{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MMPDO47PB6463QZWTD3P7LNFSE","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":"1803f30ff081f323d3081fa213ff5e58b79cf586c387f729de5d5381ab6f6716","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-21T22:19:17Z","title_canon_sha256":"ae91b810110b95a4e09e0c16269f45aff94ae456457e069758e2da45c617f0bf"},"schema_version":"1.0","source":{"id":"1401.5507","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5507","created_at":"2026-05-18T01:32:57Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5507v2","created_at":"2026-05-18T01:32:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5507","created_at":"2026-05-18T01:32:57Z"},{"alias_kind":"pith_short_12","alias_value":"MMPDO47PB646","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MMPDO47PB6463QZW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MMPDO47P","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:94a5730d8261567782d307e69dba885257668d1122da3d6d3f2b42b7c07631ac","target":"graph","created_at":"2026-05-18T01:32:57Z","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 [90] the first-named author gave a working definition of a family of automorphic L-functions. Since then there have been a number of works [33], [107], [67] [47], [66] and especially [98] by the second and third-named authors which make it possible to give a conjectural answer for the symmetry type of a family and in particular the universality class predicted in [64] for the distribution of the zeros near s=1/2. In this note we carry this out after introducing some basic invariants associated to a family.","authors_text":"Nicolas Templier, Peter Sarnak, Sug-Woo Shin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-21T22:19:17Z","title":"Families of L-functions and their Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5507","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":"sha256:392995b6ddc3275ee6f56cd44e51ec51e048014d0851c68c066a60c08e6fbff6","target":"record","created_at":"2026-05-18T01:32:57Z","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":"1803f30ff081f323d3081fa213ff5e58b79cf586c387f729de5d5381ab6f6716","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-01-21T22:19:17Z","title_canon_sha256":"ae91b810110b95a4e09e0c16269f45aff94ae456457e069758e2da45c617f0bf"},"schema_version":"1.0","source":{"id":"1401.5507","kind":"arxiv","version":2}},"canonical_sha256":"631e3773ef0fb9edc33698f6ffada5911e814e6a7624ce89df68d01b3c171fa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"631e3773ef0fb9edc33698f6ffada5911e814e6a7624ce89df68d01b3c171fa8","first_computed_at":"2026-05-18T01:32:57.913718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:57.913718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sV0P2qXpxT7YCQPm5TzAbECWT9q6uYRTYeADvHhfyF5R9Dnq0dcG5lttKUbetKP1LQyeInbj9nBNzZS4WmqhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:57.914282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5507","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:392995b6ddc3275ee6f56cd44e51ec51e048014d0851c68c066a60c08e6fbff6","sha256:94a5730d8261567782d307e69dba885257668d1122da3d6d3f2b42b7c07631ac"],"state_sha256":"6bb354a89996ed2e4387056b7a589cdaf3ab739e5fee2606eb412d145d6a17e5"}