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We show that if $W$ is weakly compact and the orbit space $R^k/G$ is compact for each $k\\in\\oN$, then the orbit space $W/G$ is compact when $W$ is equiped with the norm topology induced by $\\|.\\|_R$.\n  As a consequence we derive the existence of limits of edge-colouring models which answers a question posed by Lov\\'asz. It forms the edge-colouring counterpart"},"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":"1210.2204","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-08T09:47:06Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"516aba0b94406226cfbc10c0370fee7ac5df24f8b15bf342ccacc2ba125725f7","abstract_canon_sha256":"2db2e6df34bc986f9991d7b0f5fa1d88b288af50b11f73c9180983ae28c154c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:56.834911Z","signature_b64":"hQqTj7X/i/yt4Up+i2ELmwyrU6dprYLNqzMEAqQZh7mXkNoIZNLIacIBpuBEIXAwhV7XSIq/yOfprU1ZCzZ0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"170e9a70a3da1a3942072170c9713748a46b6a72bbc7cf0bd6f8cbc1b6d0151b","last_reissued_at":"2026-05-18T01:39:56.834488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:56.834488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compact orbit spaces in Hilbert spaces and limits of edge-colouring models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.CO","authors_text":"Alexander Schrijver, Guus Regts","submitted_at":"2012-10-08T09:47:06Z","abstract_excerpt":"Let $G$ be a group of orthogonal transformations of a real Hilbert space $H$. 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