{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QFH5H7JW2K3NGHPBCEQWKJALYF","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":"65d9190dbd488d54da8e6fcf571935d492a78566ad9f22c6edfe9e17547f5671","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-03T05:20:32Z","title_canon_sha256":"6a1f5d0b81ad49ff25820499a2db9dc30f6100dc5df6efe0e33a216805065704"},"schema_version":"1.0","source":{"id":"1805.01119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01119","created_at":"2026-05-18T00:16:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01119v1","created_at":"2026-05-18T00:16:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01119","created_at":"2026-05-18T00:16:52Z"},{"alias_kind":"pith_short_12","alias_value":"QFH5H7JW2K3N","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QFH5H7JW2K3NGHPB","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QFH5H7JW","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:c750a8748e08041d755f90db50e5bb2976aae94578a4a62470dd30d47ad18687","target":"graph","created_at":"2026-05-18T00:16:52Z","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":"In this paper, we exhibit upper and lower bounds with explicit constants for some objects related to entire $L$-functions in the critical strip, under the generalized Riemann hypothesis. The examples include the entire Dirichlet $L$-functions $L(s,\\chi)$ for primitive characters $\\chi$.","authors_text":"Andr\\'es Chirre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-03T05:20:32Z","title":"A note on entire $L$-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01119","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:b33de2e930b016a7a4ccbeca3849c317bc9d51b1a8b5c0f35f6e8b4b1e065ce3","target":"record","created_at":"2026-05-18T00:16:52Z","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":"65d9190dbd488d54da8e6fcf571935d492a78566ad9f22c6edfe9e17547f5671","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-03T05:20:32Z","title_canon_sha256":"6a1f5d0b81ad49ff25820499a2db9dc30f6100dc5df6efe0e33a216805065704"},"schema_version":"1.0","source":{"id":"1805.01119","kind":"arxiv","version":1}},"canonical_sha256":"814fd3fd36d2b6d31de1112165240bc1402fc66a1ea969c5cb610fa9be5a96d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"814fd3fd36d2b6d31de1112165240bc1402fc66a1ea969c5cb610fa9be5a96d8","first_computed_at":"2026-05-18T00:16:52.494881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:52.494881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vUmArp4E+qhLpNEBWDlg1Bb9IcvUt39l6RMeJRaFT3SjT6VHgrTkgOWmL3hdfGiycxOEITQt/qYUxjX9LhkDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:52.495567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b33de2e930b016a7a4ccbeca3849c317bc9d51b1a8b5c0f35f6e8b4b1e065ce3","sha256:c750a8748e08041d755f90db50e5bb2976aae94578a4a62470dd30d47ad18687"],"state_sha256":"244b5b0180ed8819c697035dfa51efaf978d8baef6806827a737c664bad4e754"}