{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:YJAXBPGG4GVWLIVBOXZVHBLZZU","short_pith_number":"pith:YJAXBPGG","canonical_record":{"source":{"id":"2006.16886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-30T15:18:52Z","cross_cats_sorted":[],"title_canon_sha256":"acd235ede2151338267dadf8338a096ad08156f63e9dbc55ed28a8990cb55b4a","abstract_canon_sha256":"ae8b46c1a29617f48183fab75d52c6247e720fc51248c7d3d262de669473018b"},"schema_version":"1.0"},"canonical_sha256":"c24170bcc6e1ab65a2a175f3538579cd355f251797e06bf77ce359726b78d3a5","source":{"kind":"arxiv","id":"2006.16886","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.16886","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"2006.16886v1","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.16886","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"YJAXBPGG4GVW","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"pith_short_16","alias_value":"YJAXBPGG4GVWLIVB","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"pith_short_8","alias_value":"YJAXBPGG","created_at":"2026-07-05T01:14:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:YJAXBPGG4GVWLIVBOXZVHBLZZU","target":"record","payload":{"canonical_record":{"source":{"id":"2006.16886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-30T15:18:52Z","cross_cats_sorted":[],"title_canon_sha256":"acd235ede2151338267dadf8338a096ad08156f63e9dbc55ed28a8990cb55b4a","abstract_canon_sha256":"ae8b46c1a29617f48183fab75d52c6247e720fc51248c7d3d262de669473018b"},"schema_version":"1.0"},"canonical_sha256":"c24170bcc6e1ab65a2a175f3538579cd355f251797e06bf77ce359726b78d3a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:14:59.062733Z","signature_b64":"8DIk0L/7q/13LZ4VyhMSCS6efrSvctVd4TXTG/vJBu3pAaiEOSpdfVLefTCLSm7qkuDOZO76LQ6AInJ/zULKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c24170bcc6e1ab65a2a175f3538579cd355f251797e06bf77ce359726b78d3a5","last_reissued_at":"2026-07-05T01:14:59.062376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:14:59.062376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.16886","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":"2026-07-05T01:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/lS2KbLpLdPpAnpGN2OS4fzkue/SPOPVOTXZpf2oLQpWa3NiK2Ko6ixq3/qQtw/oIcCDmSdQy+YYwg/RhrQ4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:19:33.053064Z"},"content_sha256":"6cef775f5a465b385388d28d33535ab65de42f7e9f0589cce31aeab8f930c17e","schema_version":"1.0","event_id":"sha256:6cef775f5a465b385388d28d33535ab65de42f7e9f0589cce31aeab8f930c17e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:YJAXBPGG4GVWLIVBOXZVHBLZZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower Order Terms for Expected Value of Traces of Frobenius of a Family of Cyclic Covers of $\\mathbb{P}^1_{\\mathbb{F}_q}$ and One-Level Densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Patrick Meisner","submitted_at":"2020-06-30T15:18:52Z","abstract_excerpt":"We consider the expected value of $\\mbox{Tr}(\\Theta_C^n)$ where $C$ runs over a thin family of $r$-cyclic covers of $\\mathbb{P}^1_{\\mathbb{F}_q}$ for any $r$. We obtain many lower order terms dependent on the divisors of $r$. We use these results to calculate the one-level density of the family and hypothesize a refined one-level density result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16886","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.16886/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mazyWpKQ1RzfKPrRWeV9j+IsLfxqLte3LEFI1uu9AFwb0lJ7pDammnUaZnVMdpCCjmAZe2xIlj5VogpjEKa+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:19:33.053858Z"},"content_sha256":"6f85e1be6a88b24a31d72e85d3548dad66ac1b99f01502d590f0bc10cbc7e903","schema_version":"1.0","event_id":"sha256:6f85e1be6a88b24a31d72e85d3548dad66ac1b99f01502d590f0bc10cbc7e903"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJAXBPGG4GVWLIVBOXZVHBLZZU/bundle.json","state_url":"https://pith.science/pith/YJAXBPGG4GVWLIVBOXZVHBLZZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJAXBPGG4GVWLIVBOXZVHBLZZU/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":"2026-08-10T02:19:33Z","links":{"resolver":"https://pith.science/pith/YJAXBPGG4GVWLIVBOXZVHBLZZU","bundle":"https://pith.science/pith/YJAXBPGG4GVWLIVBOXZVHBLZZU/bundle.json","state":"https://pith.science/pith/YJAXBPGG4GVWLIVBOXZVHBLZZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJAXBPGG4GVWLIVBOXZVHBLZZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:YJAXBPGG4GVWLIVBOXZVHBLZZU","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":"ae8b46c1a29617f48183fab75d52c6247e720fc51248c7d3d262de669473018b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-30T15:18:52Z","title_canon_sha256":"acd235ede2151338267dadf8338a096ad08156f63e9dbc55ed28a8990cb55b4a"},"schema_version":"1.0","source":{"id":"2006.16886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.16886","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"2006.16886v1","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.16886","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"YJAXBPGG4GVW","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"pith_short_16","alias_value":"YJAXBPGG4GVWLIVB","created_at":"2026-07-05T01:14:59Z"},{"alias_kind":"pith_short_8","alias_value":"YJAXBPGG","created_at":"2026-07-05T01:14:59Z"}],"graph_snapshots":[{"event_id":"sha256:6f85e1be6a88b24a31d72e85d3548dad66ac1b99f01502d590f0bc10cbc7e903","target":"graph","created_at":"2026-07-05T01:14:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.16886/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the expected value of $\\mbox{Tr}(\\Theta_C^n)$ where $C$ runs over a thin family of $r$-cyclic covers of $\\mathbb{P}^1_{\\mathbb{F}_q}$ for any $r$. We obtain many lower order terms dependent on the divisors of $r$. We use these results to calculate the one-level density of the family and hypothesize a refined one-level density result.","authors_text":"Patrick Meisner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-30T15:18:52Z","title":"Lower Order Terms for Expected Value of Traces of Frobenius of a Family of Cyclic Covers of $\\mathbb{P}^1_{\\mathbb{F}_q}$ and One-Level Densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.16886","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":"sha256:6cef775f5a465b385388d28d33535ab65de42f7e9f0589cce31aeab8f930c17e","target":"record","created_at":"2026-07-05T01:14:59Z","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":"ae8b46c1a29617f48183fab75d52c6247e720fc51248c7d3d262de669473018b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-30T15:18:52Z","title_canon_sha256":"acd235ede2151338267dadf8338a096ad08156f63e9dbc55ed28a8990cb55b4a"},"schema_version":"1.0","source":{"id":"2006.16886","kind":"arxiv","version":1}},"canonical_sha256":"c24170bcc6e1ab65a2a175f3538579cd355f251797e06bf77ce359726b78d3a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c24170bcc6e1ab65a2a175f3538579cd355f251797e06bf77ce359726b78d3a5","first_computed_at":"2026-07-05T01:14:59.062376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:14:59.062376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8DIk0L/7q/13LZ4VyhMSCS6efrSvctVd4TXTG/vJBu3pAaiEOSpdfVLefTCLSm7qkuDOZO76LQ6AInJ/zULKDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:14:59.062733Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.16886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cef775f5a465b385388d28d33535ab65de42f7e9f0589cce31aeab8f930c17e","sha256:6f85e1be6a88b24a31d72e85d3548dad66ac1b99f01502d590f0bc10cbc7e903"],"state_sha256":"ccd6e323e7fe54b33e30206041355999807db6329ae3887202bd98acb8f7f1b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D9bjP2HC7Cf0ug4iVw+AuB6kxo1A5c393PA3ASccfVlWtruRYAmtikzLFWCfmrkxtq0Mz0XIEKX3Wz/EOU0mDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T02:19:33.059454Z","bundle_sha256":"677ec707c25320746b586b899d97bd78a81a3b1656d2d1ffd63f4cbfa4b7914c"}}