{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:R7NV2NHLVWH37IAY5DT7OH4V23","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":"111cf1b535a45062db0b277cc461fd9d824f62ca44b5604daaf8ab1fcd183d52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-05T15:54:39Z","title_canon_sha256":"b8f57bae4e9206a712893a52375e7c47793177c9532817b5ce5309227e28c00b"},"schema_version":"1.0","source":{"id":"1308.1022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1022","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1022v1","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1022","created_at":"2026-05-18T03:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"R7NV2NHLVWH3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R7NV2NHLVWH37IAY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R7NV2NHL","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:5ee956be3949290837d925e35e025477f09f2ffbf4ca2277187f76f6529e62dd","target":"graph","created_at":"2026-05-18T03:16:40Z","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":"The effective version of Chebotarev's density theorem under the Generalized Riemann Hypothesis and the Artin conjecture (cf. Iwaniec and Kowalski's Analytic Number Theory, 5.13) involves a numerical invariant of a subset $D$ of a finite group $G$ that we call the Littlewood Complexity of $D$. We study this invariant in detail. Using this study, and a new application of the large sieve, we give improved versions of two standard questions related to Chebotarev: the bound on the first prime in a Frobenian set, and the asymptotic of the set of primes with given Frobenius in an infinite Galois exte","authors_text":"Jo\\\"el Bella\\\"iche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-05T15:54:39Z","title":"Th\\'eor\\`eme de Chebotarev et complexit\\'e de Littlewood"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1022","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":"sha256:068194c916a0454b8b70334ce80fbdffc0b1498fb84d7d9f2bfc37be635c46f5","target":"record","created_at":"2026-05-18T03:16:40Z","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":"111cf1b535a45062db0b277cc461fd9d824f62ca44b5604daaf8ab1fcd183d52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-05T15:54:39Z","title_canon_sha256":"b8f57bae4e9206a712893a52375e7c47793177c9532817b5ce5309227e28c00b"},"schema_version":"1.0","source":{"id":"1308.1022","kind":"arxiv","version":1}},"canonical_sha256":"8fdb5d34ebad8fbfa018e8e7f71f95d6d350ce823c12c391cbe4dc22abb65229","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fdb5d34ebad8fbfa018e8e7f71f95d6d350ce823c12c391cbe4dc22abb65229","first_computed_at":"2026-05-18T03:16:40.920635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:40.920635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V6x6WedRsNmayUPde+FueK9YXGc6CBYfntxBsQJUOQhbgBAh15hNiVt+VWj6USziCHS0r8aIrlUkZf4DovxkDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:40.921335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:068194c916a0454b8b70334ce80fbdffc0b1498fb84d7d9f2bfc37be635c46f5","sha256:5ee956be3949290837d925e35e025477f09f2ffbf4ca2277187f76f6529e62dd"],"state_sha256":"2eaa0f7b9ac98a987d7929e5c656a69f0e23c678ead240b90d1f3820d68e01f9"}