{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SURD76Q4GDPJ7XVVDKDRT4VC3E","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":"078326ec6dfa928124666f731479b2f9069194b1a678acf36e7b810cdbcb2f99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-09-11T18:05:55Z","title_canon_sha256":"f98053e48b6063221c574b663ae4767d7456ec36025b6b073d74bb5c79db8cf6"},"schema_version":"1.0","source":{"id":"2509.09771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.09771","created_at":"2026-07-05T12:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"2509.09771v1","created_at":"2026-07-05T12:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.09771","created_at":"2026-07-05T12:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"SURD76Q4GDPJ","created_at":"2026-07-05T12:09:48Z"},{"alias_kind":"pith_short_16","alias_value":"SURD76Q4GDPJ7XVV","created_at":"2026-07-05T12:09:48Z"},{"alias_kind":"pith_short_8","alias_value":"SURD76Q4","created_at":"2026-07-05T12:09:48Z"}],"graph_snapshots":[{"event_id":"sha256:0755a3f21010270835bba30ca2c51c9b3d9efdf9a5e5ebcf41a59616b985c0dc","target":"graph","created_at":"2026-07-05T12:09:48Z","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/2509.09771/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate large values of Dirichlet polynomials with multiplicative coefficients $\\sum_{n\\le N}f(n)n^{it}$, where $1\\ll t\\le T$ for large $T$. We prove an improved Omega result in the region $\\exp((\\log T)^{\\frac12+\\varepsilon})\\le N\\le\\sqrt T$, where $T$ is large. We also show an Omega result when $\\log N$ is around $\\sqrt{\\log T\\log_2T}$.","authors_text":"Hao Zhang, Shengbo Zhao, Weijia Wang, Yutong Song, Zikang Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-09-11T18:05:55Z","title":"Large values of Dirichlet polynomials with multiplicative coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09771","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:c843e20af26aac752911ab055835083b7e06771b6bcafff28c4680e24e96a36c","target":"record","created_at":"2026-07-05T12:09:48Z","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":"078326ec6dfa928124666f731479b2f9069194b1a678acf36e7b810cdbcb2f99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-09-11T18:05:55Z","title_canon_sha256":"f98053e48b6063221c574b663ae4767d7456ec36025b6b073d74bb5c79db8cf6"},"schema_version":"1.0","source":{"id":"2509.09771","kind":"arxiv","version":1}},"canonical_sha256":"95223ffa1c30de9fdeb51a8719f2a2d90c4f9b25603694c964aa290aa238e555","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95223ffa1c30de9fdeb51a8719f2a2d90c4f9b25603694c964aa290aa238e555","first_computed_at":"2026-07-05T12:09:48.933078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:09:48.933078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+fyqL+YLcGTkx55pJqcdT8Cjy5yyA8zpDfBLNv0T3moiII0ca0D1qX+Lp3i/tCiL2icKAkqCw833G8kXrakDg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:09:48.933591Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.09771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c843e20af26aac752911ab055835083b7e06771b6bcafff28c4680e24e96a36c","sha256:0755a3f21010270835bba30ca2c51c9b3d9efdf9a5e5ebcf41a59616b985c0dc"],"state_sha256":"21e84006d755a3d20cd53f255e35eed5e58e047d263381cf7120433c59d64745"}