{"paper":{"title":"The Aurellion Function: A Recursive Fast-Growing Hierarchy Beyond Knuth Notation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Daniel Vodrazka (Independent theorist)","submitted_at":"2025-06-05T14:12:03Z","abstract_excerpt":"We introduce the Aurellion Function, a novel recursively defined fast-growing hierarchy based on Knuth's up-arrow notation, defined by $A_1 = 10 \\uparrow\\uparrow\\uparrow 10$, $A_{n+1} = 10 \\uparrow^{A_n} 10$, where the number of arrows in the operation increases superexponentially with $n$. We analyze its growth rate relative to classical hierarchies such as the fast-growing hierarchy $(f_\\alpha)_{\\alpha < \\varepsilon_0}$, and discuss its provability status in formal arithmetic. We provide formal bounds showing $A_n$ dominates all functions provably total in Peano Arithmetic, situating the Aur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05067","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/2506.05067/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"}