{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CZV7GWEQ26BITXKPCRZIZTXQSR","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":"f78d91e95f5e612c6c4d006fc940a9304eb853dd0e47771bf514d33ddd18bee8","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-12T07:30:58Z","title_canon_sha256":"2aafcd32026a81718fb5f60f39a01fdbd00aa8f413407d94db3d313010b6edfa"},"schema_version":"1.0","source":{"id":"1408.2646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2646","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2646v1","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2646","created_at":"2026-05-18T02:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"CZV7GWEQ26BI","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CZV7GWEQ26BITXKP","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CZV7GWEQ","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:4f5f8d48412ed23d0af59bf096472d847c3e7cfb4a8c7dfec16905b4231a37ea","target":"graph","created_at":"2026-05-18T02:05:24Z","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":"We establish an approximation of the activity current $T_c$ in the parameter space of a holomorphic family $f$ of rational functions having a marked critical point $c$ by parameters for which $c$ is periodic under $f$, i.e., is a superattracting periodic point. This partly generalizes a Dujardin--Favre theorem for rational functions having preperiodic points, and refines a Bassanelli--Berteloot theorem on a similar approximation of the bifurcation current $T_f$ of the holomorphic family $f$. The proof is based on a dynamical counterpart of this approximation.","authors_text":"Y\\^usuke Okuyama","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-12T07:30:58Z","title":"Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2646","kind":"arxiv","version":1},"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":"sha256:4c70f12402d5428b605224c4b0fb3eb9fe42118467d1d140bebcf8e9821500ad","target":"record","created_at":"2026-05-18T02:05:24Z","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":"f78d91e95f5e612c6c4d006fc940a9304eb853dd0e47771bf514d33ddd18bee8","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-12T07:30:58Z","title_canon_sha256":"2aafcd32026a81718fb5f60f39a01fdbd00aa8f413407d94db3d313010b6edfa"},"schema_version":"1.0","source":{"id":"1408.2646","kind":"arxiv","version":1}},"canonical_sha256":"166bf35890d78289dd4f14728ccef09446859ddc2b62dcfb076763b88804cefa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"166bf35890d78289dd4f14728ccef09446859ddc2b62dcfb076763b88804cefa","first_computed_at":"2026-05-18T02:05:24.302911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:24.302911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4FmtJtmvmlN5rW3WHGaxDH8/gaB1SMM+aMmW4/1gQh+UANUvysx5wfuBH2EtgRly0k4Ea5ba5CgcLSGgIAA/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:24.303526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c70f12402d5428b605224c4b0fb3eb9fe42118467d1d140bebcf8e9821500ad","sha256:4f5f8d48412ed23d0af59bf096472d847c3e7cfb4a8c7dfec16905b4231a37ea"],"state_sha256":"98637c1bec5cb695fea24ba08bd9353be7468b9e0258a7da16b9bfef101e3f93"}