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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.21049","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-19T02:28:35Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"2046c0b9a1609aa2b295189cbe9eeff00f023bc4bbb17d94b5917d2140a6e625","abstract_canon_sha256":"cfe446e1bfa8b37956f8b6e92118265ab39790393c2fe6043f6f801667f99c21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:28.210537Z","signature_b64":"+tashIDXbm2mXQHj8n4AUWhLMJ2pCwW5U5BgGIpjl7vuNbwtW57WtpLY+HDGMnQvZhDtuwh5gdALy5apD+LzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59f92a32b23d2491a2f1fc2e593302bf88ed8c10747d987cac038a01d43d9f52","last_reissued_at":"2026-06-23T01:12:28.210034Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:28.210034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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