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Assume $K$ is a compact set of fixed points of $\\varphi$ and $U$ is a neighborhood of $K$ containing no other fixed points.\n  Theorem: If the Dold fixed-point index of $\\varphi_t|U$ is nonzero for sufficiently small $t>0$, then ${\\rm Fix} (G) \\cap K \\ne \\emptyset$."},"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":"1405.2331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-05-09T19:55:29Z","cross_cats_sorted":[],"title_canon_sha256":"52c8b0f21bf25da6313418ec7755d964e82bb0c8f49bedcb2c103ba82c63afe5","abstract_canon_sha256":"0540f36d308b149c304b9d58f6f982e2301181cae0403f8932d236ce54099ae8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:32.759437Z","signature_b64":"3yEHXdBqG9S7M7VaTryVSbSDN2J4BomFE4fgv9I4dJLcVoxRx47Tnftbw7LJ0+nv7OUMre9a4hjVihVyoLWiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fccfa58df0d3b886c41323e616f984ebbb1b1267cf33a73d915705975d5e8f5a","last_reissued_at":"2026-05-18T01:21:32.758763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:32.758763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed points of local actions of nilpotent Lie groups on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Morris W. 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