{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CKNFEIHABLK6RJDRX256VMHP3H","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":"03deb6c997fdc245daedc0d2d7a31b9186bc160c048d3919d3fe6720bb2670d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-25T22:16:43Z","title_canon_sha256":"d51d6343358b1d39abb078f042ef5a52ddc11e71e2d19a8e23a5e47f9b9e6b0d"},"schema_version":"1.0","source":{"id":"1601.06833","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06833","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06833v1","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06833","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"CKNFEIHABLK6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CKNFEIHABLK6RJDR","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CKNFEIHA","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:c46772f248581e941af5ee16a02809537c795b1ad7680e782eefdb15841d8d81","target":"graph","created_at":"2026-05-17T23:53:13Z","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 study the $1$-level density of low-lying zeros of Dirichlet $L$-functions attached to real primitive characters of conductor at most $X$. Under the Generalized Riemann Hypothesis, we give an asymptotic expansion of this quantity in descending powers of $\\log X$, which is valid when the support of the Fourier transform of the corresponding even test function $\\phi$ is contained in $(-2,2)$. We uncover a phase transition when the supremum $\\sigma$ of the support of $\\hat \\phi$ reaches $1$, both in the main term and in the lower order terms. A new lower order term appearing at $\\sigma=1$ invol","authors_text":"Anders S\\\"odergren, Daniel Fiorilli, James Parks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-25T22:16:43Z","title":"Low-lying zeros of quadratic Dirichlet $L$-functions: Lower order terms for extended support"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06833","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:c7a927b07a571df899207962dd8cad9185c53e1f4bd0ea1a68868ae591a1a4d6","target":"record","created_at":"2026-05-17T23:53:13Z","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":"03deb6c997fdc245daedc0d2d7a31b9186bc160c048d3919d3fe6720bb2670d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-25T22:16:43Z","title_canon_sha256":"d51d6343358b1d39abb078f042ef5a52ddc11e71e2d19a8e23a5e47f9b9e6b0d"},"schema_version":"1.0","source":{"id":"1601.06833","kind":"arxiv","version":1}},"canonical_sha256":"129a5220e00ad5e8a471bebbeab0efd9c73e18512a97027402cde69af12da07a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"129a5220e00ad5e8a471bebbeab0efd9c73e18512a97027402cde69af12da07a","first_computed_at":"2026-05-17T23:53:13.406748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:13.406748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ldhSjVf4wBHKlOOQ5Ji8lYDPZ86CZwe9Upyybsoe0u4FBX83pegp+fVDBZHwkmtd4WN6f/DzNpGCdTEL8rfpDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:13.407495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06833","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a927b07a571df899207962dd8cad9185c53e1f4bd0ea1a68868ae591a1a4d6","sha256:c46772f248581e941af5ee16a02809537c795b1ad7680e782eefdb15841d8d81"],"state_sha256":"6dcd2723788c878c2785985970d509222210b446bd353cfd8ade550393739d24"}