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Specifically, we characterize the pairs (C,A) of compact connected abelian groups C and subgroups A such that A \\cong q(G) and C \\cong q(\\widetilde G). As a consequence, we show that for every positive integer n or n=\\omega, there exist plenty of abelian pseudocompact perfectly minimal n-dimensional groups G such that the quasi-component of G is not dense in the quasi-component of the completion of G."},"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":"1007.4285","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-07-24T21:54:44Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"05652f39d810e23b6d688f4fd67ba450be20e95072f6f8f039efdf474b46fc86","abstract_canon_sha256":"c89ec336fcdeebb603741fefb837f44d877be87f5c7795e37c9e5e72d3e52dd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:01.406352Z","signature_b64":"jGLm7RIbwifazuC9nXwKsc0bby00ztHST02H5pMdXj+ZJ0xOT9k5I6+TSVwOWMTJ5UC581HI+QYjo4AOj5rGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7a785b70f0060d5eeeb592dfdff50364c25afa1453df359ffe0d1fb8f5d62ad","last_reissued_at":"2026-05-18T04:00:01.405792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:01.405792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the quasi-component of pseudocompact abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"D. 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