{"paper":{"title":"(In)Efficient Market States and Rough Volatility Detected via Grunwald-Letnikov Fractional Derivative","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["q-fin.MF"],"primary_cat":"q-fin.ST","authors_text":"Daniele Angelini","submitted_at":"2026-06-26T10:23:02Z","abstract_excerpt":"Testing self-similarity in fractional processes from a single observed trajectory is difficult under long-range dependence, because the associated Kolmogorov--Smirnov (KS) statistic undergoes a phase transition when $H>1/2$. In this regime, the classical limit collapses to a non-functional absolute Gaussian law and finite-sample convergence becomes severely distorted. This paper introduces a regime-adaptive KS/GL--KS framework based on the discrete Gr\\\"{u}nwald--Letnikov (GL) fractional derivative. The GL filter removes the low-frequency long-memory singularity while preserving the finite-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27932","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/2606.27932/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"}