{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OGSLNH7QIXDOQHQ67ZLXZAVGUZ","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":"c8b9b34d4f830708f2fd842c0569c5a3069f2c99f0a7753f9a27517230711f98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T14:25:34Z","title_canon_sha256":"884aa0c80841f38a7aecbf8965a390cdb11f9f489e98a379f243fc46501ee010"},"schema_version":"1.0","source":{"id":"1007.4732","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4732","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4732v2","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4732","created_at":"2026-05-18T04:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"OGSLNH7QIXDO","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OGSLNH7QIXDOQHQ6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OGSLNH7Q","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:1fbef2536a1e8daeea3ce172da36d2f5cb3fe35b1c69795077c8e529844466a8","target":"graph","created_at":"2026-05-18T04:42:45Z","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":"Let F in S_k(Sp(2g, Z)) be a cuspidal Siegel eigenform of genus g with normalized Hecke eigenvalues mu_F(n). Suppose that the associated automorphic representation pi_F is locally tempered everywhere. For each c>0 we consider the set of primes p for which |mu_F(p)| >= c and we provide an explicit upper bound on the density of this set. In the case g=2, we also provide an explicit upper bound on the density of the set of primes p for which mu_F(p) >= c.","authors_text":"Abhishek Saha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T14:25:34Z","title":"Prime density results for Hecke eigenvalues of a Siegel cusp form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4732","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":"sha256:87c59ebeb9daa7c1740634962998d63883518097d03b927d2a67aeb238f67cfa","target":"record","created_at":"2026-05-18T04:42:45Z","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":"c8b9b34d4f830708f2fd842c0569c5a3069f2c99f0a7753f9a27517230711f98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-07-27T14:25:34Z","title_canon_sha256":"884aa0c80841f38a7aecbf8965a390cdb11f9f489e98a379f243fc46501ee010"},"schema_version":"1.0","source":{"id":"1007.4732","kind":"arxiv","version":2}},"canonical_sha256":"71a4b69ff045c6e81e1efe577c82a6a67d719d03ea97b117592225e2043a33d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71a4b69ff045c6e81e1efe577c82a6a67d719d03ea97b117592225e2043a33d8","first_computed_at":"2026-05-18T04:42:45.479556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:45.479556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"69rR76t0cSR0EAWRaXJj1bsFhBgpzsgI5cSnm35rBZHoRVDvUd271EcX8mZLDBJyLgYoaEntPeVXSLy+6r+jDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:45.480196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4732","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87c59ebeb9daa7c1740634962998d63883518097d03b927d2a67aeb238f67cfa","sha256:1fbef2536a1e8daeea3ce172da36d2f5cb3fe35b1c69795077c8e529844466a8"],"state_sha256":"ff8887a904b40fcbaabefb64e5c51af9c0bf7ad80760b7a430a1de72d03f014f"}