{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KSB6NOYZX77AUFEQIBVPNQELXT","short_pith_number":"pith:KSB6NOYZ","canonical_record":{"source":{"id":"1302.6021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T09:19:11Z","cross_cats_sorted":[],"title_canon_sha256":"2760b77c9eac00b5ab26d3b5f6db70050aa163cdc752aa03f742f609da1f0787","abstract_canon_sha256":"6e557f9e4ff512e9062526c9680264c925495a9bde2c5faf53f5097368d2cfea"},"schema_version":"1.0"},"canonical_sha256":"5483e6bb19bffe0a1490406af6c08bbcfca484057d9f5d53cd1ed59dadf4a489","source":{"kind":"arxiv","id":"1302.6021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6021","created_at":"2026-05-18T03:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6021v1","created_at":"2026-05-18T03:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6021","created_at":"2026-05-18T03:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"KSB6NOYZX77A","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KSB6NOYZX77AUFEQ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KSB6NOYZ","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KSB6NOYZX77AUFEQIBVPNQELXT","target":"record","payload":{"canonical_record":{"source":{"id":"1302.6021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T09:19:11Z","cross_cats_sorted":[],"title_canon_sha256":"2760b77c9eac00b5ab26d3b5f6db70050aa163cdc752aa03f742f609da1f0787","abstract_canon_sha256":"6e557f9e4ff512e9062526c9680264c925495a9bde2c5faf53f5097368d2cfea"},"schema_version":"1.0"},"canonical_sha256":"5483e6bb19bffe0a1490406af6c08bbcfca484057d9f5d53cd1ed59dadf4a489","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:27.010278Z","signature_b64":"2aqRYNQjQrZ97NHrmdrq5WH0idgxGS7eqPSgXKu19Yc+n7i+u0wIB3ZNEfv/VfbCGNL98TYkJ53Yqq8iHM5AAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5483e6bb19bffe0a1490406af6c08bbcfca484057d9f5d53cd1ed59dadf4a489","last_reissued_at":"2026-05-18T03:25:27.009815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:27.009815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.6021","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"04w186zmRVd8YDdCoiLZ4xZWN1V2XiRK18FAjtDHes8zYGplGpaGl/1BF3+W3gsXFQaF8NYYBB5hg8UNrfEYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:16:01.591025Z"},"content_sha256":"c09146c0a3691c43be9f8b139014384f93bf1ea74168818ba6d8c9bc4496fcd5","schema_version":"1.0","event_id":"sha256:c09146c0a3691c43be9f8b139014384f93bf1ea74168818ba6d8c9bc4496fcd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KSB6NOYZX77AUFEQIBVPNQELXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twists of automorphic L-functions at the central point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"H. M. Bui","submitted_at":"2013-02-25T09:19:11Z","abstract_excerpt":"We study the nonvanishing of twists of automorphic L-functions at the centre of the critical strip. Given a primitive character \\chi modulo D satisfying some technical conditions, we prove that the twisted L-functions L(f.\\chi,s) do not vanish at s=1/2 for a positive proportion of primitive forms of weight 2 and level q, for large prime q. We also investigate the central values of high derivatives of L(f.\\chi,s), and from that derive an upper bound for the average analytic rank of the studied L-functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6021","kind":"arxiv","version":1},"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":"2026-05-18T03:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JjiK4lMqtVkKcTxCBSbg3dQZ+usMt4moi1DLL76U19+27wnarnafLxleDlGy3Tc6pxnhHfPYrMjp9tCL6E7aDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:16:01.591606Z"},"content_sha256":"c68c7de8ae459e3ffa6e89612ca94fdba2117c67b96e2a477a1867b6aa394d2b","schema_version":"1.0","event_id":"sha256:c68c7de8ae459e3ffa6e89612ca94fdba2117c67b96e2a477a1867b6aa394d2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSB6NOYZX77AUFEQIBVPNQELXT/bundle.json","state_url":"https://pith.science/pith/KSB6NOYZX77AUFEQIBVPNQELXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSB6NOYZX77AUFEQIBVPNQELXT/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":"2026-06-07T09:16:01Z","links":{"resolver":"https://pith.science/pith/KSB6NOYZX77AUFEQIBVPNQELXT","bundle":"https://pith.science/pith/KSB6NOYZX77AUFEQIBVPNQELXT/bundle.json","state":"https://pith.science/pith/KSB6NOYZX77AUFEQIBVPNQELXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSB6NOYZX77AUFEQIBVPNQELXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KSB6NOYZX77AUFEQIBVPNQELXT","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":"6e557f9e4ff512e9062526c9680264c925495a9bde2c5faf53f5097368d2cfea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T09:19:11Z","title_canon_sha256":"2760b77c9eac00b5ab26d3b5f6db70050aa163cdc752aa03f742f609da1f0787"},"schema_version":"1.0","source":{"id":"1302.6021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6021","created_at":"2026-05-18T03:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6021v1","created_at":"2026-05-18T03:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6021","created_at":"2026-05-18T03:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"KSB6NOYZX77A","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KSB6NOYZX77AUFEQ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KSB6NOYZ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:c68c7de8ae459e3ffa6e89612ca94fdba2117c67b96e2a477a1867b6aa394d2b","target":"graph","created_at":"2026-05-18T03:25:27Z","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 study the nonvanishing of twists of automorphic L-functions at the centre of the critical strip. Given a primitive character \\chi modulo D satisfying some technical conditions, we prove that the twisted L-functions L(f.\\chi,s) do not vanish at s=1/2 for a positive proportion of primitive forms of weight 2 and level q, for large prime q. We also investigate the central values of high derivatives of L(f.\\chi,s), and from that derive an upper bound for the average analytic rank of the studied L-functions.","authors_text":"H. M. Bui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T09:19:11Z","title":"Twists of automorphic L-functions at the central point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6021","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:c09146c0a3691c43be9f8b139014384f93bf1ea74168818ba6d8c9bc4496fcd5","target":"record","created_at":"2026-05-18T03:25:27Z","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":"6e557f9e4ff512e9062526c9680264c925495a9bde2c5faf53f5097368d2cfea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T09:19:11Z","title_canon_sha256":"2760b77c9eac00b5ab26d3b5f6db70050aa163cdc752aa03f742f609da1f0787"},"schema_version":"1.0","source":{"id":"1302.6021","kind":"arxiv","version":1}},"canonical_sha256":"5483e6bb19bffe0a1490406af6c08bbcfca484057d9f5d53cd1ed59dadf4a489","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5483e6bb19bffe0a1490406af6c08bbcfca484057d9f5d53cd1ed59dadf4a489","first_computed_at":"2026-05-18T03:25:27.009815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:27.009815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2aqRYNQjQrZ97NHrmdrq5WH0idgxGS7eqPSgXKu19Yc+n7i+u0wIB3ZNEfv/VfbCGNL98TYkJ53Yqq8iHM5AAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:27.010278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c09146c0a3691c43be9f8b139014384f93bf1ea74168818ba6d8c9bc4496fcd5","sha256:c68c7de8ae459e3ffa6e89612ca94fdba2117c67b96e2a477a1867b6aa394d2b"],"state_sha256":"dc6c78d8748faa48a0084e1381b1f816d11520dea95f0606769fce1e6bf56948"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TVw0GSNVazI8Pm/T8a76fJZssEBcSTYafCjp5jpT6NO9c6+UfG8JdOMFp4Yr6EtleIzqZ08QHgW/ApgF6YlnBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:16:01.594573Z","bundle_sha256":"f5cd4f1e0680b18b99c57b0dc0a6add6fa265234112d417fb11afe5336047075"}}