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We prove $\\displaystyle \\Gamma^\\Delta(dx)\n  =\n  -\\frac{n^\\top a(x)n}{2\\sqrt{1+\\alpha^2}}\\,\\sigma_\\Delta(dx)$, with $n=(1,-\\alpha)$, so the diagonal component is non-positive and strictly negative under local ellipticity. This implies that every interior kink point lies in the continuation region. We further show that th"},"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":"2606.18214","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-16T17:44:18Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"28dc660a1ba23fb58452b48dc23da93475c7c3e82207d28c8922307839b0d0f4","abstract_canon_sha256":"310cca820e6320e23bd88bdaa86754b4979f5da04784c583ed2a5bfd0cc4b5d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:51.241979Z","signature_b64":"7DnbXhIpbiKNXKOswisMuqKVGsndWxylHw4fWFLC73qE4q88GGDidgBoMEgsnunP7oTq82L2TG18Q7FBu9UYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3742dee0639999cab03db10f8e448cad425967e352b8ca43f805226260b3fbe6","last_reissued_at":"2026-06-19T16:10:51.241603Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:51.241603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time and Killed Resolvents in Reflected Optimal Stopping with a Max Payoff","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Louis Shuo Wang, Ye Liang","submitted_at":"2026-06-16T17:44:18Z","abstract_excerpt":"We study infinite-horizon optimal stopping for normally reflected two-dimensional diffusions in the positive quadrant with max payoff \\(G(x_1,x_2)=x_1\\vee\\alpha x_2\\). The non-smooth payoff produces a singular stopping-gain measure on the kink set \\(\\Delta=\\{x_1=\\alpha x_2\\}\\). We prove $\\displaystyle \\Gamma^\\Delta(dx)\n  =\n  -\\frac{n^\\top a(x)n}{2\\sqrt{1+\\alpha^2}}\\,\\sigma_\\Delta(dx)$, with $n=(1,-\\alpha)$, so the diagonal component is non-positive and strictly negative under local ellipticity. This implies that every interior kink point lies in the continuation region. 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