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Our main result says that $\\supp(\\mu_\\bif)$ has maximal Hausdorff dimension $2(2d-2)$. As a consequence, the set of degree $d$ rational maps having $2d-2$ distinct neutral cycles is dense in a set of full Hausdorff dimension."},"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":"1103.2656","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-14T13:05:07Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"3aa1fb5b8f7727c924e6d27256e022badce42e7391bbb58eb8220f9b50cf6203","abstract_canon_sha256":"f55c49482e1ed63dec2ed9cbd12ab1bb1d9aea413e45b9757769fc4c7fbd2661"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:36.806432Z","signature_b64":"Anr1ks+grr34OCMpBjfV7k8cltfi7qnZZTlpjnB1gRupRFZxtEB99XWIk3Ooyetl/IfTp6eLsxVz+V9yd/TEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2efa3f3cfa17c0af553d2c444288964dd08f0619ec1e8c127f908db924e1a620","last_reissued_at":"2026-05-18T03:59:36.805900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:36.805900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong bifurcation loci of full Hausdorff dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Thomas Gauthier","submitted_at":"2011-03-14T13:05:07Z","abstract_excerpt":"In the moduli space $\\mathcal{M}_d$ of degree $d$ rational maps, the bifurcation locus is the support of a closed $(1,1)$ positive current $T_\\bif$ which is called the bifurcation current. 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