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A subset E of G is said to be qc-dense in G provided that \\chi(E) \\subseteq \\phi([-1/4,1/4]) holds only for the trivial character \\chi \\in \\hat{G}, where \\phi : R --> T = R/Z is the canonical homomorphism. A super-sequence is a non-empty compact Hausdorff space S with at most one non-isolated point (to which S converges). We prove that an infinite compact abelian group G is connected if and only if its arc component G_a contains a super"},"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":"0812.2888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2008-12-15T19:30:11Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"37d76606960106f7e9396527a7cd9ad7f5e0c9d00581aa54a833ac2ca2dbee2a","abstract_canon_sha256":"954a4e1b15c880381d3fe2fa576601753b67a02e0724f991e5ed8f15da1b485e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:24.643949Z","signature_b64":"BQ83xB1ThISoTFZ0646v99OjLCW/JY5n8c64vLcDMR+fAn+vppAcPtznVVi+x6PPBzXWY/mf+CdV1dc/VFIpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b0053dcd45328506890d48628ee433e3c7ef08316f6922dc19770a77611faef","last_reissued_at":"2026-05-18T03:56:24.643203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:24.643203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Super-sequences in the arc component of a compact connected group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Dikran Dikranjan, Dmitri Shakhmatov","submitted_at":"2008-12-15T19:30:11Z","abstract_excerpt":"Let G be an abelian topological group. 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