{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SLDB3JUB3ZNLU5LQDPR7R2YGEX","short_pith_number":"pith:SLDB3JUB","canonical_record":{"source":{"id":"1512.04030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T10:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"d0ca472db86d5d05867e03472e59892070a9c7363a4d262bbf0f9ee8731167e6","abstract_canon_sha256":"6173561fd49f38c0080e832145697295b2a847ff0188ac719fa293ba178bf1ab"},"schema_version":"1.0"},"canonical_sha256":"92c61da681de5aba75701be3f8eb0625f7054411179bd3d51498f04c2b8160ea","source":{"kind":"arxiv","id":"1512.04030","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04030","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04030v2","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04030","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"SLDB3JUB3ZNL","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SLDB3JUB3ZNLU5LQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SLDB3JUB","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SLDB3JUB3ZNLU5LQDPR7R2YGEX","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T10:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"d0ca472db86d5d05867e03472e59892070a9c7363a4d262bbf0f9ee8731167e6","abstract_canon_sha256":"6173561fd49f38c0080e832145697295b2a847ff0188ac719fa293ba178bf1ab"},"schema_version":"1.0"},"canonical_sha256":"92c61da681de5aba75701be3f8eb0625f7054411179bd3d51498f04c2b8160ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:14.301182Z","signature_b64":"2m++f4tCuT6b1fTb4t6k8V7M2D2tmi2O5vBTH16AquFgoTL7SKUV0t77uyfncmWYkGxfY4aW9OPJ3xtblTy1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92c61da681de5aba75701be3f8eb0625f7054411179bd3d51498f04c2b8160ea","last_reissued_at":"2026-05-18T00:55:14.300730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:14.300730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04030","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":"2026-05-18T00:55:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9ognbaTm7Fg/KMBFbSgxp85sQJGO2zxIBL3Io6WjlOD/nLQ+nQid3CZbTi4ompLC3uw84ul3b1HbfwCea5QAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:20:59.882092Z"},"content_sha256":"55f9f02c1b35a54a8892c6c9f30aed01429dfd66b7e06dcf93498770bad394a6","schema_version":"1.0","event_id":"sha256:55f9f02c1b35a54a8892c6c9f30aed01429dfd66b7e06dcf93498770bad394a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SLDB3JUB3ZNLU5LQDPR7R2YGEX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonvanishing of Dirichlet L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hieu T. Ngo, Rizwanur Khan","submitted_at":"2015-12-13T10:06:47Z","abstract_excerpt":"We show that for at least 3/8 of the primitive Dirichlet characters $\\chi$ of large prime modulus, the central value $L(1/2,\\chi)$ does not vanish."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04030","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":"2026-05-18T00:55:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qf2JHyL+qAESYgtljopDd5SbqzliSwQ+vSdGGStVGEs9SrixTO53wpnPdrvF7ST+uD6fLvtEYxSbIPhcX7e4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:20:59.882503Z"},"content_sha256":"468c7d8ea420bfbe55e8caea42ad23da770da47b8e79f8c67caaa4323f327f20","schema_version":"1.0","event_id":"sha256:468c7d8ea420bfbe55e8caea42ad23da770da47b8e79f8c67caaa4323f327f20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SLDB3JUB3ZNLU5LQDPR7R2YGEX/bundle.json","state_url":"https://pith.science/pith/SLDB3JUB3ZNLU5LQDPR7R2YGEX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SLDB3JUB3ZNLU5LQDPR7R2YGEX/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":"2026-05-26T07:20:59Z","links":{"resolver":"https://pith.science/pith/SLDB3JUB3ZNLU5LQDPR7R2YGEX","bundle":"https://pith.science/pith/SLDB3JUB3ZNLU5LQDPR7R2YGEX/bundle.json","state":"https://pith.science/pith/SLDB3JUB3ZNLU5LQDPR7R2YGEX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SLDB3JUB3ZNLU5LQDPR7R2YGEX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SLDB3JUB3ZNLU5LQDPR7R2YGEX","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":"6173561fd49f38c0080e832145697295b2a847ff0188ac719fa293ba178bf1ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T10:06:47Z","title_canon_sha256":"d0ca472db86d5d05867e03472e59892070a9c7363a4d262bbf0f9ee8731167e6"},"schema_version":"1.0","source":{"id":"1512.04030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04030","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04030v2","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04030","created_at":"2026-05-18T00:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"SLDB3JUB3ZNL","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SLDB3JUB3ZNLU5LQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SLDB3JUB","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:468c7d8ea420bfbe55e8caea42ad23da770da47b8e79f8c67caaa4323f327f20","target":"graph","created_at":"2026-05-18T00:55:14Z","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 show that for at least 3/8 of the primitive Dirichlet characters $\\chi$ of large prime modulus, the central value $L(1/2,\\chi)$ does not vanish.","authors_text":"Hieu T. Ngo, Rizwanur Khan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T10:06:47Z","title":"Nonvanishing of Dirichlet L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04030","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":"sha256:55f9f02c1b35a54a8892c6c9f30aed01429dfd66b7e06dcf93498770bad394a6","target":"record","created_at":"2026-05-18T00:55:14Z","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":"6173561fd49f38c0080e832145697295b2a847ff0188ac719fa293ba178bf1ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T10:06:47Z","title_canon_sha256":"d0ca472db86d5d05867e03472e59892070a9c7363a4d262bbf0f9ee8731167e6"},"schema_version":"1.0","source":{"id":"1512.04030","kind":"arxiv","version":2}},"canonical_sha256":"92c61da681de5aba75701be3f8eb0625f7054411179bd3d51498f04c2b8160ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92c61da681de5aba75701be3f8eb0625f7054411179bd3d51498f04c2b8160ea","first_computed_at":"2026-05-18T00:55:14.300730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:14.300730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2m++f4tCuT6b1fTb4t6k8V7M2D2tmi2O5vBTH16AquFgoTL7SKUV0t77uyfncmWYkGxfY4aW9OPJ3xtblTy1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:14.301182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55f9f02c1b35a54a8892c6c9f30aed01429dfd66b7e06dcf93498770bad394a6","sha256:468c7d8ea420bfbe55e8caea42ad23da770da47b8e79f8c67caaa4323f327f20"],"state_sha256":"7634e248cdf38df7b72aaa53614f18b2bc25c4bf878e3bcd7c8e374a0da49992"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PZbTQ+DMIe/tLyrrlv+jkDGIJClHwnFtogWlq2oezvGaRBdfLfw7f6t8QpLvXa2Je58BhzOkM+Ny/iuKkVFiAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:20:59.885060Z","bundle_sha256":"2e92073269f88eadb47571fa81e666363244d989ddccb7244f8738eb1e24e0c0"}}