{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:US25KBI4KCQ4TZYTZGI7QTSWUA","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":"c213070d92e61c4c8d8d52976bad7e1343f8227cc80f3ca3f1cfb80c482de8a4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-04-12T10:31:19Z","title_canon_sha256":"4c91977451949d84aefebb67db6a25478cc753231e3dff9db9d9fd8731b44452"},"schema_version":"1.0","source":{"id":"2404.08380","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.08380","created_at":"2026-07-05T11:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"2404.08380v2","created_at":"2026-07-05T11:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.08380","created_at":"2026-07-05T11:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"US25KBI4KCQ4","created_at":"2026-07-05T11:52:12Z"},{"alias_kind":"pith_short_16","alias_value":"US25KBI4KCQ4TZYT","created_at":"2026-07-05T11:52:12Z"},{"alias_kind":"pith_short_8","alias_value":"US25KBI4","created_at":"2026-07-05T11:52:12Z"}],"graph_snapshots":[{"event_id":"sha256:17dd7c8f1b3cfa50b4f7e1e2dd1900a47f2ace9326782b6829d6c732d548e9d2","target":"graph","created_at":"2026-07-05T11:52:12Z","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/2404.08380/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By means of a Fourier optimization framework, we improve the current asymptotic bounds under GRH for two classical problems in number theory: the problem of estimating the least quadratic non-residue modulo a prime, and the problem of estimating the least prime in an arithmetic progression.","authors_text":"Antonio Pedro Ramos, Emanuel Carneiro, Emily Quesada-Herrera, Micah B. Milinovich","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-04-12T10:31:19Z","title":"Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.08380","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":"sha256:09215e2bde518e42779b2029a660a4fee9974cb0f1eb56db0bbda77a7187a51b","target":"record","created_at":"2026-07-05T11:52:12Z","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":"c213070d92e61c4c8d8d52976bad7e1343f8227cc80f3ca3f1cfb80c482de8a4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-04-12T10:31:19Z","title_canon_sha256":"4c91977451949d84aefebb67db6a25478cc753231e3dff9db9d9fd8731b44452"},"schema_version":"1.0","source":{"id":"2404.08380","kind":"arxiv","version":2}},"canonical_sha256":"a4b5d5051c50a1c9e713c991f84e56a0349381cbcf7435ffa054fbfe70380277","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4b5d5051c50a1c9e713c991f84e56a0349381cbcf7435ffa054fbfe70380277","first_computed_at":"2026-07-05T11:52:12.857060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:52:12.857060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"srvHmERYQeH+AAfnUVYWszrtAD2QxALWD1d+R/YRU+ZAru68wXK35K1KwavAZ0r8ThwEGsUIROPT3G5XsyB7CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:52:12.857503Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.08380","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09215e2bde518e42779b2029a660a4fee9974cb0f1eb56db0bbda77a7187a51b","sha256:17dd7c8f1b3cfa50b4f7e1e2dd1900a47f2ace9326782b6829d6c732d548e9d2"],"state_sha256":"92ed9d59cf45930e7f2b1fd1a820d348f6b9b54debbdc342ff3329b37408e4d1"}