{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EA5TG5MVWKUZ4HVLQIQNP22C2O","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":"0135f76965b37cb375add72c530d9963a15b3ad5154570d9e4e322889fb2f0aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-01T17:17:10Z","title_canon_sha256":"96f7ac2c248a5f99a7776f8e850e7ac31e422e0e3799a3297d890587dd45ed93"},"schema_version":"1.0","source":{"id":"2607.01184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01184","created_at":"2026-07-02T01:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01184v1","created_at":"2026-07-02T01:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01184","created_at":"2026-07-02T01:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"EA5TG5MVWKUZ","created_at":"2026-07-02T01:18:31Z"},{"alias_kind":"pith_short_16","alias_value":"EA5TG5MVWKUZ4HVL","created_at":"2026-07-02T01:18:31Z"},{"alias_kind":"pith_short_8","alias_value":"EA5TG5MV","created_at":"2026-07-02T01:18:31Z"}],"graph_snapshots":[{"event_id":"sha256:449485a4f59dd62a985f8a08f72d1c87db00275b52bf4bfd355173bc459d3c69","target":"graph","created_at":"2026-07-02T01:18:31Z","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/2607.01184/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish sharp lower bounds for the Dirichlet character moments $\\frac{1}{r-1} \\sum_{\\chi \\; \\text{mod} \\; r} |\\sum_{n \\leq x} \\chi(n)|^{2q}$, where $r$ is a large prime, $1 \\leq x \\leq r^{0.499}$, and $0 \\leq q \\leq 1$ is real. These match the better than squareroot cancellation upper bounds obtained in previous work of the author. We prove the same sharp lower bounds for the moments $\\frac{1}{T} \\int_{0}^{T} |\\sum_{n \\leq x} n^{it}|^{2q} dt$ of zeta sums, and more generally for moments of character sums $\\sum_{n \\leq x} h(n) \\chi(n)$ with suitably bounded multiplicative twist $h(n)$.\n  T","authors_text":"Adam J. Harper","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-01T17:17:10Z","title":"Lower bounds for low moments of character sums, I: Short sums with general multiplicative weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01184","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":"sha256:17c1f995a2c1bdf2e700a585e9726100598515ad1550c0f3db8afe2a8456bdca","target":"record","created_at":"2026-07-02T01:18:31Z","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":"0135f76965b37cb375add72c530d9963a15b3ad5154570d9e4e322889fb2f0aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-01T17:17:10Z","title_canon_sha256":"96f7ac2c248a5f99a7776f8e850e7ac31e422e0e3799a3297d890587dd45ed93"},"schema_version":"1.0","source":{"id":"2607.01184","kind":"arxiv","version":1}},"canonical_sha256":"203b337595b2a99e1eab8220d7eb42d39a215a76ae89a3144b70d74fa277b2ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"203b337595b2a99e1eab8220d7eb42d39a215a76ae89a3144b70d74fa277b2ef","first_computed_at":"2026-07-02T01:18:31.961384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:18:31.961384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GyV35Ryj2sQP6K+Y1BJsLEVztBAsNHBGFJkqxaEuM7NEjpe9+v7tEAEYv4ekA5pHvAyF3SGKQ8gGQBPedUenDQ==","signature_status":"signed_v1","signed_at":"2026-07-02T01:18:31.961856Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17c1f995a2c1bdf2e700a585e9726100598515ad1550c0f3db8afe2a8456bdca","sha256:449485a4f59dd62a985f8a08f72d1c87db00275b52bf4bfd355173bc459d3c69"],"state_sha256":"5dc29b9c4316bc9aee6eb27fbcc8a674be5c5eff5ad8f44a2416c07332db0273"}