{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T3VPPVZBUM6RRCPSVCIIUSSZZY","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":"cd028e0c95f021aba88c0c8a8e143e6c985da55862b0d8763d8f3964b7b8f6cd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-27T11:10:14Z","title_canon_sha256":"476c48514235d60ac1652f0c844231695199ceca704b2986c21faf5ae5b2072b"},"schema_version":"1.0","source":{"id":"1607.08037","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08037","created_at":"2026-05-18T00:58:54Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08037v3","created_at":"2026-05-18T00:58:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08037","created_at":"2026-05-18T00:58:54Z"},{"alias_kind":"pith_short_12","alias_value":"T3VPPVZBUM6R","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T3VPPVZBUM6RRCPS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T3VPPVZB","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:97facdbf73fa8408b87fce374655684b28fa0ed2354af0b789ec0dd54a8373eb","target":"graph","created_at":"2026-05-18T00:58:54Z","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 the equidistribution of the sequence of the averaged pullbacks of a Dirac measure at any value in $\\mathbb{C}\\setminus\\{0\\}$ under the derivatives of the iterations of a polynomials $f\\in\\mathbb{C}[z]$ of degree more than one towards the $f$-equilibrium (or canonical) measure $\\mu_f$ on $\\mathbb{P}^1$. We also show that for every $C^2$ test function on $\\mathbb{P}^1$, the convergence is exponentially fast up to a polar subset of exceptional values in $\\mathbb{C}$. A parameter space analog of the latter quantitative result for the monic and centered unicritical polynomials family i","authors_text":"Y\\^usuke Okuyama","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-27T11:10:14Z","title":"Value distribution of the sequences of the derivatives of iterated polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08037","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":"sha256:1632a1122b1917eb7e638dcc0bb510ab873d838ab1d69c3bb026fddcb9362e21","target":"record","created_at":"2026-05-18T00:58:54Z","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":"cd028e0c95f021aba88c0c8a8e143e6c985da55862b0d8763d8f3964b7b8f6cd","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-07-27T11:10:14Z","title_canon_sha256":"476c48514235d60ac1652f0c844231695199ceca704b2986c21faf5ae5b2072b"},"schema_version":"1.0","source":{"id":"1607.08037","kind":"arxiv","version":3}},"canonical_sha256":"9eeaf7d721a33d1889f2a8908a4a59ce2a0cd3d681b3d65ca7b40c10d7cc6b15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9eeaf7d721a33d1889f2a8908a4a59ce2a0cd3d681b3d65ca7b40c10d7cc6b15","first_computed_at":"2026-05-18T00:58:54.977247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:54.977247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1st5lzG4YPi3W99PTCjJRUbGMmgZfZIVDs4jUteZG/XDmbVkZwEDEd4cFcQj7+1ETGxRq9b7ekTK86hRopcZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:54.977747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08037","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1632a1122b1917eb7e638dcc0bb510ab873d838ab1d69c3bb026fddcb9362e21","sha256:97facdbf73fa8408b87fce374655684b28fa0ed2354af0b789ec0dd54a8373eb"],"state_sha256":"5d0aa3a970bd1bca21f01944bc86a84f501a4f33ef1b3d21821d3fa7f2a96d90"}