{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RATHU7EPSIO5TI7QHU7CTZQH4S","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":"2f6057803b107db99f0fbc4d6433cc778279c2d462032eb829989c2658f2f91c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T06:49:47Z","title_canon_sha256":"dbbe996170f7fa512d2529cfd31f49668e85f37cf76b40d0c59ff8a3f347998d"},"schema_version":"1.0","source":{"id":"1409.2219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2219","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2219v1","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2219","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"RATHU7EPSIO5","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RATHU7EPSIO5TI7Q","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RATHU7EP","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:c474c1661990b6064a591df0cf7032b7d125cc002f262bda76f59ae9dae720ae","target":"graph","created_at":"2026-05-18T02:43:17Z","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":"We give an explicit upper bound for non-principal Dirichlet $L$-functions on the line $s=1+it$. This result can be applied to improve the error in the zero-counting formulae for these functions.","authors_text":"Adrian Dudek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T06:49:47Z","title":"An Explicit Result for $|L(1+it,\\chi)|$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2219","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":"sha256:249187853079a0c4a321daf2db519a90cf7f962bb1f0b82cf510b18ad43c1e42","target":"record","created_at":"2026-05-18T02:43:17Z","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":"2f6057803b107db99f0fbc4d6433cc778279c2d462032eb829989c2658f2f91c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T06:49:47Z","title_canon_sha256":"dbbe996170f7fa512d2529cfd31f49668e85f37cf76b40d0c59ff8a3f347998d"},"schema_version":"1.0","source":{"id":"1409.2219","kind":"arxiv","version":1}},"canonical_sha256":"88267a7c8f921dd9a3f03d3e29e607e49ccbb88debde66a2ed5b0a980b4ced43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88267a7c8f921dd9a3f03d3e29e607e49ccbb88debde66a2ed5b0a980b4ced43","first_computed_at":"2026-05-18T02:43:17.576505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:17.576505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yOKIT5IxgnyMY3aZqReu7Iq5C7m98MxnRSMDh4a4dNbOBCRNzgqjgeDpxJewtpjz8fK0PfJDYV6t+uJC9yWdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:17.576949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:249187853079a0c4a321daf2db519a90cf7f962bb1f0b82cf510b18ad43c1e42","sha256:c474c1661990b6064a591df0cf7032b7d125cc002f262bda76f59ae9dae720ae"],"state_sha256":"a5955512998c2b98df63ce49ad3540c50741a2e89e790f6ef0564d3dd8d78964"}