{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Q5KTNOLYKST6F66VUMMJHRYSY5","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":"441ac0378d20d8e5b16b26e5d1ffa71df9c6e84b7654e32ff3c40f8df30e431c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-08-12T17:00:49Z","title_canon_sha256":"805d836b6eef54e8bcf0021ec0142a665f4641e2fd360c5e9098085e51704f9b"},"schema_version":"1.0","source":{"id":"2608.12257","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.12257","created_at":"2026-08-13T01:30:38Z"},{"alias_kind":"arxiv_version","alias_value":"2608.12257v1","created_at":"2026-08-13T01:30:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.12257","created_at":"2026-08-13T01:30:38Z"},{"alias_kind":"pith_short_12","alias_value":"Q5KTNOLYKST6","created_at":"2026-08-13T01:30:38Z"},{"alias_kind":"pith_short_16","alias_value":"Q5KTNOLYKST6F66V","created_at":"2026-08-13T01:30:38Z"},{"alias_kind":"pith_short_8","alias_value":"Q5KTNOLY","created_at":"2026-08-13T01:30:38Z"}],"graph_snapshots":[{"event_id":"sha256:9d8983c1b994f3add190f6365809f1d01ec9f4dacef2f73b325a98019970f06f","target":"graph","created_at":"2026-08-13T01:30:38Z","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/2608.12257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\pi$ and $\\pi'$ be unitary cuspidal automorphic representations of $\\mathrm{GL}(n)$ and $\\mathrm{GL}(n')$ over a number field $F$. Let $\\mathfrak{C}_{\\pi}$ be the analytic conductor of $\\pi$. We develop a new approach to zero-free regions for $L$-functions via lower bounds for power sums, proving for all $\\varepsilon>0$ the existence of ineffective constants $c=c_{n,F,\\varepsilon}>0$ and $c'=c'_{n,F,\\pi',\\varepsilon}>0$ such that the standard $L$-function $L(s,\\pi)$ satisfies \\[ |L(\\sigma+it,\\pi)|\\geq c(\\mathfrak{C}_{\\pi}(|t|+3))^{-\\varepsilon},\\qquad \\sigma\\geq 1-c(\\mathfrak{C}_{\\pi}(|t|","authors_text":"Jesse Thorner","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-08-12T17:00:49Z","title":"Power sums and Siegel-type zero-free regions for L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12257","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:bd63bcdc3e25edb3e8bde365b2619d303ab3af27d008d8f57e45f96e16343182","target":"record","created_at":"2026-08-13T01:30:38Z","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":"441ac0378d20d8e5b16b26e5d1ffa71df9c6e84b7654e32ff3c40f8df30e431c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-08-12T17:00:49Z","title_canon_sha256":"805d836b6eef54e8bcf0021ec0142a665f4641e2fd360c5e9098085e51704f9b"},"schema_version":"1.0","source":{"id":"2608.12257","kind":"arxiv","version":1}},"canonical_sha256":"875536b97854a7e2fbd5a31893c712c75e5e8a074daed52407006096fc9d76b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"875536b97854a7e2fbd5a31893c712c75e5e8a074daed52407006096fc9d76b8","first_computed_at":"2026-08-13T01:30:38.281941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-13T01:30:38.281941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KsGgXNwdgijK7XahaxADPBa/84EfM1qnEmEeOnQzzMBngwslpGf9iNN2QG6N3J6y4YPpm5xY8GasYAHxXcFHAw==","signature_status":"signed_v1","signed_at":"2026-08-13T01:30:38.284281Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.12257","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd63bcdc3e25edb3e8bde365b2619d303ab3af27d008d8f57e45f96e16343182","sha256:9d8983c1b994f3add190f6365809f1d01ec9f4dacef2f73b325a98019970f06f"],"state_sha256":"e3b5dda08ed52852a0624ccd93392905622e8234af4d106047af4e5b24cab812"}