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Let K be a locally maximal compact set of zeroes of X.\n  THEOREM Assume the Poincar'e-Hopf index of X at K is nonzero, and the k-jet of X at each point of K is nontrivial. If g is a supersolvable Lie algebra of C^k vector fields that track X, then the elements of g have a common zero in K.\n  Applications are made to attractors and transformation groups."},"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":"1506.02185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-06T19:45:29Z","cross_cats_sorted":[],"title_canon_sha256":"752c551277e744ec93dc7a27808a6a26a17b3e7faed7d6b3ab9f448034693afc","abstract_canon_sha256":"95ab2da52f8267211180e328425777cf028a5ddec169b9fef7cf8c7d6fe34493"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:51.908984Z","signature_b64":"Bn4pWJypwG0TqYATFhTAo0tD4XSS3PqiusXCWVutYGhSk2ra85Ub6vcgA7mOb2SWVTBqai64X5SmaSLuPOWlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abf8bb4e627694d1e9ddf7637d50d439cf227c50012c6612c6ae97d91bc716de","last_reissued_at":"2026-05-18T01:55:51.908493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:51.908493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Common zeroes of families of smooth vector fields 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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