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As its application, we show that if $D$ is an $\\mathbb{R}$-Cartier divisor on a strongly $F$-regular projective variety, then the non-nef locus of $D$ coincides with the restricted base locus of $D$. This is a generalization of a result of Musta\\c{t}\\v{a} to the singular case and can be viewed as a char"},"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":"1602.02996","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-09T14:28:47Z","cross_cats_sorted":[],"title_canon_sha256":"3d1605aa24bac9c2baa36f9eb36766238d88a00aad47fe63e29d2cac724f0189","abstract_canon_sha256":"48d052204c611d7ee14c98c87c4f923e110ac9eedff71f10a35eab6514b5b35e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:48.698075Z","signature_b64":"VcwKokZcWILSlRSFGuMjXdBmx73JligbNg4d2x/nZRyxa9hPdQQZP183xNCg2X2YS1KBjb24x1iL556tbKshCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b8a22b17a9fced03c044cf3e061828d2a14e7f367b5edef857f9c3bb66c5016","last_reissued_at":"2026-05-18T00:37:48.697281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:48.697281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of test ideals of divisors with small multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kenta Sato","submitted_at":"2016-02-09T14:28:47Z","abstract_excerpt":"Let $(X, \\Delta)$ be a log pair in characteristic $p>0$ and $P$ be a (not necessarily closed) point of $X$. 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