{"paper":{"title":"Near-Maximum Circuit Lower Bounds for Exponential Time with Merlin-Arthur Queries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hanlin Ren, Ryan Williams","submitted_at":"2026-07-10T20:33:08Z","abstract_excerpt":"We prove a near-maximum ($2^n / n$) circuit lower bound for the complexity class $\\mathsf{E}^{\\mathrm{pr}\\mathsf{MA}}/_1$, corresponding to exponential time with access to a promise-$\\mathsf{MA}$ oracle and one bit of advice. Our proof incorporates the iterative win-win paradigm (Chen--Lu--Oliveira--Ren--Santhanam, FOCS'23), the reduction from the Range Avoidance problem to circuit lower bounds (Je\\v{r}\\'abek, Ann. Pure Appl. Log. '04; Korten, FOCS'21), and the PCP theorem. Crucial to our proof is the analysis of the complexity class $\\mathsf{P}^\\mathsf{NP}[{\\textsf{#rounds}}=r, {\\textsf{lengt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09963","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09963/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}