{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3HAHEQ7V2TVAR4WQNSKUUIIJ3B","short_pith_number":"pith:3HAHEQ7V","canonical_record":{"source":{"id":"1211.6725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-28T20:08:15Z","cross_cats_sorted":[],"title_canon_sha256":"5f2733b69719bbc77f3df6c19f2d291f04beb56f5de479de7526a1edf6ed0a78","abstract_canon_sha256":"38ccf8a0eb76e70395940391e7648a46782f1e7ca6f1593ae3e879301475ca7f"},"schema_version":"1.0"},"canonical_sha256":"d9c07243f5d4ea08f2d06c954a2109d876d54a1412fa19e5ae45d82efc7afd05","source":{"kind":"arxiv","id":"1211.6725","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6725","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6725v2","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6725","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"3HAHEQ7V2TVA","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3HAHEQ7V2TVAR4WQ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3HAHEQ7V","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3HAHEQ7V2TVAR4WQNSKUUIIJ3B","target":"record","payload":{"canonical_record":{"source":{"id":"1211.6725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-28T20:08:15Z","cross_cats_sorted":[],"title_canon_sha256":"5f2733b69719bbc77f3df6c19f2d291f04beb56f5de479de7526a1edf6ed0a78","abstract_canon_sha256":"38ccf8a0eb76e70395940391e7648a46782f1e7ca6f1593ae3e879301475ca7f"},"schema_version":"1.0"},"canonical_sha256":"d9c07243f5d4ea08f2d06c954a2109d876d54a1412fa19e5ae45d82efc7afd05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:38.630379Z","signature_b64":"VqV5YmmSa3of7AYKeD7jCRxoT6G1Ez2Uvrlb6iY8VQ1yJ9YSuEizYNRHnDQG66vQOVoYUq6IXVzfUrMLAyViCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9c07243f5d4ea08f2d06c954a2109d876d54a1412fa19e5ae45d82efc7afd05","last_reissued_at":"2026-05-18T03:33:38.629610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:38.629610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.6725","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5AdUFwDbcuWgi5uH7gGJ1/IIY1cMtzB108IN9afqDlWCyudRQ+D72DRggb3BQWMxSuF5K6iJgjZvPw5U7kyFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:37:33.625475Z"},"content_sha256":"3090e3495a51d08973eee4adc1abb8964fb1b81cc9d00f678a237bf32a84c9d4","schema_version":"1.0","event_id":"sha256:3090e3495a51d08973eee4adc1abb8964fb1b81cc9d00f678a237bf32a84c9d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3HAHEQ7V2TVAR4WQNSKUUIIJ3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple zeros of primitive Dirichlet $L$-functions and the asymptotic large sieve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maksym Radziwi\\l\\l, Sheng-chi Liu, Vorrapan Chandee, Yoonbok Lee","submitted_at":"2012-11-28T20:08:15Z","abstract_excerpt":"Assuming the Generalized Riemann Hypothesis (GRH), we show using the asymptotic large sieve that 91% of the zeros of primitive Dirichlet $L$-functions are simple. This improves on earlier work of \\\"{O}zl\\\"{u}k which gives a proportion of at most 86%. We further compute an $q$-analogue of the Pair Correlation Function $F(\\alpha)$ averaged over all primitive Dirichlet $L$-functions in the range $|\\alpha| < 2$ . Previously such a result was available only when the average included all the characters $\\chi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6725","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xG1r09spzE1ZDBBdxXV6hIlBzBYmLP1km4Q+g2vLywT4zxxs62wn4J6Pa0hZM92G9Nug1vb1geAsR6N3/z5CAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:37:33.626144Z"},"content_sha256":"86f4afbd6b79d1a6efd4d5a2488f3cfbc006a305d723c26aa1e319b7e3254b4e","schema_version":"1.0","event_id":"sha256:86f4afbd6b79d1a6efd4d5a2488f3cfbc006a305d723c26aa1e319b7e3254b4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HAHEQ7V2TVAR4WQNSKUUIIJ3B/bundle.json","state_url":"https://pith.science/pith/3HAHEQ7V2TVAR4WQNSKUUIIJ3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