{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QNNQRSGUG3G4YF6ISVTLRXKYIL","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":"43c8aa715bc6786a2fcc6c1d349cc22fd84f83488d15ce840eb5d81544ab9c3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T08:01:54Z","title_canon_sha256":"6687ef03fcbc1d4509a77b693489fa53dcf6fe51f74b5a3a721a2cfdfa4af61d"},"schema_version":"1.0","source":{"id":"2607.25403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25403","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25403v1","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25403","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"QNNQRSGUG3G4","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_16","alias_value":"QNNQRSGUG3G4YF6I","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_8","alias_value":"QNNQRSGU","created_at":"2026-07-29T01:25:13Z"}],"graph_snapshots":[{"event_id":"sha256:ce518d8952aa09a02aba6e4425b415be431573d69509638ad746f2d535e53056","target":"graph","created_at":"2026-07-29T01:25:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.25403/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we show a new lower bound for extreme values of quadratic Dirichlet $L$-functions with prime-related moduli, which generalizes the work of Darbar and Maiti in 2025, and sharpens a recent work of Gao in 2026.","authors_text":"Hao Zhang, Shengbo Zhao, Weijia Wang, Zikang Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T08:01:54Z","title":"Extreme values of quadratic Dirichlet $L$-functions with prime-related moduli"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25403","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:ea1cf7069ef90b597837e9be267580464c98d4c3c3d9d445292ab4ddbb1358fd","target":"record","created_at":"2026-07-29T01:25:13Z","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":"43c8aa715bc6786a2fcc6c1d349cc22fd84f83488d15ce840eb5d81544ab9c3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T08:01:54Z","title_canon_sha256":"6687ef03fcbc1d4509a77b693489fa53dcf6fe51f74b5a3a721a2cfdfa4af61d"},"schema_version":"1.0","source":{"id":"2607.25403","kind":"arxiv","version":1}},"canonical_sha256":"835b08c8d436cdcc17c89566b8dd5842ec10b7b663793cb29ba4f416eddda678","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"835b08c8d436cdcc17c89566b8dd5842ec10b7b663793cb29ba4f416eddda678","first_computed_at":"2026-07-29T01:25:13.853294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T01:25:13.853294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wU/G7lynOICgq5sHBU2eCgMLohfqIbBd5cWAilvWbE6dqPO7cImxVfIlc6FXLGKZXZm/wQTCJZNKEXCAinmiDw==","signature_status":"signed_v1","signed_at":"2026-07-29T01:25:13.854128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.25403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea1cf7069ef90b597837e9be267580464c98d4c3c3d9d445292ab4ddbb1358fd","sha256:ce518d8952aa09a02aba6e4425b415be431573d69509638ad746f2d535e53056"],"state_sha256":"7a025898ee488e62bcded8e9ff6b5f89ce325d7d6682b82ade5d72fdb801afdc"}