{"paper":{"title":"The Fourth-Root Complexity of Data Movement","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.PF","cs.PL"],"primary_cat":"cs.CC","authors_text":"Chen Ding","submitted_at":"2026-06-29T22:01:50Z","abstract_excerpt":"Time complexity typically assumes $O(1)$ cost per data access. This paper presents an analysis based on an abstract memory hierarchy. For a common class of applications, it shows that the data-access cost scales with the fourth root of data size, that is, as data size $N$ increases, the cost of each access increases at the rate of $N^\\frac{1}{4}$.\n  While the analysis does not predict performance, it predicts scalability. Specifically, the paper provides a precise analysis that shows the constant-factor difference between cases where the miss ratio follows a power law versus an exponential dec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30948","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/2606.30948/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"}