HAHEQ7V2TVAR4WQNSKUUIIJ3B/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T06:37:33Z","links":{"resolver":"https://pith.science/pith/3HAHEQ7V2TVAR4WQNSKUUIIJ3B","bundle":"https://pith.science/pith/3HAHEQ7V2TVAR4WQNSKUUIIJ3B/bundle.json","state":"https://pith.science/pith/3HAHEQ7V2TVAR4WQNSKUUIIJ3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HAHEQ7V2TVAR4WQNSKUUIIJ3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3HAHEQ7V2TVAR4WQNSKUUIIJ3B","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":"38ccf8a0eb76e70395940391e7648a46782f1e7ca6f1593ae3e879301475ca7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-28T20:08:15Z","title_canon_sha256":"5f2733b69719bbc77f3df6c19f2d291f04beb56f5de479de7526a1edf6ed0a78"},"schema_version":"1.0","source":{"id":"1211.6725","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6725","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6725v2","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6725","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"3HAHEQ7V2TVA","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3HAHEQ7V2TVAR4WQ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3HAHEQ7V","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:86f4afbd6b79d1a6efd4d5a2488f3cfbc006a305d723c26aa1e319b7e3254b4e","target":"graph","created_at":"2026-05-18T03:33:38Z","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":"Assuming the Generalized Riemann Hypothesis (GRH), we show using the asymptotic large sieve that 91% of the zeros of primitive Dirichlet $L$-functions are simple. This improves on earlier work of \\\"{O}zl\\\"{u}k which gives a proportion of at most 86%. We further compute an $q$-analogue of the Pair Correlation Function $F(\\alpha)$ averaged over all primitive Dirichlet $L$-functions in the range $|\\alpha| < 2$ . Previously such a result was available only when the average included all the characters $\\chi$.","authors_text":"Maksym Radziwi\\l\\l, Sheng-chi Liu, Vorrapan Chandee, Yoonbok Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-28T20:08:15Z","title":"Simple zeros of primitive Dirichlet $L$-functions and the asymptotic large sieve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6725","kind":"arxiv","version":2},"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":"sha256:3090e3495a51d08973eee4adc1abb8964fb1b81cc9d00f678a237bf32a84c9d4","target":"record","created_at":"2026-05-18T03:33:38Z","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":"38ccf8a0eb76e70395940391e7648a46782f1e7ca6f1593ae3e879301475ca7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-28T20:08:15Z","title_canon_sha256":"5f2733b69719bbc77f3df6c19f2d291f04beb56f5de479de7526a1edf6ed0a78"},"schema_version":"1.0","source":{"id":"1211.6725","kind":"arxiv","version":2}},"canonical_sha256":"d9c07243f5d4ea08f2d06c954a2109d876d54a1412fa19e5ae45d82efc7afd05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9c07243f5d4ea08f2d06c954a2109d876d54a1412fa19e5ae45d82efc7afd05","first_computed_at":"2026-05-18T03:33:38.629610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:38.629610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VqV5YmmSa3of7AYKeD7jCRxoT6G1Ez2Uvrlb6iY8VQ1yJ9YSuEizYNRHnDQG66vQOVoYUq6IXVzfUrMLAyViCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:38.630379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6725","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3090e3495a51d08973eee4adc1abb8964fb1b81cc9d00f678a237bf32a84c9d4","sha256:86f4afbd6b79d1a6efd4d5a2488f3cfbc006a305d723c26aa1e319b7e3254b4e"],"state_sha256":"ce4068ddb0d8afbf6df4f43c2a979c61080964bac51f468125a02ff9069d4e98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OL9epj7XkVqQRRUIe4bD3IXRzQEz0QC2CIe8AikDoxB5WIK5q2Kpu5czrSiSNAMXvZe/R0PbeBOBao0YdNaGDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:37:33.628731Z","bundle_sha256":"2907acd3dcc377f9b404a914d83913883aeb34619c92e6306977e4b0144c2990"}}