{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F35D6PH2C7AK6VJ5FRCEFCEWJX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f55c49482e1ed63dec2ed9cbd12ab1bb1d9aea413e45b9757769fc4c7fbd2661","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-14T13:05:07Z","title_canon_sha256":"3aa1fb5b8f7727c924e6d27256e022badce42e7391bbb58eb8220f9b50cf6203"},"schema_version":"1.0","source":{"id":"1103.2656","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2656","created_at":"2026-05-18T03:59:36Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2656v3","created_at":"2026-05-18T03:59:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2656","created_at":"2026-05-18T03:59:36Z"},{"alias_kind":"pith_short_12","alias_value":"F35D6PH2C7AK","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F35D6PH2C7AK6VJ5","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F35D6PH2","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:b8fcbdb377056a147ff2f7292c1aed808d4b7b390febe7fc1f62d95e6596ef64","target":"graph","created_at":"2026-05-18T03:59:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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. This current gives rise to a measure $\\mu_\\bif:=(T_\\bif)^{2d-2}$ whose support is the seat of strong bifurcations. 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.","authors_text":"Thomas Gauthier","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-14T13:05:07Z","title":"Strong bifurcation loci of full Hausdorff dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2656","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0c728720ac8245d38212d381bb87df29cad505b94031f452214f661f41ef8816","target":"record","created_at":"2026-05-18T03:59:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f55c49482e1ed63dec2ed9cbd12ab1bb1d9aea413e45b9757769fc4c7fbd2661","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-14T13:05:07Z","title_canon_sha256":"3aa1fb5b8f7727c924e6d27256e022badce42e7391bbb58eb8220f9b50cf6203"},"schema_version":"1.0","source":{"id":"1103.2656","kind":"arxiv","version":3}},"canonical_sha256":"2efa3f3cfa17c0af553d2c444288964dd08f0619ec1e8c127f908db924e1a620","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2efa3f3cfa17c0af553d2c444288964dd08f0619ec1e8c127f908db924e1a620","first_computed_at":"2026-05-18T03:59:36.805900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:36.805900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Anr1ks+grr34OCMpBjfV7k8cltfi7qnZZTlpjnB1gRupRFZxtEB99XWIk3Ooyetl/IfTp6eLsxVz+V9yd/TEAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:36.806432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2656","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c728720ac8245d38212d381bb87df29cad505b94031f452214f661f41ef8816","sha256:b8fcbdb377056a147ff2f7292c1aed808d4b7b390febe7fc1f62d95e6596ef64"],"state_sha256":"ca27e3f2253d69c92d9659d4e0e82a951046c9cbc7a880994759071713d90841"}