{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CXGXA5WAGLSSG6WHPMKL2H7BK6","short_pith_number":"pith:CXGXA5WA","canonical_record":{"source":{"id":"1905.10362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-23T14:15:54Z","cross_cats_sorted":[],"title_canon_sha256":"031f49f41c417af3c63fd828253290f163f573ee18912c48a9e2a197e72b003a","abstract_canon_sha256":"cac9a9bd9e9a013ac3acb0977fe48e212b98150f9d7666bea559e004d8aa50e1"},"schema_version":"1.0"},"canonical_sha256":"15cd7076c032e5237ac77b14bd1fe157b271fd217d9a3cae41864ec02dd02bfb","source":{"kind":"arxiv","id":"1905.10362","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10362","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10362v2","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10362","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"CXGXA5WAGLSS","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"pith_short_16","alias_value":"CXGXA5WAGLSSG6WH","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"pith_short_8","alias_value":"CXGXA5WA","created_at":"2026-07-05T02:04:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CXGXA5WAGLSSG6WHPMKL2H7BK6","target":"record","payload":{"canonical_record":{"source":{"id":"1905.10362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-23T14:15:54Z","cross_cats_sorted":[],"title_canon_sha256":"031f49f41c417af3c63fd828253290f163f573ee18912c48a9e2a197e72b003a","abstract_canon_sha256":"cac9a9bd9e9a013ac3acb0977fe48e212b98150f9d7666bea559e004d8aa50e1"},"schema_version":"1.0"},"canonical_sha256":"15cd7076c032e5237ac77b14bd1fe157b271fd217d9a3cae41864ec02dd02bfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:04:39.154070Z","signature_b64":"6Qn7p7sMENv4fxYUZk2y0j3oIgwcHvk83Mw7WKNwePwJbiwS2qttfyhRkIyg25rG9w4LwUiVuvVVf3Bb2D4WDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15cd7076c032e5237ac77b14bd1fe157b271fd217d9a3cae41864ec02dd02bfb","last_reissued_at":"2026-07-05T02:04:39.153482Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:04:39.153482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.10362","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":"2026-07-05T02:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ae9RFRTDZn55eWO3zNk2YlQn25Otd0+1oCp18J1bBodTw3WxRfGfdM6dsLyG494vIBfu0q9tjMjd9m9nhxk5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:49:28.958183Z"},"content_sha256":"4a5b323c603724fcab2e09586297227161dcfa50b958ac49c08093c6b5c16e6b","schema_version":"1.0","event_id":"sha256:4a5b323c603724fcab2e09586297227161dcfa50b958ac49c08093c6b5c16e6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CXGXA5WAGLSSG6WHPMKL2H7BK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower Order Terms for the One-Level Density of a Symplectic Family of Hecke L-Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ezra Waxman","submitted_at":"2019-05-23T14:15:54Z","abstract_excerpt":"In this paper we apply the $L$-function Ratios Conjecture to compute the one-level density for a symplectic family of $L$-functions attached to Hecke characters of infinite order. When the support of the Fourier transform of the corresponding test function $f$ reaches $1$, we observe a transition in the main term, as well as in the lower order term. The transition in the lower order term is in line with behavior recently observed by D. Fiorilli, J. Parks, and A. S\\\"odergren in their study of a symplectic family of quadratic Dirichlet $L$-functions. We then directly calculate main and lower ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10362","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.10362/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":"2026-07-05T02:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bGdVq1oLDnEVsK8tNOhA1sGmhYCVgjYHeLowdIZAzhYlREt25Af/yJxcIDvuiccrWKYwPR66SHxGsu+tbkwYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:49:28.958707Z"},"content_sha256":"0c9cf2f673f1367b5ea9043b3214090d68c98a82b1da52f38b422525b543d281","schema_version":"1.0","event_id":"sha256:0c9cf2f673f1367b5ea9043b3214090d68c98a82b1da52f38b422525b543d281"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXGXA5WAGLSSG6WHPMKL2H7BK6/bundle.json","state_url":"https://pith