{"paper":{"title":"Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.LO","authors_text":"Kirill Osipov","submitted_at":"2026-08-05T14:01:07Z","abstract_excerpt":"We introduce bounded step recursion and a three-parameter hierarchy refining the Grzegorczyk hierarchy. For a strictly increasing function $\\varphi:\\mathbb N\\to\\mathbb N$ with $\\varphi(x)\\ge x+1$, its generalized inverse $$\\rho_\\varphi(y)=\\min\\{z:\\varphi(z)\\ge y\\}$$ replaces the ordinary predecessor and generates the descent schedule $y,\\rho_\\varphi(y),\\rho_\\varphi^{[2]}(y),\\ldots,0$. From a Grzegorczyk basis $B_m$, composition, and bounded step recursion with step $g_n^{[l]}$, we define classes $H^m_{n,l}$, where $m$ measures the initial-function strength, $n$ selects a growth scale, and $l$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04871","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/2608.04871/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"}