{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GY423AXOJXB2FZNFXHU2DPLQVO","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":"cbda14decdbd39126258806acd4adf12cb523fdb6cd72b391d7f45ac60b2024c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-09-20T11:59:43Z","title_canon_sha256":"e2abb9bf9196be8a384f17a29bba87c9e90893fc83f16fb9809b3c14b7801963"},"schema_version":"1.0","source":{"id":"2409.13436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.13436","created_at":"2026-07-05T09:09:35Z"},{"alias_kind":"arxiv_version","alias_value":"2409.13436v1","created_at":"2026-07-05T09:09:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.13436","created_at":"2026-07-05T09:09:35Z"},{"alias_kind":"pith_short_12","alias_value":"GY423AXOJXB2","created_at":"2026-07-05T09:09:35Z"},{"alias_kind":"pith_short_16","alias_value":"GY423AXOJXB2FZNF","created_at":"2026-07-05T09:09:35Z"},{"alias_kind":"pith_short_8","alias_value":"GY423AXO","created_at":"2026-07-05T09:09:35Z"}],"graph_snapshots":[{"event_id":"sha256:0cba3900edbaa8e168a2fad64547cceea007bd09bcac7350aad6003a6dd87dec","target":"graph","created_at":"2026-07-05T09:09:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.13436/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any real $k\\geq 2$ and large prime $q$, we prove a lower bound on the $2k$-th moment of the Dirichlet character sum\n  \\begin{equation*}\n  \\frac{1}{\\phi(q)} \\sum_{\\substack{\\chi \\text{ mod }q\\\\ \\chi\\neq \\chi_0}} \\Big| \\sum_{n\\leq x} \\chi(n)\\Big|^{2k}, \\end{equation*} where $1\\leq x\\leq q$, and $\\chi$ is summed over the set of non-trivial Dirichlet characters mod $q$. Our bound is known to be optimal up to a constant factor under the Generalised Riemann Hypothesis. We also get a sharp lower bound on moments of theta functions using the same method.","authors_text":"Barnab\\'as Szab\\'o","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-09-20T11:59:43Z","title":"A lower bound on high moments of character sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.13436","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":"sha256:6f6dbba735edb09a6b4ed58c0c027a6749597aeee2c5c86fc12be661d4eac7fa","target":"record","created_at":"2026-07-05T09:09:35Z","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":"cbda14decdbd39126258806acd4adf12cb523fdb6cd72b391d7f45ac60b2024c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-09-20T11:59:43Z","title_canon_sha256":"e2abb9bf9196be8a384f17a29bba87c9e90893fc83f16fb9809b3c14b7801963"},"schema_version":"1.0","source":{"id":"2409.13436","kind":"arxiv","version":1}},"canonical_sha256":"3639ad82ee4dc3a2e5a5b9e9a1bd70ab96f36fdb9266f4ef8eeee3d2a4475959","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3639ad82ee4dc3a2e5a5b9e9a1bd70ab96f36fdb9266f4ef8eeee3d2a4475959","first_computed_at":"2026-07-05T09:09:35.372091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:09:35.372091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R314ux44gna562gkGmp4edw9d4lRWg05YlpPKhAf7lQuvQUvSVS3tm5tkNmci41JbZCqeth2dmNLmwWVsZuUCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:09:35.372670Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.13436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f6dbba735edb09a6b4ed58c0c027a6749597aeee2c5c86fc12be661d4eac7fa","sha256:0cba3900edbaa8e168a2fad64547cceea007bd09bcac7350aad6003a6dd87dec"],"state_sha256":"a4863e92ad225a4c94ed240fd5dc8422f1ae598e02e5cac8685ac0fea5ff28bd"}