{"paper":{"title":"Locality of rough path lifts","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Emilio Ferrucci, Ilya Chevyrev","submitted_at":"2026-06-19T02:28:35Z","abstract_excerpt":"Every H\\\"older continuous path $X$ admits a geometric rough path lift $\\boldsymbol{X}$ by the Lyons-Victoir extension theorem. A natural question that emerges when lifting more than one path at once is that of locality, namely whether the lift $\\boldsymbol{X}_{s,t}$ only depends on the increments $X_{s,u}$, $u \\in [s,t]$. We investigate the locality of rough path lifts in deterministic and stochastic settings.\n  On the deterministic side, we show that no local, homogeneous rough path lift can be defined on $\\gamma$-H\\\"older paths for all $\\gamma\\leq 1/2$. More strongly, we show that no L\\'evy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21049","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/2606.21049/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"}