ac0cf7b8e8b12fd463c44cc8ca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"964a99ee8ca839503175ec3dc13d435325ea0ac0cf7b8e8b12fd463c44cc8ca8","first_computed_at":"2026-05-18T01:35:04.813908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:04.813908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BLDO2Y921MVUNbR45q7ChSp6/fx3tpi2sZCA9889vsIhftJemLkFuI9qzf0r658dOHWYFeIs8ER0Pkv1jM0xAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:04.814554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b1cbdd854bf61955c80cc8acf17e6173a116d4ff01de8324bdb86b49aef8ae5","sha256:db50367d8f3867173c9fb41cae6c935aa183ea14a7031e2eb421988b361cbbe8"],"state_sha256":"e1cf29daf2be034378544f34b27d550e9de434b865ba786575f264f5e538a91e"}