{"paper":{"title":"On the Universality of Probe Complexity in $\\mathcal{N}=4$ SYM","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Eric L. Graef, Hendrik J.R. Van Zyl, Horatiu Nastase, Jeff Murugan","submitted_at":"2026-06-19T18:08:51Z","abstract_excerpt":"We investigate Krylov complexity for single-trace operators dual to open strings attached to giant gravitons in planar $\\mathcal{N}=4$ super Yang-Mills theory. We show that in protected and few-body sectors, Krylov dynamics is governed by orthogonal polynomial theory associated to the seed spectral measure, leading to bounded Lanczos coefficients determined solely by spectral support. In particular, for fixed magnon number $M$ and open-string length $L\\rightarrow\\infty$, we derive $a_n=2Mg$ and $b_n\\rightarrow Mg$, demonstrating integrable, band-limited dynamics. This establishes that such sec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21662","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/2606.21662/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"}