.science/pith/CXGXA5WAGLSSG6WHPMKL2H7BK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXGXA5WAGLSSG6WHPMKL2H7BK6/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":"2026-08-15T21:49:28Z","links":{"resolver":"https://pith.science/pith/CXGXA5WAGLSSG6WHPMKL2H7BK6","bundle":"https://pith.science/pith/CXGXA5WAGLSSG6WHPMKL2H7BK6/bundle.json","state":"https://pith.science/pith/CXGXA5WAGLSSG6WHPMKL2H7BK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXGXA5WAGLSSG6WHPMKL2H7BK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CXGXA5WAGLSSG6WHPMKL2H7BK6","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":"cac9a9bd9e9a013ac3acb0977fe48e212b98150f9d7666bea559e004d8aa50e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-23T14:15:54Z","title_canon_sha256":"031f49f41c417af3c63fd828253290f163f573ee18912c48a9e2a197e72b003a"},"schema_version":"1.0","source":{"id":"1905.10362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10362","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10362v2","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10362","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"CXGXA5WAGLSS","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"pith_short_16","alias_value":"CXGXA5WAGLSSG6WH","created_at":"2026-07-05T02:04:39Z"},{"alias_kind":"pith_short_8","alias_value":"CXGXA5WA","created_at":"2026-07-05T02:04:39Z"}],"graph_snapshots":[{"event_id":"sha256:0c9cf2f673f1367b5ea9043b3214090d68c98a82b1da52f38b422525b543d281","target":"graph","created_at":"2026-07-05T02:04:39Z","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/1905.10362/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we apply the $L$-function Ratios Conjecture to compute the one-level density for a symplectic family of $L$-functions attached to Hecke characters of infinite order. When the support of the Fourier transform of the corresponding test function $f$ reaches $1$, we observe a transition in the main term, as well as in the lower order term. The transition in the lower order term is in line with behavior recently observed by D. Fiorilli, J. Parks, and A. S\\\"odergren in their study of a symplectic family of quadratic Dirichlet $L$-functions. We then directly calculate main and lower ord","authors_text":"Ezra Waxman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-23T14:15:54Z","title":"Lower Order Terms for the One-Level Density of a Symplectic Family of Hecke L-Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10362","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":"sha256:4a5b323c603724fcab2e09586297227161dcfa50b958ac49c08093c6b5c16e6b","target":"record","created_at":"2026-07-05T02:04:39Z","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":"cac9a9bd9e9a013ac3acb0977fe48e212b98150f9d7666bea559e004d8aa50e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-23T14:15:54Z","title_canon_sha256":"031f49f41c417af3c63fd828253290f163f573ee18912c48a9e2a197e72b003a"},"schema_version":"1.0","source":{"id":"1905.10362","kind":"arxiv","version":2}},"canonical_sha256":"15cd7076c032e5237ac77b14bd1fe157b271fd217d9a3cae41864ec02dd02bfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15cd7076c032e5237ac77b14bd1fe157b271fd217d9a3cae41864ec02dd02bfb","first_computed_at":"2026-07-05T02:04:39.153482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:04:39.153482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Qn7p7sMENv4fxYUZk2y0j3oIgwcHvk83Mw7WKNwePwJbiwS2qttfyhRkIyg25rG9w4LwUiVuvVVf3Bb2D4WDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:04:39.154070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.10362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a5b323c603724fcab2e09586297227161dcfa50b958ac49c08093c6b5c16e6b","sha256:0c9cf2f673f1367b5ea9043b3214090d68c98a82b1da52f38b422525b543d281"],"state_sha256":"364909b649dd657e9473d255409c554530bb3a7f88924f331fbb41907c82782a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lm6SA+1vCIK2vYcXQfUx6eb9WSiqQqcmjKvbRde6DiCMO/N9/DEnKfn0B9YqzR0mYlbOfiCzthQgS7gZLgDwAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T21:49:28.962976Z","bundle_sha256":"67e64999db1cbe0024f400de7d5853462f606efafb51afb0d667a7ecc5188b98"}}