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More specifically, let $B_R(0)$ be the ball of radius $R > 0$ about the origin in $R^d$, for $d=1,3$. Let $\\mathcal{I}_R (V_0)$ be the set of real-valued potentials in $C_0^\\infty( \\overline{B}_R(0); R)$ so that the corresponding Schr\\\"odinger operators have the same resonances, including multiplicities, as $H_{V_0}$. We prove that the set $\\mathcal{I}_R (V_0)$ is a compact subset of $C_0^\\infty"},"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":"1803.02172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-03-06T13:47:43Z","cross_cats_sorted":[],"title_canon_sha256":"620bdabb9ad37a2a39a9901e93eebe6b4e59da2b637f3a3e632e8a2f83d96217","abstract_canon_sha256":"497c33a69ad3c98b07be9e5baca188126737f4e45b42fc9631e0ee305f113bbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:55.597886Z","signature_b64":"xQEFNKSHsd7cD/iHcmSNcoRiV9uRHp6xvSkGB/yYcd7gdsiVgrM0j87AKk9qtKwTwjLFx12E2EwTbaZiivAZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db02b3131b9f27c66497afbf514fa6e1b2771520abe3886df5a748d671e6c28a","last_reissued_at":"2026-05-18T00:21:55.597200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:55.597200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compactness of iso-resonant potentials for Schr\\\"odinger operators in dimensions one and three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Peter D. Hislop, Robert Wolf","submitted_at":"2018-03-06T13:47:43Z","abstract_excerpt":"We prove compactness of a restricted set of real-valued, compactly supported potentials $V$ for which the corresponding Schr\\\"odinger operators $H_V$ have the same resonances, including multiplicities. More specifically, let $B_R(0)$ be the ball of radius $R > 0$ about the origin in $R^d$, for $d=1,3$. Let $\\mathcal{I}_R (V_0)$ be the set of real-valued potentials in $C_0^\\infty( \\overline{B}_R(0); R)$ so that the corresponding Schr\\\"odinger operators have the same resonances, including multiplicities, as $H_{V_0}$. 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