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While soon after, in 1978, the ADHM construction gave a complete description of the moduli spaces of instantons on $\\mathbb{R}^4$, the case of the Euclidean Schwarzschild manifold has resisted many efforts for the past 40 years.\n  By exploring a correspondence between the planar Abelian vortices and spherically symmetric instantons on ES, we obtain: "},"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":"1710.11535","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-31T15:39:31Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"a20b2629ceb6f624210d24d47946e30c60c5fabbe52204f9b3b89b970383eaad","abstract_canon_sha256":"e1030268a5d7498818d7a74abba33732150d431a955369b52b0592648e4bce01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:52.113751Z","signature_b64":"59mgrXmyh5hNAcOBBGpYFO4vUO9fSJ4qYztT74yDqgTdTgtRG1BlEgt1jXXErzPcXPPwQfSxGGxyhxqQiHqBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03497ca74fe25176f92c4c7ce7c0fea1bf215f72a3afd770273dbe0ddff3ab44","last_reissued_at":"2026-05-18T00:10:52.113032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:52.113032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From vortices to instantons on the Euclidean Schwarzschild manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"\\'Akos Nagy, Gon\\c{c}alo Oliveira","submitted_at":"2017-10-31T15:39:31Z","abstract_excerpt":"The first irreducible solution of the $\\mathrm{SU} (2)$ self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on $\\mathbb{R}^4$ were discovered. 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